4730:
struggle, has nothing more to gain from reducing his price. One major objection to this is that there is no solution under this assumption, in that there is no limit to the downward movement... If
Cournot's formulation conceals this obvious result, it is because he most inadvertently introduces as D and D' the two proprietors' respective outputs, and by considering them as independent variables, he assumes that should either proprietor change his output then the other proprietor's output could remain constant. It quite obviously could not.
3343:
257:
4347:
545:
His model can be grasped more easily if we slightly embellish it. Suppose that there are two owners of mineral water springs, each able to produce unlimited quantities at zero price. Suppose that instead of selling water to the public they offer it to a middle man. Each proprietor notifies the middle
837:
regarded equality of price in
Cournot as "a particular condition, not... abstractly necessary in cases of imperfect competition". Jean Magnan de Bornier says that in Cournot's theory "each owner will use price as a variable to control quantity" without saying how one price can govern two quantities.
821:
A feature of
Cournot's model is that a single price applies to both proprietors. He justified this assumption by saying that "dès lors le prix est nécessairement le même pour l'un et l'autre propriétaire". de Bornier expands on this by saying that "the obvious conclusion that only a single price can
1073:
is the marginal cost. This assumption tells us that both firms face the same cost-per-unit produced. Therefore, as each firm's profit is equal to its revenues minus costs, where revenue equals the number of units produced multiplied by the market price, we can denote the profit functions for firm 1
868:
market structure; the following example provides a straightforward analysis of the
Cournot model for the case of Duopoly. Therefore, suppose we have a market consisting of only two firms which we will call firm 1 and firm 2. For simplicity, we assume each firm faces the same marginal cost. That is,
3630:
Since proprietors move towards the equilibrium position it follows that the equilibrium is stable, but
Cournot remarks that if the red and blue curves were interchanged then this would cease to be true. He adds that it is easy to see that the corresponding diagram would be inadmissible since, for
528:
to maximize profits, and this restriction is essential, since
Cournot tells us that if they came to an understanding between each other so as each to obtain the maximum possible revenue, then completely different results would be obtained, indistinguishable from the consumer's point of view from
4729:
Cournot assumes that one of the proprietors will reduce his price to attract buyers to him, and that the other will in turn reduce his price even more to attract buyers back to him. They will only stop undercutting each other in this way, when either proprietor, even if the other abandoned the
825:
Later on
Cournot writes that a proprietor can adjust his supply "en modifiant correctement le prix". Again, this is nonsense: it is impossible for a single price to be simultaneously under the control of two suppliers. If there is a single price, then it must be determined by the market as a
92:
An essential assumption of this model is the "not conjecture" that each firm aims to maximize profits, based on the expectation that its own output decision will not have an effect on the decisions of its rivals. Price is a commonly known decreasing function of total output. All firms know
4725:, was drawn to Cournot's book by Walras's high praise of it. Bertrand was critical of Cournot's reasoning and assumptions, Bertrand claimed that "removing the symbols would reduce the book to just a few pages". His summary of Cournot's theory of duopoly has remained influential:
218:
The maths in
Cournot's book is elementary and the presentation not difficult to follow. The account below follows Cournot's words and diagrams closely. The diagrams were presumably included as an oversized plate in the original edition, and are missing from some modern reprints.
850:
Cournot's duopolists are not true profit-maximizers. Either supplier could increase his or her profits by cutting out the middle man and cornering the market by marginally undercutting his or her rival; thus the middle man can be seen as a mechanism for restricting competition.
809:
Each proprietor is assumed to know the amount being supplied by his or her rival, and to adjust his or her own supply in the light of it to maximize his or her profits. The position of equilibrium is one in which neither proprietor is inclined to adjust the quantity supplied.
171:
The consequence of this is that in equilibrium, each firm's expectations of how other firms will act are shown to be correct; when all is revealed, no firm wants to change its output decision. This idea of stability was later taken up and built upon as a description of
4704:
with the curve. Hence, the price diminishes indefinitely as the number of proprietors increases. With an infinite number of proprietors, the price becomes zero; or more generally, if we allow for costs of production, the price becomes the marginal cost.
1933:
1799:
167:
for given (exogenous) output levels of the other firm(s) in the market. He then showed that a stable equilibrium occurs where these functions intersect (i.e., the simultaneous solution of the best response functions of each firm).
537:
Cournot presents a mathematically correct analysis of the equilibrium condition corresponding to a certain logically consistent model of duopolist behaviour. However his model is not stated and is not particularly natural
4001:, and the turning point of this value is a maximum. Evidently, the sales quantity which maximizes monetary value is reached before the maximum possible sales quantity (which corresponds to a value of 0). So, the root
2101:
Now that we have two equations describing the states at which each firm is producing at the profit-maximizing quantity, we can simply solve this system of equations to obtain each firm's optimal level of output,
4751:
will remain fixed, while his own price is adjusted. Under this hypothesis each would undersell the other as long as any profit remained, so that the final result would be identical with the result of unlimited
1660:
1543:
2437:. We can be sure this setup gives us the equilibrium levels as neither firm has an incentive to change their level of output as doing so will harm the firm at the benefit of their rival. Now substituting in
2292:
2696:
2216:
37:
model used to describe an industry structure in which companies compete on the amount of output they will produce, which they decide on independently of each other and at the same time. It is named after
227:
Cournot's discussion of oligopoly draws on two theoretical advances made in earlier pages of his book. Both have passed (with some adjustment) into microeconomic theory, particularly within subfield of
3157:
3050:
159:). The model was one of a number that Cournot set out "explicitly and with mathematical precision" in the volume. Specifically, Cournot constructed profit functions for each firm, and then used
1230:
1152:
3822:
4454:
2555:
2030:
2888:
2826:
2096:
2060:
4673:
4283:
4122:
3267:
1051:
329:
It follows that his demand curves do some of the work of modern supply curves, since producers who are able to limit the amount sold have an influence on
Cournot's demand curve.
4341:
2435:
1392:
3573:
3488:
446:
3544:
3459:
3430:
202:
Reactions to this aspect of
Cournot's theory have ranged from searing condemnation to half-hearted endorsement. It has received sympathy in recent years as a contribution to
199:
found Cournot's treatment of oligopoly "brilliant and suggestive, but not free from serious objections". He arranged for a translation to be made by Nathaniel Bacon in 1897.
3669:
3972:
3899:
3313:
1299:
757:
952:
3204:
2502:
2140:
2000:
1978:
3741:
480:
1805:
1671:
117:
equals the total quantity produced by all firms. Each firm takes the quantity set by its competitors as a given, evaluates its residual demand, and then behaves as a
2764:
2734:
2032:, and therefore production beyond this point results in the firm losing money for each additional unit produced. Notice that at the profit-maximizing quantity where
2002:). Intuitively, this suggests that firms will produce up to the point where it remains profitable to do so, as any further production past this point will mean that
1334:
711:
4053:
4026:
3999:
3926:
3853:
3696:
3625:
3515:
3401:
3374:
2942:
2915:
2585:
2462:
2362:
2335:
1071:
999:
914:
784:
394:
362:
4702:
4558:
4529:
1424:
636:
509:
323:
4584:
4500:
4612:
4474:
4391:
4371:
4222:
4202:
4182:
4162:
4142:
3593:
3337:
2605:
2382:
2315:
1956:
1253:
972:
887:
804:
676:
656:
607:
587:
564:
294:
111:
264:
Cournot was wary of psychological notions of demand, defining it simply as the amount sold of a particular good (helped along by the fact that the French word
3163:
The equlibirum position is found by solving these two equations simultaneously. This is most easily done by adding and subtracting them, turning them into:
3349:
Cournot goes further than this simple solution, investigating the stability of the equilibrium. Each of his original equations defines a relation between
542:
remarked that observed practice constituted a "natural objection to the Cournot quantity model"), and "his words and the mathematics do not quite match".
5473:
4938:
5293:
2337:, and output quantity of rival firms. The functions can be thought of as describing a firm's "Best Response" to the other firm's level of output.
829:
Cournot's account threw his English translator (Nathaniel Bacon) so completely off-balance that his words were corrected to "properly adjusting
3319:
Thus, we see that the two proprietors supply equal quantities, and that the total quantity sold is the root of a single nonlinear equation in
5605:
3855:
sold when the price is zero (which is the maximum quantity the public is willing to consume), while the second states that the derivative of
546:
man of the quantity he or she intends to produce. The middle man finds the market-clearing price, which is determined by the demand function
6504:
4737:
was unimpressed by Bertrand's critique, concluding from it that Bertrand 'wrote his article without consulting the books he criticised'.
2344:
using our "Best Response" functions above for the output quantity of firms 1 and 2. Recall that both firms face the same cost-per-unit (
1549:
1432:
6321:
5856:
5654:
2222:
6140:
5959:
5155:
2610:
2148:
113:, the total number of firms in the market, and take the output of the others as given. The market price is set at a level such that
2560:
This equilibrium value describes the optimal level of output for firms 1 and 2, where each firm is producing an output quantity of
332:
Cournot remarks that the demand curve will usually be a decreasing function of price, and that the total value of the good sold is
4998:
3461:
from the red curve to maximize his or her revenue. But then, by similar reasoning, the first proprietor will adjust his supply to
6682:
5761:
5544:
6230:
364:, which will generally increase to a maximum and then decline towards 0. The condition for a maximum is that the derivative of
2297:
These functions describe each firm's optimal (profit-maximizing) quantity of output given the price firms face in the market,
6677:
5771:
5037:
4874:
6100:
4756:
Fisher seemed to regard Bertrand as having been the first to present this model, and it has since entered the literature as
3057:
2950:
6672:
6281:
5699:
5674:
4779:
134:; i.e., if either of the producers, misled as to his true interest, leaves it temporarily, he will be brought back to it.
6631:
6057:
5811:
5801:
5736:
5412:
5301:
842:, perhaps in despair, remarked that "the actual process of price formation in Cournot's theory is somewhat mysterious".
5851:
5831:
5421:
5129:
1158:
1080:
6316:
214:
In current language and interpretation, Cournot postulated a particular game to represent an oligopolistic market...
6565:
6286:
5944:
5786:
5781:
6667:
6601:
6524:
6260:
5816:
5741:
5598:
4866:
2507:
566:
and the aggregate supply. He or she sells the water at this price, passing the proceeds back to the proprietors.
2005:
6616:
6349:
6235:
6032:
5826:
5644:
5371:
5367:
4890:
3748:
2831:
2769:
2065:
834:
232:
where Cournot's assumptions can be relaxed to study various Market Structures and Industries, for example, the
148:
39:
6419:
4396:
2035:
838:
A. J. Nichol claimed that Cournot's theory makes no sense unless "prices are directly determined by buyers".
6621:
6220:
6190:
5846:
5634:
5147:
5046:
4804:
822:
exist at a given moment" follows from "an essential assumption concerning his model, product homogeneity".
233:
229:
160:
58:
6555:
2384:). Therefore, using this symmetrical relationship between firms we find the equilibrium quantity by fixing
6646:
6626:
6606:
6225:
6130:
5989:
5939:
5934:
5866:
5836:
5756:
5684:
4586:. Hence, prices are lower under duopoly than under monopoly, and quantities sold are accordingly higher.
1004:
5664:
5310:
4784:
245:
6105:
6090:
2387:
1339:
4743:
outlined a model of duopoly similar to the one Bertrand had accused Cournot of analysing incorrectly:
3549:
3464:
1665:
As firms are assumed to be profit-maximizers, the first-order conditions (F.O.C.s) for each firm are:
6439:
6424:
6311:
6306:
6210:
6195:
6160:
6125:
5724:
5669:
5591:
4908:
4774:
4757:
3520:
3435:
3406:
4617:
4227:
4066:
3634:
3211:
2944:
should be 0, and the mirror-image reasoning applies to his or her rival. We thus get the equations:
155:
as a way of describing the competition with a market for spring water dominated by two suppliers (a
6596:
6165:
6002:
5929:
5909:
5766:
5649:
4288:
3931:
3858:
3272:
1301:. For example's sake, let us assume that price (inverse demand function) is linear and of the form
1258:
716:
2917:
under his control, giving the condition that the partial derivative of his profit with respect to
919:
6687:
6575:
6434:
6265:
6245:
6095:
5974:
5879:
5806:
5751:
5433:
5384:
5133:
5060:
5010:
4828:
Bertrand's review is most easily found in Margaret Chevaillier's English translation appended to
3169:
2467:
2105:
1983:
1961:
1928:{\displaystyle {\frac {\partial \Pi _{2}(q_{1},q_{2})}{\partial q_{2}}}=a-bq_{1}-2bq_{2}-\chi =0}
1794:{\displaystyle {\frac {\partial \Pi _{1}(q_{1},q_{2})}{\partial q_{1}}}=a-2bq_{1}-bq_{2}-\chi =0}
399:
54:
4794:
3704:
813:
It needs mental contortions to imagine the same market behaviour arising without a middle man.
6560:
6529:
6484:
6379:
6250:
6205:
6180:
6110:
5984:
5914:
5904:
5796:
5746:
5694:
5573:
5257:
5249:
5245:
5151:
5088:
4870:
237:
207:
114:
5092:
1235:
In the above profit functions we have price as a function of total output which we denote as
6641:
6636:
6570:
6534:
6514:
6474:
6444:
6399:
6354:
6339:
6296:
6150:
5791:
5728:
5714:
5679:
5425:
5314:
5241:
5206:
5104:
5050:
5002:
4957:
4912:
4799:
4769:
4747:
A more natural hypothesis, and one often tacitly adopted, is that each assumes his rival's
2739:
2709:
2341:
1304:
681:
4031:
4004:
3977:
3904:
3831:
3674:
3598:
3493:
3379:
3352:
2920:
2893:
2563:
2504:
and solving we obtain the symmetric (same for each firm) output quantity in Equilibrium as
2440:
2347:
2320:
1056:
977:
892:
762:
451:
367:
335:
6539:
6499:
6454:
6369:
6364:
6085:
6037:
5924:
5689:
5659:
5629:
5536:
5468:
4809:
4734:
4714:
4678:
4534:
4505:
4502:, while the duopoly price is given by the intersection of the curve with the steeper line
1400:
612:
485:
299:
192:
173:
6404:
4563:
4479:
5501:[he wrote his article without looking at the books of the authors he criticized]
5499:
il a rédigé son article sans avoir sous les yeux les livres des auteurs qu'il critiquait
5485:. Tome I, Vol. 4, Fascicle 4, Chapter I-26 (in French). Translated from German edition.
51:
6479:
6469:
6459:
6394:
6384:
6374:
6359:
6155:
6135:
6120:
6115:
6075:
6042:
6027:
6022:
6012:
5821:
5373:
Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences
4718:
4597:
4459:
4376:
4356:
4207:
4187:
4167:
4147:
4127:
3578:
3322:
2590:
2367:
2300:
1941:
1238:
957:
872:
789:
661:
641:
592:
572:
549:
279:
191:
credited him as a forerunner. This led to an unsympathetic review of Cournot's book by
188:
96:
5210:
6661:
6519:
6509:
6464:
6449:
6429:
6255:
6200:
6175:
6047:
6017:
6007:
5994:
5899:
5841:
5776:
5709:
5437:
5237:
5229:
5028:
5014:
4904:
4740:
826:
consequence of the proprietors' decisions on matters under their individual control.
241:
196:
164:
5559:
5410:
Nichol, Archibald J. (1934). "A Re-Appraisal of Cournot's Theory of Duopoly Price".
6494:
6489:
6344:
5919:
5549:
5190:
5142:
4961:
4916:
839:
539:
72:
17:
5563:
4894:
4860:
6611:
6414:
6409:
6389:
6185:
6170:
5979:
5949:
5884:
5874:
5704:
5639:
5615:
4789:
203:
85:
4937:
Van den Berg, Anita; Bos, Iwan; Herings, P. Jean-Jacques; Peters, Hans (2012).
6240:
5894:
5478:
5318:
5234:
Strategy and Market Structure: Competition, Oligopoly, and the Theory of Games
4856:
3403:
which may be drawn on a graph. If the first proprietor was providing quantity
1958:
is producing at the profit-maximizing level of output when the marginal cost (
6145:
6065:
5889:
5567:
5137:
3342:
65:
4989:
Morrison, Clarence C. (1998). "Cournot, bertrand, and modern game theory".
256:
5108:
4560:
occurs to the left of (i.e., at a lower price than) its intersection with
6580:
6080:
5202:
4953:
3575:, and so forth until equilibrium is reached at the point of intersection
236:
model. Cournot's discussion of monopoly influenced later writers such as
118:
34:
5583:
4346:
2890:. The first proprietor maximizes profit by optimizing over the parameter
864:
Cournot's model of competition is typically presented for the case of a
151:(1801–1877) first outlined his theory of competition in his 1838 volume
88:, usually seeking to maximize profit given their competitors' decisions.
42:(1801–1877) who was inspired by observing competition in a spring water
6301:
6291:
5969:
5253:
5065:
5006:
3546:. This will lead to the second proprietor adapting to the supply value
865:
272:, meaning 'demand' ). He formalised it mathematically as follows:
156:
43:
4896:
Recherches sur les Principes Mathématiques de la Théorie des Richesses
3490:
to give him or her the maximum return as shown by the blue curve when
153:
Recherches sur les Principes Mathématiques de la Théorie des Richesses
141:
Recherches sur les Principes Mathématiques de la Théorie des Richesses
5380:
5055:
5032:
5429:
4901:
Researches Into the Mathematical Principles of the Theory of Wealth
6070:
5486:
4675:. The price can be read from the diagram from the intersection of
1655:{\displaystyle \Pi _{2}(q_{1},q_{2})=(a-bq_{1}-bq_{2}-\chi )q_{2}}
1538:{\displaystyle \Pi _{1}(q_{1},q_{2})=(a-bq_{1}-bq_{2}-\chi )q_{1}}
4939:"Dynamic Cournot duopoly with intertemporal capacity constraints"
5282:: "thus the price is necessarily the same for both proprietors".
5261:
5587:
2287:{\displaystyle q_{2}={\frac {a-\chi }{2b}}-{\dfrac {q_{1}}{2}}}
4531:. Regardless of the shape of the curve, its intersection with
2691:{\displaystyle Q=q_{1}^{*}+q_{2}^{*}={\frac {2(a-\chi )}{3b}}}
2211:{\displaystyle q_{1}={\frac {a-\chi }{2b}}-{\frac {q_{2}}{2}}}
75:, i.e., each firm's output decision affects the good's price;
4903:]. Economic classics. Translated by Bacon, Nathaniel T.
4345:
3341:
5483:
Encyclopédie des sciences mathématiques pures et appliquées
4063:
We have seen that Cournot's system reduces to the equation
4028:
of the first equation is necessarily greater than the root
1336:. So, the inverse demand function can then be rewritten as
268:, meaning 'sales quantity', has the same initial letter as
5294:"The "Cournot-Bertrand Debate": A Historical Perspective"
4204:
in the other. If we re-express this equation in terms of
2098:
which is why we set the above equations equal to zero.
4681:
4620:
4600:
4566:
4537:
4508:
4482:
4462:
4399:
4379:
4359:
4291:
4230:
4210:
4190:
4170:
4150:
4130:
4069:
4034:
4007:
3980:
3974:
is the monetary value of an aggregate sales quantity
3934:
3907:
3861:
3834:
3751:
3707:
3677:
3637:
3601:
3581:
3552:
3523:
3496:
3467:
3438:
3409:
3382:
3355:
3325:
3275:
3214:
3172:
3152:{\displaystyle f(D_{1}+D_{2})+D_{2}f'(D_{1}+D_{2})=0}
3060:
3045:{\displaystyle f(D_{1}+D_{2})+D_{1}f'(D_{1}+D_{2})=0}
2953:
2923:
2896:
2834:
2772:
2742:
2712:
2613:
2593:
2566:
2510:
2470:
2443:
2390:
2370:
2350:
2323:
2303:
2266:
2225:
2151:
2108:
2068:
2038:
2008:
1986:
1964:
1944:
1808:
1674:
1552:
1435:
1403:
1397:
Now, substituting our equation for price in place of
1342:
1307:
1261:
1241:
1161:
1083:
1059:
1007:
980:
960:
922:
895:
875:
792:
765:
719:
684:
664:
644:
615:
595:
575:
552:
488:
454:
402:
370:
338:
302:
282:
99:
50:
There is more than one firm and all firms produce a
6589:
6548:
6330:
6274:
6056:
5958:
5865:
5723:
5622:
276:We will regard the sales quantity or annual demand
187:Cournot's economic theory was little noticed until
81:
Firms compete in quantities rather than prices; and
5472:
4696:
4667:
4606:
4578:
4552:
4523:
4494:
4468:
4448:
4385:
4365:
4335:
4277:
4216:
4196:
4176:
4156:
4136:
4116:
4047:
4020:
3993:
3966:
3920:
3893:
3847:
3816:
3735:
3690:
3663:
3619:
3587:
3567:
3538:
3509:
3482:
3453:
3432:, then the second proprietor would adopt quantity
3424:
3395:
3368:
3331:
3307:
3261:
3198:
3151:
3044:
2936:
2909:
2882:
2820:
2758:
2728:
2690:
2599:
2579:
2549:
2496:
2456:
2429:
2376:
2356:
2329:
2309:
2286:
2210:
2134:
2090:
2054:
2024:
1994:
1972:
1950:
1927:
1793:
1654:
1537:
1418:
1386:
1328:
1293:
1247:
1224:
1146:
1065:
1045:
993:
966:
946:
908:
881:
798:
778:
751:
705:
670:
650:
630:
601:
581:
558:
503:
474:
440:
388:
356:
317:
288:
105:
2706:The revenues accruing to the two proprietors are
4946:International Journal of Industrial Organization
1225:{\displaystyle \Pi _{2}(Q)=p(Q)q_{2}-\chi q_{2}}
1147:{\displaystyle \Pi _{1}(Q)=p(Q)q_{1}-\chi q_{1}}
3828:The first of these corresponds to the quantity
2142:for firms 1 and 2 respectively. So, we obtain:
128:
4984:
4982:
4980:
4978:
4862:Intermediate Microeconomics: A Modern Approach
2587:. So, at equilibrium, the total market output
163:to construct a function representing a firm's
5599:
1426:we can write each firm's profit function as:
8:
941:
929:
176:, of which Cournot equilibria are a subset.
4723:Théorie Mathématique de la Richesse Sociale
4393:, then we may draw a curve of the function
2550:{\displaystyle q^{*}={\frac {a-\chi }{3b}}}
5606:
5592:
5584:
5541:Games and Strategic Behavior (PDF version)
5520:
5504:
5455:
5443:
5354:
5267:
5216:
5193:(1989). "Theories of oligopoly behavior".
5083:
5081:
4829:
4285:, which can be compared with the equation
3631:instance, it is necessarily the case that
2025:{\displaystyle {\text{MC}}>{\text{MR}}}
678:and the market-clearing price is given by
524:Cournot insists that each duopolist seeks
251:
64:Firms do not cooperate, i.e., there is no
5341:: "by appropriately modifying the price".
5185:
5183:
5064:
5054:
4680:
4619:
4599:
4565:
4536:
4507:
4481:
4476:for which this curve intersects the line
4461:
4409:
4398:
4378:
4358:
4290:
4229:
4209:
4189:
4169:
4149:
4129:
4068:
4039:
4033:
4012:
4006:
3985:
3979:
3955:
3939:
3933:
3912:
3906:
3882:
3866:
3860:
3839:
3833:
3817:{\displaystyle f(D_{2})+D_{2}f'(D_{2})=0}
3799:
3778:
3762:
3750:
3718:
3706:
3682:
3676:
3655:
3642:
3636:
3600:
3580:
3559:
3558:
3557:
3551:
3530:
3529:
3528:
3522:
3501:
3495:
3474:
3473:
3472:
3466:
3445:
3444:
3443:
3437:
3416:
3415:
3414:
3408:
3387:
3381:
3360:
3354:
3324:
3299:
3286:
3274:
3213:
3190:
3177:
3171:
3134:
3121:
3100:
3084:
3071:
3059:
3027:
3014:
2993:
2977:
2964:
2952:
2928:
2922:
2901:
2895:
2883:{\displaystyle f(D_{1}+D_{2})\cdot D_{2}}
2874:
2858:
2845:
2833:
2821:{\displaystyle f(D_{1}+D_{2})\cdot D_{1}}
2812:
2796:
2783:
2771:
2750:
2741:
2720:
2711:
2656:
2647:
2642:
2629:
2624:
2612:
2592:
2571:
2565:
2524:
2515:
2509:
2488:
2475:
2469:
2448:
2442:
2421:
2408:
2395:
2389:
2369:
2349:
2322:
2302:
2272:
2265:
2239:
2230:
2224:
2197:
2191:
2165:
2156:
2150:
2126:
2113:
2107:
2091:{\displaystyle {\text{MC}}-{\text{MR}}=0}
2077:
2069:
2067:
2047:
2039:
2037:
2017:
2009:
2007:
1987:
1985:
1965:
1963:
1943:
1907:
1888:
1863:
1845:
1832:
1819:
1809:
1807:
1773:
1757:
1729:
1711:
1698:
1685:
1675:
1673:
1646:
1627:
1611:
1583:
1570:
1557:
1551:
1529:
1510:
1494:
1466:
1453:
1440:
1434:
1402:
1378:
1362:
1341:
1306:
1285:
1272:
1260:
1240:
1216:
1200:
1166:
1160:
1138:
1122:
1088:
1082:
1058:
1037:
1018:
1006:
985:
979:
959:
921:
900:
894:
874:
791:
770:
764:
743:
730:
718:
683:
663:
643:
614:
594:
574:
551:
487:
453:
401:
369:
337:
301:
281:
130:The state of equilibrium... is therefore
98:
5397:
5072:
4851:
4849:
4614:proprietors, the price equation becomes
4449:{\displaystyle u=-{\frac {F(p)}{F'(p)}}}
255:
244:during the 1930s revival of interest in
195:which in turn received heavy criticism.
84:The firms are economically rational and
5350:
5338:
5279:
5174:
4845:
4821:
2055:{\displaystyle {\text{MC}}={\text{MR}}}
855:Finding the Cournot duopoly equilibrium
5516:
296:, for any commodity, to be a function
5554:The Theory of Industrial Organization
5477:[Mathematical economics]. In
786:is the amount supplied by proprietor
7:
5580:(1954). Discusses Cournot at length.
5489:: Gauthier-Villars. pp. 591–640
5033:"Cournot and mathematical economics"
1980:) is equal to the marginal revenue (
260:Cournot's curve of 'demand or sales'
222:
5195:Handbook of Industrial Organization
3698:is 0, the two equations reduce to:
3671:. To verify this, notice that when
1046:{\displaystyle C(q_{i})=\chi q_{i}}
143:(1838), translated by Bacon (1897).
5655:First-player and second-player win
5038:The Quarterly Journal of Economics
1856:
1816:
1812:
1722:
1682:
1678:
1554:
1437:
1163:
1085:
25:
2430:{\displaystyle q_{1}=q_{2}=q^{*}}
1387:{\displaystyle p=a-bq_{1}-bq_{2}}
252:The 'Law of Demand' or 'of Sales'
46:. It has the following features:
5762:Coalition-proof Nash equilibrium
5292:de Bornier, Jean Magnan (1992).
5093:"The legacy of Augustin Cournot"
3568:{\displaystyle y_{\textsf {ll}}}
3483:{\displaystyle x_{\textsf {ll}}}
5422:The University of Chicago Press
4343:obtained earlier for monopoly.
3539:{\displaystyle y_{\textsf {l}}}
3454:{\displaystyle y_{\textsf {l}}}
3425:{\displaystyle x_{\textsf {l}}}
1255:and for two firms we must have
5772:Evolutionarily stable strategy
4962:10.1016/j.ijindorg.2011.08.002
4668:{\displaystyle F(p)+npF'(p)=0}
4656:
4650:
4630:
4624:
4440:
4434:
4421:
4415:
4324:
4318:
4301:
4295:
4278:{\displaystyle F(p)+2pF'(p)=0}
4266:
4260:
4240:
4234:
4117:{\displaystyle 2f(D)+Df'(D)=0}
4105:
4099:
4082:
4076:
3961:
3948:
3888:
3875:
3805:
3792:
3768:
3755:
3724:
3711:
3664:{\displaystyle m_{1}>m_{2}}
3614:
3602:
3262:{\displaystyle 2f(D)+Df'(D)=0}
3250:
3244:
3227:
3221:
3140:
3114:
3090:
3064:
3033:
3007:
2983:
2957:
2864:
2838:
2802:
2776:
2674:
2662:
1851:
1825:
1717:
1691:
1639:
1595:
1589:
1563:
1522:
1478:
1472:
1446:
1413:
1407:
1193:
1187:
1178:
1172:
1115:
1109:
1100:
1094:
1024:
1011:
700:
694:
625:
619:
514:
498:
492:
469:
463:
435:
429:
412:
406:
383:
377:
351:
345:
312:
306:
223:Cournot's conceptual framework
1:
5700:Simultaneous action selection
5211:10.1016/S1573-448X(89)01009-5
4795:Hotelling's linear city model
4336:{\displaystyle F(p)+pF'(p)=0}
3967:{\displaystyle D_{2}f(D_{2})}
3894:{\displaystyle D_{2}f(D_{2})}
3308:{\displaystyle D=D_{1}+D_{2}}
1294:{\displaystyle Q=q_{1}+q_{2}}
752:{\displaystyle D=D_{1}+D_{2}}
78:The number of firms is fixed;
6632:List of games in game theory
5812:Quantal response equilibrium
5802:Perfect Bayesian equilibrium
5737:Bayes correlated equilibrium
5578:History of Economic Analysis
5413:Journal of Political Economy
5302:History of Political Economy
5097:Cahiers d'Ă©conomie politique
4456:. The monopoly price is the
4353:If we plot another variable
1938:The F.O.C.s state that firm
1001:units of output is given by
947:{\displaystyle i\in \{1,2\}}
889:'s output quantity, denoted
529:those entailed by monopoly.
6101:Optional prisoner's dilemma
5832:Self-confirming equilibrium
5560:Oligoply Theory made Simple
4144:is functionally related to
3199:{\displaystyle D_{1}=D_{2}}
2497:{\displaystyle q_{1},q_{2}}
2135:{\displaystyle q_{1},q_{2}}
1995:{\displaystyle {\text{MR}}}
1973:{\displaystyle {\text{MC}}}
817:Interpretative difficulties
589:for mineral water at price
532:
441:{\displaystyle F(p)+pF'(p)}
6704:
6566:Principal variation search
6282:Aumann's agreement theorem
5945:Strategy-stealing argument
5857:Trembling hand equilibrium
5787:Markov perfect equilibrium
5782:Mertens-stable equilibrium
4867:W. W. Norton & Company
3736:{\displaystyle f(D_{2})=0}
2340:We can now find a Cournot-
139:Antoine Augustin Cournot,
6602:Combinatorial game theory
6261:Princess and monster game
5817:Quasi-perfect equilibrium
5742:Bayesian Nash equilibrium
5319:10.1215/00182702-24-3-623
4991:Atlantic Economic Journal
4891:Cournot, Antoine Augustin
4713:The French mathematician
6617:Evolutionary game theory
6350:Antoine Augustin Cournot
6236:Guess 2/3 of the average
6033:Strictly determined game
5827:Satisfaction equilibrium
5645:Escalation of commitment
4780:Bertrand–Edgeworth model
4708:
4059:Comparison with monopoly
4055:of the second equation.
3595:, whose coordinates are
515:Cournot's duopoly theory
149:Antoine Augustin Cournot
40:Antoine Augustin Cournot
6683:Competition (economics)
6622:Glossary of game theory
6221:Stackelberg competition
5847:Strong Nash equilibrium
5474:"Économie mathématique"
5385:C. Kegan Paul & Co.
5148:Dictionnaires Le Robert
5047:Oxford University Press
4917:2027/hvd.32044024354821
4805:Stackelberg competition
1074:and firm 2 as follows:
234:Stackelberg Competition
230:Industrial Organization
206:rather than economics.
161:partial differentiation
59:product differentiation
6647:Tragedy of the commons
6627:List of game theorists
6607:Confrontation analysis
6317:Sprague–Grundy theorem
5837:Sequential equilibrium
5757:Correlated equilibrium
4754:
4732:
4698:
4669:
4608:
4590:Extension to oligopoly
4580:
4554:
4525:
4496:
4470:
4450:
4387:
4367:
4350:
4337:
4279:
4218:
4198:
4178:
4158:
4138:
4118:
4049:
4022:
3995:
3968:
3922:
3895:
3849:
3818:
3737:
3692:
3665:
3621:
3589:
3569:
3540:
3511:
3484:
3455:
3426:
3397:
3370:
3346:
3333:
3309:
3263:
3200:
3153:
3046:
2938:
2911:
2884:
2822:
2760:
2759:{\displaystyle pD_{2}}
2730:
2729:{\displaystyle pD_{1}}
2692:
2601:
2581:
2551:
2498:
2458:
2431:
2378:
2358:
2331:
2311:
2288:
2212:
2136:
2092:
2056:
2026:
1996:
1974:
1952:
1929:
1795:
1656:
1539:
1420:
1388:
1330:
1329:{\displaystyle p=a-bQ}
1295:
1249:
1226:
1148:
1067:
1047:
995:
968:
948:
910:
883:
800:
780:
753:
707:
706:{\displaystyle p=f(D)}
672:
652:
632:
603:
583:
560:
505:
476:
442:
390:
358:
327:
319:
290:
261:
216:
146:
107:
6678:Non-cooperative games
6420:Jean-François Mertens
5311:Duke University Press
5246:John Wiley & Sons
5109:10.3406/cep.2000.1287
4909:The Macmillan Company
4785:Conjectural variation
4745:
4727:
4699:
4670:
4609:
4581:
4555:
4526:
4497:
4471:
4451:
4388:
4368:
4349:
4338:
4280:
4219:
4199:
4184:in one direction and
4179:
4159:
4139:
4119:
4050:
4048:{\displaystyle m_{2}}
4023:
4021:{\displaystyle m_{1}}
3996:
3994:{\displaystyle D_{2}}
3969:
3923:
3921:{\displaystyle D_{2}}
3896:
3850:
3848:{\displaystyle D_{2}}
3819:
3738:
3693:
3691:{\displaystyle D_{1}}
3666:
3622:
3620:{\displaystyle (x,y)}
3590:
3570:
3541:
3512:
3510:{\displaystyle D_{2}}
3485:
3456:
3427:
3398:
3396:{\displaystyle D_{2}}
3371:
3369:{\displaystyle D_{1}}
3345:
3334:
3310:
3264:
3201:
3154:
3047:
2939:
2937:{\displaystyle D_{1}}
2912:
2910:{\displaystyle D_{1}}
2885:
2823:
2761:
2731:
2693:
2602:
2582:
2580:{\displaystyle q^{*}}
2552:
2499:
2459:
2457:{\displaystyle q^{*}}
2432:
2379:
2359:
2357:{\displaystyle \chi }
2332:
2330:{\displaystyle \chi }
2317:, the marginal cost,
2312:
2289:
2213:
2137:
2093:
2057:
2027:
1997:
1975:
1953:
1930:
1796:
1657:
1540:
1421:
1389:
1331:
1296:
1250:
1227:
1149:
1068:
1066:{\displaystyle \chi }
1048:
996:
994:{\displaystyle q_{i}}
974:'s cost of producing
969:
949:
911:
909:{\displaystyle q_{i}}
884:
801:
781:
779:{\displaystyle D_{i}}
754:
708:
673:
653:
633:
604:
584:
561:
533:Cournot's price model
506:
482:is the derivative of
477:
475:{\displaystyle F'(p)}
448:, should be 0 (where
443:
391:
389:{\displaystyle pF(p)}
359:
357:{\displaystyle pF(p)}
320:
291:
274:
259:
246:imperfect competition
212:
108:
6673:Eponyms in economics
6549:Search optimizations
6425:Jennifer Tour Chayes
6312:Revelation principle
6307:Purification theorem
6246:Nash bargaining game
6211:Bertrand competition
6196:El Farol Bar problem
6161:Electronic mail game
6126:Lewis signaling game
5670:Hierarchy of beliefs
4865:(Seventh ed.).
4775:Bertrand competition
4758:Bertrand competition
4697:{\displaystyle u=np}
4679:
4618:
4598:
4564:
4553:{\displaystyle u=2p}
4535:
4524:{\displaystyle u=2p}
4506:
4480:
4460:
4397:
4377:
4357:
4289:
4228:
4208:
4188:
4168:
4148:
4128:
4067:
4032:
4005:
3978:
3932:
3905:
3859:
3832:
3749:
3705:
3675:
3635:
3599:
3579:
3550:
3521:
3494:
3465:
3436:
3407:
3380:
3353:
3323:
3273:
3212:
3170:
3058:
2951:
2921:
2894:
2832:
2770:
2740:
2710:
2611:
2591:
2564:
2508:
2468:
2441:
2388:
2368:
2348:
2321:
2301:
2223:
2149:
2106:
2066:
2036:
2006:
1984:
1962:
1942:
1806:
1672:
1550:
1433:
1419:{\displaystyle p(Q)}
1401:
1340:
1305:
1259:
1239:
1159:
1081:
1057:
1005:
978:
958:
920:
893:
873:
790:
763:
717:
682:
662:
642:
631:{\displaystyle F(p)}
613:
593:
573:
569:The consumer demand
550:
520:Monopoly and duopoly
504:{\displaystyle F(p)}
486:
452:
400:
368:
336:
318:{\displaystyle F(p)}
300:
280:
97:
57:, i.e., there is no
6597:Bounded rationality
6216:Cournot competition
6166:Rock paper scissors
6141:Battle of the sexes
6131:Volunteer's dilemma
6003:Perfect information
5930:Dominant strategies
5767:Epsilon-equilibrium
5650:Extensive-form game
5134:Rey-Debove, Josette
4709:Bertrand's critique
4579:{\displaystyle u=p}
4495:{\displaystyle u=p}
4224:, it tells us that
2652:
2634:
31:Cournot competition
18:Cournot equilibrium
6576:Paranoid algorithm
6556:Alpha–beta pruning
6435:John Maynard Smith
6266:Rendezvous problem
6106:Traveler's dilemma
6096:Gift-exchange game
6091:Prisoner's dilemma
6008:Large Poisson game
5975:Bargaining problem
5880:Backward induction
5852:Subgame perfection
5807:Proper equilibrium
5556:, MIT Press, 1988.
5089:Friedman, James W.
5007:10.1007/BF02299359
4694:
4665:
4604:
4576:
4550:
4521:
4492:
4466:
4446:
4383:
4363:
4351:
4333:
4275:
4214:
4194:
4174:
4154:
4134:
4114:
4045:
4018:
3991:
3964:
3918:
3891:
3845:
3814:
3733:
3688:
3661:
3617:
3585:
3565:
3536:
3507:
3480:
3451:
3422:
3393:
3366:
3347:
3329:
3305:
3259:
3196:
3149:
3042:
2934:
2907:
2880:
2818:
2756:
2726:
2688:
2638:
2620:
2597:
2577:
2547:
2494:
2454:
2427:
2374:
2354:
2327:
2307:
2284:
2282:
2208:
2132:
2088:
2052:
2022:
1992:
1970:
1948:
1925:
1791:
1652:
1535:
1416:
1384:
1326:
1291:
1245:
1222:
1144:
1063:
1043:
991:
964:
944:
906:
879:
796:
776:
749:
703:
668:
648:
628:
599:
579:
556:
501:
472:
438:
386:
354:
315:
286:
262:
180:The legacy of the
103:
6655:
6654:
6561:Aspiration window
6530:Suzanne Scotchmer
6485:Oskar Morgenstern
6380:Donald B. Gillies
6322:Zermelo's theorem
6251:Induction puzzles
6206:Fair cake-cutting
6181:Public goods game
6111:Coordination game
5985:Intransitive game
5915:Forward induction
5797:Pareto efficiency
5777:Gibbs equilibrium
5747:Berge equilibrium
5695:Simultaneous game
5574:Shumpeter, Joseph
5564:Surfing Economics
4717:, when reviewing
4607:{\displaystyle n}
4469:{\displaystyle p}
4444:
4386:{\displaystyle p}
4366:{\displaystyle u}
4217:{\displaystyle p}
4197:{\displaystyle F}
4177:{\displaystyle f}
4157:{\displaystyle p}
4137:{\displaystyle D}
3588:{\displaystyle i}
3561:
3532:
3476:
3447:
3418:
3332:{\displaystyle D}
2686:
2600:{\displaystyle Q}
2545:
2377:{\displaystyle p}
2310:{\displaystyle p}
2281:
2260:
2206:
2186:
2080:
2072:
2050:
2042:
2020:
2012:
1990:
1968:
1951:{\displaystyle i}
1870:
1736:
1248:{\displaystyle Q}
967:{\displaystyle i}
882:{\displaystyle i}
869:for a given firm
799:{\displaystyle i}
671:{\displaystyle f}
651:{\displaystyle F}
638:; the inverse of
602:{\displaystyle p}
582:{\displaystyle D}
559:{\displaystyle F}
289:{\displaystyle D}
238:Edward Chamberlin
208:James W. Friedman
106:{\displaystyle N}
86:act strategically
16:(Redirected from
6695:
6668:Economics models
6642:Topological game
6637:No-win situation
6535:Thomas Schelling
6515:Robert B. Wilson
6475:Merrill M. Flood
6445:John von Neumann
6355:Ariel Rubinstein
6340:Albert W. Tucker
6191:War of attrition
6151:Matching pennies
5792:Nash equilibrium
5715:Mechanism design
5680:Normal-form game
5635:Cooperative game
5608:
5601:
5594:
5585:
5524:
5514:
5508:
5502:
5496:
5494:
5476:
5469:Pareto, Vilfredo
5465:
5459:
5453:
5447:
5441:
5407:
5401:
5395:
5393:
5391:
5378:
5368:Edgeworth, F. Y.
5364:
5358:
5348:
5342:
5336:
5330:
5329:
5327:
5325:
5298:
5289:
5283:
5277:
5271:
5265:
5226:
5220:
5214:
5187:
5178:
5172:
5166:
5164:
5140:, eds. (2000) .
5126:
5120:
5119:
5117:
5115:
5085:
5076:
5070:
5068:
5058:
5025:
5019:
5018:
4986:
4973:
4972:
4970:
4968:
4943:
4934:
4928:
4927:
4925:
4923:
4887:
4881:
4880:
4853:
4833:
4826:
4800:Nash equilibrium
4770:Aggregative game
4703:
4701:
4700:
4695:
4674:
4672:
4671:
4666:
4649:
4613:
4611:
4610:
4605:
4585:
4583:
4582:
4577:
4559:
4557:
4556:
4551:
4530:
4528:
4527:
4522:
4501:
4499:
4498:
4493:
4475:
4473:
4472:
4467:
4455:
4453:
4452:
4447:
4445:
4443:
4433:
4424:
4410:
4392:
4390:
4389:
4384:
4372:
4370:
4369:
4364:
4342:
4340:
4339:
4334:
4317:
4284:
4282:
4281:
4276:
4259:
4223:
4221:
4220:
4215:
4203:
4201:
4200:
4195:
4183:
4181:
4180:
4175:
4163:
4161:
4160:
4155:
4143:
4141:
4140:
4135:
4123:
4121:
4120:
4115:
4098:
4054:
4052:
4051:
4046:
4044:
4043:
4027:
4025:
4024:
4019:
4017:
4016:
4000:
3998:
3997:
3992:
3990:
3989:
3973:
3971:
3970:
3965:
3960:
3959:
3944:
3943:
3927:
3925:
3924:
3919:
3917:
3916:
3901:with respect to
3900:
3898:
3897:
3892:
3887:
3886:
3871:
3870:
3854:
3852:
3851:
3846:
3844:
3843:
3823:
3821:
3820:
3815:
3804:
3803:
3791:
3783:
3782:
3767:
3766:
3742:
3740:
3739:
3734:
3723:
3722:
3697:
3695:
3694:
3689:
3687:
3686:
3670:
3668:
3667:
3662:
3660:
3659:
3647:
3646:
3626:
3624:
3623:
3618:
3594:
3592:
3591:
3586:
3574:
3572:
3571:
3566:
3564:
3563:
3562:
3545:
3543:
3542:
3537:
3535:
3534:
3533:
3516:
3514:
3513:
3508:
3506:
3505:
3489:
3487:
3486:
3481:
3479:
3478:
3477:
3460:
3458:
3457:
3452:
3450:
3449:
3448:
3431:
3429:
3428:
3423:
3421:
3420:
3419:
3402:
3400:
3399:
3394:
3392:
3391:
3375:
3373:
3372:
3367:
3365:
3364:
3338:
3336:
3335:
3330:
3314:
3312:
3311:
3306:
3304:
3303:
3291:
3290:
3268:
3266:
3265:
3260:
3243:
3205:
3203:
3202:
3197:
3195:
3194:
3182:
3181:
3158:
3156:
3155:
3150:
3139:
3138:
3126:
3125:
3113:
3105:
3104:
3089:
3088:
3076:
3075:
3051:
3049:
3048:
3043:
3032:
3031:
3019:
3018:
3006:
2998:
2997:
2982:
2981:
2969:
2968:
2943:
2941:
2940:
2935:
2933:
2932:
2916:
2914:
2913:
2908:
2906:
2905:
2889:
2887:
2886:
2881:
2879:
2878:
2863:
2862:
2850:
2849:
2827:
2825:
2824:
2819:
2817:
2816:
2801:
2800:
2788:
2787:
2765:
2763:
2762:
2757:
2755:
2754:
2735:
2733:
2732:
2727:
2725:
2724:
2697:
2695:
2694:
2689:
2687:
2685:
2677:
2657:
2651:
2646:
2633:
2628:
2606:
2604:
2603:
2598:
2586:
2584:
2583:
2578:
2576:
2575:
2556:
2554:
2553:
2548:
2546:
2544:
2536:
2525:
2520:
2519:
2503:
2501:
2500:
2495:
2493:
2492:
2480:
2479:
2463:
2461:
2460:
2455:
2453:
2452:
2436:
2434:
2433:
2428:
2426:
2425:
2413:
2412:
2400:
2399:
2383:
2381:
2380:
2375:
2363:
2361:
2360:
2355:
2342:Nash Equilibrium
2336:
2334:
2333:
2328:
2316:
2314:
2313:
2308:
2293:
2291:
2290:
2285:
2283:
2277:
2276:
2267:
2261:
2259:
2251:
2240:
2235:
2234:
2217:
2215:
2214:
2209:
2207:
2202:
2201:
2192:
2187:
2185:
2177:
2166:
2161:
2160:
2141:
2139:
2138:
2133:
2131:
2130:
2118:
2117:
2097:
2095:
2094:
2089:
2081:
2078:
2073:
2070:
2061:
2059:
2058:
2053:
2051:
2048:
2043:
2040:
2031:
2029:
2028:
2023:
2021:
2018:
2013:
2010:
2001:
1999:
1998:
1993:
1991:
1988:
1979:
1977:
1976:
1971:
1969:
1966:
1957:
1955:
1954:
1949:
1934:
1932:
1931:
1926:
1912:
1911:
1893:
1892:
1871:
1869:
1868:
1867:
1854:
1850:
1849:
1837:
1836:
1824:
1823:
1810:
1800:
1798:
1797:
1792:
1778:
1777:
1762:
1761:
1737:
1735:
1734:
1733:
1720:
1716:
1715:
1703:
1702:
1690:
1689:
1676:
1661:
1659:
1658:
1653:
1651:
1650:
1632:
1631:
1616:
1615:
1588:
1587:
1575:
1574:
1562:
1561:
1544:
1542:
1541:
1536:
1534:
1533:
1515:
1514:
1499:
1498:
1471:
1470:
1458:
1457:
1445:
1444:
1425:
1423:
1422:
1417:
1393:
1391:
1390:
1385:
1383:
1382:
1367:
1366:
1335:
1333:
1332:
1327:
1300:
1298:
1297:
1292:
1290:
1289:
1277:
1276:
1254:
1252:
1251:
1246:
1231:
1229:
1228:
1223:
1221:
1220:
1205:
1204:
1171:
1170:
1153:
1151:
1150:
1145:
1143:
1142:
1127:
1126:
1093:
1092:
1072:
1070:
1069:
1064:
1052:
1050:
1049:
1044:
1042:
1041:
1023:
1022:
1000:
998:
997:
992:
990:
989:
973:
971:
970:
965:
953:
951:
950:
945:
915:
913:
912:
907:
905:
904:
888:
886:
885:
880:
805:
803:
802:
797:
785:
783:
782:
777:
775:
774:
758:
756:
755:
750:
748:
747:
735:
734:
712:
710:
709:
704:
677:
675:
674:
669:
657:
655:
654:
649:
637:
635:
634:
629:
608:
606:
605:
600:
588:
586:
585:
580:
565:
563:
562:
557:
510:
508:
507:
502:
481:
479:
478:
473:
462:
447:
445:
444:
439:
428:
395:
393:
392:
387:
363:
361:
360:
355:
324:
322:
321:
316:
295:
293:
292:
287:
144:
112:
110:
109:
104:
21:
6703:
6702:
6698:
6697:
6696:
6694:
6693:
6692:
6658:
6657:
6656:
6651:
6585:
6571:max^n algorithm
6544:
6540:William Vickrey
6500:Reinhard Selten
6455:Kenneth Binmore
6370:David K. Levine
6365:Daniel Kahneman
6332:
6326:
6302:Negamax theorem
6292:Minimax theorem
6270:
6231:Diner's dilemma
6086:All-pay auction
6052:
6038:Stochastic game
5990:Mean-field game
5961:
5954:
5925:Markov strategy
5861:
5727:
5719:
5690:Sequential game
5675:Information set
5660:Game complexity
5630:Congestion game
5618:
5612:
5562:, Chapter 6 of
5533:
5531:Further reading
5528:
5527:
5521:de Bornier 1992
5515:
5511:
5505:de Bornier 1992
5492:
5490:
5467:
5466:
5462:
5456:de Bornier 1992
5454:
5450:
5444:de Bornier 1992
5409:
5408:
5404:
5389:
5387:
5376:
5366:
5365:
5361:
5355:de Bornier 1992
5349:
5345:
5337:
5333:
5323:
5321:
5296:
5291:
5290:
5286:
5278:
5274:
5268:de Bornier 1992
5228:
5227:
5223:
5217:de Bornier 1992
5189:
5188:
5181:
5173:
5169:
5158:
5143:Le Petit Robert
5128:
5127:
5123:
5113:
5111:
5087:
5086:
5079:
5056:10.2307/1882115
5027:
5026:
5022:
4988:
4987:
4976:
4966:
4964:
4941:
4936:
4935:
4931:
4921:
4919:
4889:
4888:
4884:
4877:
4869:. p. 490.
4855:
4854:
4847:
4842:
4837:
4836:
4830:de Bornier 1992
4827:
4823:
4818:
4810:Tacit collusion
4766:
4715:Joseph Bertrand
4711:
4677:
4676:
4642:
4616:
4615:
4596:
4595:
4594:When there are
4592:
4562:
4561:
4533:
4532:
4504:
4503:
4478:
4477:
4458:
4457:
4426:
4425:
4411:
4395:
4394:
4375:
4374:
4355:
4354:
4310:
4287:
4286:
4252:
4226:
4225:
4206:
4205:
4186:
4185:
4166:
4165:
4146:
4145:
4126:
4125:
4091:
4065:
4064:
4061:
4035:
4030:
4029:
4008:
4003:
4002:
3981:
3976:
3975:
3951:
3935:
3930:
3929:
3908:
3903:
3902:
3878:
3862:
3857:
3856:
3835:
3830:
3829:
3795:
3784:
3774:
3758:
3747:
3746:
3714:
3703:
3702:
3678:
3673:
3672:
3651:
3638:
3633:
3632:
3597:
3596:
3577:
3576:
3553:
3548:
3547:
3524:
3519:
3518:
3497:
3492:
3491:
3468:
3463:
3462:
3439:
3434:
3433:
3410:
3405:
3404:
3383:
3378:
3377:
3356:
3351:
3350:
3321:
3320:
3295:
3282:
3271:
3270:
3236:
3210:
3209:
3186:
3173:
3168:
3167:
3130:
3117:
3106:
3096:
3080:
3067:
3056:
3055:
3023:
3010:
2999:
2989:
2973:
2960:
2949:
2948:
2924:
2919:
2918:
2897:
2892:
2891:
2870:
2854:
2841:
2830:
2829:
2808:
2792:
2779:
2768:
2767:
2746:
2738:
2737:
2716:
2708:
2707:
2704:
2678:
2658:
2609:
2608:
2589:
2588:
2567:
2562:
2561:
2537:
2526:
2511:
2506:
2505:
2484:
2471:
2466:
2465:
2444:
2439:
2438:
2417:
2404:
2391:
2386:
2385:
2366:
2365:
2346:
2345:
2319:
2318:
2299:
2298:
2268:
2252:
2241:
2226:
2221:
2220:
2193:
2178:
2167:
2152:
2147:
2146:
2122:
2109:
2104:
2103:
2064:
2063:
2062:, we must have
2034:
2033:
2004:
2003:
1982:
1981:
1960:
1959:
1940:
1939:
1903:
1884:
1859:
1855:
1841:
1828:
1815:
1811:
1804:
1803:
1769:
1753:
1725:
1721:
1707:
1694:
1681:
1677:
1670:
1669:
1642:
1623:
1607:
1579:
1566:
1553:
1548:
1547:
1525:
1506:
1490:
1462:
1449:
1436:
1431:
1430:
1399:
1398:
1374:
1358:
1338:
1337:
1303:
1302:
1281:
1268:
1257:
1256:
1237:
1236:
1212:
1196:
1162:
1157:
1156:
1134:
1118:
1084:
1079:
1078:
1055:
1054:
1033:
1014:
1003:
1002:
981:
976:
975:
956:
955:
918:
917:
896:
891:
890:
871:
870:
862:
857:
848:
819:
788:
787:
766:
761:
760:
739:
726:
715:
714:
680:
679:
660:
659:
640:
639:
611:
610:
591:
590:
571:
570:
548:
547:
535:
522:
517:
484:
483:
455:
450:
449:
421:
398:
397:
366:
365:
334:
333:
298:
297:
278:
277:
254:
225:
193:Joseph Bertrand
185:
174:Nash equilibria
145:
138:
127:
95:
94:
28:
23:
22:
15:
12:
11:
5:
6701:
6699:
6691:
6690:
6685:
6680:
6675:
6670:
6660:
6659:
6653:
6652:
6650:
6649:
6644:
6639:
6634:
6629:
6624:
6619:
6614:
6609:
6604:
6599:
6593:
6591:
6587:
6586:
6584:
6583:
6578:
6573:
6568:
6563:
6558:
6552:
6550:
6546:
6545:
6543:
6542:
6537:
6532:
6527:
6522:
6517:
6512:
6507:
6505:Robert Axelrod
6502:
6497:
6492:
6487:
6482:
6480:Olga Bondareva
6477:
6472:
6470:Melvin Dresher
6467:
6462:
6460:Leonid Hurwicz
6457:
6452:
6447:
6442:
6437:
6432:
6427:
6422:
6417:
6412:
6407:
6402:
6397:
6395:Harold W. Kuhn
6392:
6387:
6385:Drew Fudenberg
6382:
6377:
6375:David M. Kreps
6372:
6367:
6362:
6360:Claude Shannon
6357:
6352:
6347:
6342:
6336:
6334:
6328:
6327:
6325:
6324:
6319:
6314:
6309:
6304:
6299:
6297:Nash's theorem
6294:
6289:
6284:
6278:
6276:
6272:
6271:
6269:
6268:
6263:
6258:
6253:
6248:
6243:
6238:
6233:
6228:
6223:
6218:
6213:
6208:
6203:
6198:
6193:
6188:
6183:
6178:
6173:
6168:
6163:
6158:
6156:Ultimatum game
6153:
6148:
6143:
6138:
6136:Dollar auction
6133:
6128:
6123:
6121:Centipede game
6118:
6113:
6108:
6103:
6098:
6093:
6088:
6083:
6078:
6076:Infinite chess
6073:
6068:
6062:
6060:
6054:
6053:
6051:
6050:
6045:
6043:Symmetric game
6040:
6035:
6030:
6028:Signaling game
6025:
6023:Screening game
6020:
6015:
6013:Potential game
6010:
6005:
6000:
5992:
5987:
5982:
5977:
5972:
5966:
5964:
5956:
5955:
5953:
5952:
5947:
5942:
5940:Mixed strategy
5937:
5932:
5927:
5922:
5917:
5912:
5907:
5902:
5897:
5892:
5887:
5882:
5877:
5871:
5869:
5863:
5862:
5860:
5859:
5854:
5849:
5844:
5839:
5834:
5829:
5824:
5822:Risk dominance
5819:
5814:
5809:
5804:
5799:
5794:
5789:
5784:
5779:
5774:
5769:
5764:
5759:
5754:
5749:
5744:
5739:
5733:
5731:
5721:
5720:
5718:
5717:
5712:
5707:
5702:
5697:
5692:
5687:
5682:
5677:
5672:
5667:
5665:Graphical game
5662:
5657:
5652:
5647:
5642:
5637:
5632:
5626:
5624:
5620:
5619:
5613:
5611:
5610:
5603:
5596:
5588:
5582:
5581:
5571:
5557:
5547:
5532:
5529:
5526:
5525:
5509:
5460:
5458:, p. 631.
5448:
5430:10.1086/254576
5402:
5359:
5343:
5331:
5284:
5272:
5230:Shubik, Martin
5221:
5179:
5167:
5156:
5121:
5077:
5029:Fisher, Irving
5020:
4974:
4929:
4882:
4875:
4857:Varian, Hal R.
4844:
4843:
4841:
4838:
4835:
4834:
4820:
4819:
4817:
4814:
4813:
4812:
4807:
4802:
4797:
4792:
4787:
4782:
4777:
4772:
4765:
4762:
4710:
4707:
4693:
4690:
4687:
4684:
4664:
4661:
4658:
4655:
4652:
4648:
4645:
4641:
4638:
4635:
4632:
4629:
4626:
4623:
4603:
4591:
4588:
4575:
4572:
4569:
4549:
4546:
4543:
4540:
4520:
4517:
4514:
4511:
4491:
4488:
4485:
4465:
4442:
4439:
4436:
4432:
4429:
4423:
4420:
4417:
4414:
4408:
4405:
4402:
4382:
4362:
4332:
4329:
4326:
4323:
4320:
4316:
4313:
4309:
4306:
4303:
4300:
4297:
4294:
4274:
4271:
4268:
4265:
4262:
4258:
4255:
4251:
4248:
4245:
4242:
4239:
4236:
4233:
4213:
4193:
4173:
4153:
4133:
4113:
4110:
4107:
4104:
4101:
4097:
4094:
4090:
4087:
4084:
4081:
4078:
4075:
4072:
4060:
4057:
4042:
4038:
4015:
4011:
3988:
3984:
3963:
3958:
3954:
3950:
3947:
3942:
3938:
3915:
3911:
3890:
3885:
3881:
3877:
3874:
3869:
3865:
3842:
3838:
3826:
3825:
3813:
3810:
3807:
3802:
3798:
3794:
3790:
3787:
3781:
3777:
3773:
3770:
3765:
3761:
3757:
3754:
3744:
3732:
3729:
3726:
3721:
3717:
3713:
3710:
3685:
3681:
3658:
3654:
3650:
3645:
3641:
3616:
3613:
3610:
3607:
3604:
3584:
3556:
3527:
3504:
3500:
3471:
3442:
3413:
3390:
3386:
3363:
3359:
3328:
3317:
3316:
3302:
3298:
3294:
3289:
3285:
3281:
3278:
3258:
3255:
3252:
3249:
3246:
3242:
3239:
3235:
3232:
3229:
3226:
3223:
3220:
3217:
3207:
3193:
3189:
3185:
3180:
3176:
3161:
3160:
3148:
3145:
3142:
3137:
3133:
3129:
3124:
3120:
3116:
3112:
3109:
3103:
3099:
3095:
3092:
3087:
3083:
3079:
3074:
3070:
3066:
3063:
3053:
3041:
3038:
3035:
3030:
3026:
3022:
3017:
3013:
3009:
3005:
3002:
2996:
2992:
2988:
2985:
2980:
2976:
2972:
2967:
2963:
2959:
2956:
2931:
2927:
2904:
2900:
2877:
2873:
2869:
2866:
2861:
2857:
2853:
2848:
2844:
2840:
2837:
2815:
2811:
2807:
2804:
2799:
2795:
2791:
2786:
2782:
2778:
2775:
2753:
2749:
2745:
2723:
2719:
2715:
2703:
2700:
2684:
2681:
2676:
2673:
2670:
2667:
2664:
2661:
2655:
2650:
2645:
2641:
2637:
2632:
2627:
2623:
2619:
2616:
2596:
2574:
2570:
2543:
2540:
2535:
2532:
2529:
2523:
2518:
2514:
2491:
2487:
2483:
2478:
2474:
2451:
2447:
2424:
2420:
2416:
2411:
2407:
2403:
2398:
2394:
2373:
2353:
2326:
2306:
2295:
2294:
2280:
2275:
2271:
2264:
2258:
2255:
2250:
2247:
2244:
2238:
2233:
2229:
2218:
2205:
2200:
2196:
2190:
2184:
2181:
2176:
2173:
2170:
2164:
2159:
2155:
2129:
2125:
2121:
2116:
2112:
2087:
2084:
2076:
2046:
2016:
1947:
1936:
1935:
1924:
1921:
1918:
1915:
1910:
1906:
1902:
1899:
1896:
1891:
1887:
1883:
1880:
1877:
1874:
1866:
1862:
1858:
1853:
1848:
1844:
1840:
1835:
1831:
1827:
1822:
1818:
1814:
1801:
1790:
1787:
1784:
1781:
1776:
1772:
1768:
1765:
1760:
1756:
1752:
1749:
1746:
1743:
1740:
1732:
1728:
1724:
1719:
1714:
1710:
1706:
1701:
1697:
1693:
1688:
1684:
1680:
1663:
1662:
1649:
1645:
1641:
1638:
1635:
1630:
1626:
1622:
1619:
1614:
1610:
1606:
1603:
1600:
1597:
1594:
1591:
1586:
1582:
1578:
1573:
1569:
1565:
1560:
1556:
1545:
1532:
1528:
1524:
1521:
1518:
1513:
1509:
1505:
1502:
1497:
1493:
1489:
1486:
1483:
1480:
1477:
1474:
1469:
1465:
1461:
1456:
1452:
1448:
1443:
1439:
1415:
1412:
1409:
1406:
1381:
1377:
1373:
1370:
1365:
1361:
1357:
1354:
1351:
1348:
1345:
1325:
1322:
1319:
1316:
1313:
1310:
1288:
1284:
1280:
1275:
1271:
1267:
1264:
1244:
1233:
1232:
1219:
1215:
1211:
1208:
1203:
1199:
1195:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1169:
1165:
1154:
1141:
1137:
1133:
1130:
1125:
1121:
1117:
1114:
1111:
1108:
1105:
1102:
1099:
1096:
1091:
1087:
1062:
1040:
1036:
1032:
1029:
1026:
1021:
1017:
1013:
1010:
988:
984:
963:
943:
940:
937:
934:
931:
928:
925:
903:
899:
878:
861:
858:
856:
853:
847:
844:
818:
815:
795:
773:
769:
746:
742:
738:
733:
729:
725:
722:
702:
699:
696:
693:
690:
687:
667:
647:
627:
624:
621:
618:
609:is denoted by
598:
578:
555:
534:
531:
521:
518:
516:
513:
500:
497:
494:
491:
471:
468:
465:
461:
458:
437:
434:
431:
427:
424:
420:
417:
414:
411:
408:
405:
385:
382:
379:
376:
373:
353:
350:
347:
344:
341:
314:
311:
308:
305:
285:
253:
250:
224:
221:
184:
178:
136:
126:
123:
102:
90:
89:
82:
79:
76:
69:
62:
27:Economic model
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6700:
6689:
6686:
6684:
6681:
6679:
6676:
6674:
6671:
6669:
6666:
6665:
6663:
6648:
6645:
6643:
6640:
6638:
6635:
6633:
6630:
6628:
6625:
6623:
6620:
6618:
6615:
6613:
6610:
6608:
6605:
6603:
6600:
6598:
6595:
6594:
6592:
6590:Miscellaneous
6588:
6582:
6579:
6577:
6574:
6572:
6569:
6567:
6564:
6562:
6559:
6557:
6554:
6553:
6551:
6547:
6541:
6538:
6536:
6533:
6531:
6528:
6526:
6525:Samuel Bowles
6523:
6521:
6520:Roger Myerson
6518:
6516:
6513:
6511:
6510:Robert Aumann
6508:
6506:
6503:
6501:
6498:
6496:
6493:
6491:
6488:
6486:
6483:
6481:
6478:
6476:
6473:
6471:
6468:
6466:
6465:Lloyd Shapley
6463:
6461:
6458:
6456:
6453:
6451:
6450:Kenneth Arrow
6448:
6446:
6443:
6441:
6438:
6436:
6433:
6431:
6430:John Harsanyi
6428:
6426:
6423:
6421:
6418:
6416:
6413:
6411:
6408:
6406:
6403:
6401:
6400:Herbert Simon
6398:
6396:
6393:
6391:
6388:
6386:
6383:
6381:
6378:
6376:
6373:
6371:
6368:
6366:
6363:
6361:
6358:
6356:
6353:
6351:
6348:
6346:
6343:
6341:
6338:
6337:
6335:
6329:
6323:
6320:
6318:
6315:
6313:
6310:
6308:
6305:
6303:
6300:
6298:
6295:
6293:
6290:
6288:
6285:
6283:
6280:
6279:
6277:
6273:
6267:
6264:
6262:
6259:
6257:
6254:
6252:
6249:
6247:
6244:
6242:
6239:
6237:
6234:
6232:
6229:
6227:
6224:
6222:
6219:
6217:
6214:
6212:
6209:
6207:
6204:
6202:
6201:Fair division
6199:
6197:
6194:
6192:
6189:
6187:
6184:
6182:
6179:
6177:
6176:Dictator game
6174:
6172:
6169:
6167:
6164:
6162:
6159:
6157:
6154:
6152:
6149:
6147:
6144:
6142:
6139:
6137:
6134:
6132:
6129:
6127:
6124:
6122:
6119:
6117:
6114:
6112:
6109:
6107:
6104:
6102:
6099:
6097:
6094:
6092:
6089:
6087:
6084:
6082:
6079:
6077:
6074:
6072:
6069:
6067:
6064:
6063:
6061:
6059:
6055:
6049:
6048:Zero-sum game
6046:
6044:
6041:
6039:
6036:
6034:
6031:
6029:
6026:
6024:
6021:
6019:
6018:Repeated game
6016:
6014:
6011:
6009:
6006:
6004:
6001:
5999:
5997:
5993:
5991:
5988:
5986:
5983:
5981:
5978:
5976:
5973:
5971:
5968:
5967:
5965:
5963:
5957:
5951:
5948:
5946:
5943:
5941:
5938:
5936:
5935:Pure strategy
5933:
5931:
5928:
5926:
5923:
5921:
5918:
5916:
5913:
5911:
5908:
5906:
5903:
5901:
5900:De-escalation
5898:
5896:
5893:
5891:
5888:
5886:
5883:
5881:
5878:
5876:
5873:
5872:
5870:
5868:
5864:
5858:
5855:
5853:
5850:
5848:
5845:
5843:
5842:Shapley value
5840:
5838:
5835:
5833:
5830:
5828:
5825:
5823:
5820:
5818:
5815:
5813:
5810:
5808:
5805:
5803:
5800:
5798:
5795:
5793:
5790:
5788:
5785:
5783:
5780:
5778:
5775:
5773:
5770:
5768:
5765:
5763:
5760:
5758:
5755:
5753:
5750:
5748:
5745:
5743:
5740:
5738:
5735:
5734:
5732:
5730:
5726:
5722:
5716:
5713:
5711:
5710:Succinct game
5708:
5706:
5703:
5701:
5698:
5696:
5693:
5691:
5688:
5686:
5683:
5681:
5678:
5676:
5673:
5671:
5668:
5666:
5663:
5661:
5658:
5656:
5653:
5651:
5648:
5646:
5643:
5641:
5638:
5636:
5633:
5631:
5628:
5627:
5625:
5621:
5617:
5609:
5604:
5602:
5597:
5595:
5590:
5589:
5586:
5579:
5575:
5572:
5569:
5565:
5561:
5558:
5555:
5551:
5548:
5546:
5542:
5538:
5537:Holt, Charles
5535:
5534:
5530:
5522:
5518:
5513:
5510:
5506:
5500:
5488:
5484:
5480:
5475:
5470:
5464:
5461:
5457:
5452:
5449:
5445:
5439:
5435:
5431:
5427:
5423:
5419:
5415:
5414:
5406:
5403:
5399:
5398:Friedman 2000
5386:
5382:
5375:
5374:
5369:
5363:
5360:
5356:
5352:
5347:
5344:
5340:
5335:
5332:
5320:
5316:
5312:
5308:
5304:
5303:
5295:
5288:
5285:
5281:
5276:
5273:
5269:
5263:
5259:
5255:
5251:
5247:
5243:
5239:
5235:
5231:
5225:
5222:
5218:
5212:
5208:
5204:
5200:
5196:
5192:
5191:Shapiro, Carl
5186:
5184:
5180:
5177:, p. 49.
5176:
5171:
5168:
5163:
5159:
5157:2-85036-668-4
5153:
5149:
5146:(in French).
5145:
5144:
5139:
5135:
5131:
5125:
5122:
5110:
5106:
5102:
5098:
5094:
5090:
5084:
5082:
5078:
5074:
5073:Friedman 2000
5067:
5062:
5057:
5052:
5048:
5044:
5040:
5039:
5034:
5030:
5024:
5021:
5016:
5012:
5008:
5004:
5000:
4996:
4992:
4985:
4983:
4981:
4979:
4975:
4963:
4959:
4955:
4951:
4947:
4940:
4933:
4930:
4918:
4914:
4910:
4906:
4902:
4898:
4897:
4892:
4886:
4883:
4878:
4872:
4868:
4864:
4863:
4858:
4852:
4850:
4846:
4839:
4831:
4825:
4822:
4815:
4811:
4808:
4806:
4803:
4801:
4798:
4796:
4793:
4791:
4788:
4786:
4783:
4781:
4778:
4776:
4773:
4771:
4768:
4767:
4763:
4761:
4759:
4753:
4750:
4744:
4742:
4741:Irving Fisher
4738:
4736:
4731:
4726:
4724:
4720:
4716:
4706:
4691:
4688:
4685:
4682:
4662:
4659:
4653:
4646:
4643:
4639:
4636:
4633:
4627:
4621:
4601:
4589:
4587:
4573:
4570:
4567:
4547:
4544:
4541:
4538:
4518:
4515:
4512:
4509:
4489:
4486:
4483:
4463:
4437:
4430:
4427:
4418:
4412:
4406:
4403:
4400:
4380:
4360:
4348:
4344:
4330:
4327:
4321:
4314:
4311:
4307:
4304:
4298:
4292:
4272:
4269:
4263:
4256:
4253:
4249:
4246:
4243:
4237:
4231:
4211:
4191:
4171:
4151:
4131:
4111:
4108:
4102:
4095:
4092:
4088:
4085:
4079:
4073:
4070:
4058:
4056:
4040:
4036:
4013:
4009:
3986:
3982:
3956:
3952:
3945:
3940:
3936:
3913:
3909:
3883:
3879:
3872:
3867:
3863:
3840:
3836:
3811:
3808:
3800:
3796:
3788:
3785:
3779:
3775:
3771:
3763:
3759:
3752:
3745:
3730:
3727:
3719:
3715:
3708:
3701:
3700:
3699:
3683:
3679:
3656:
3652:
3648:
3643:
3639:
3628:
3611:
3608:
3605:
3582:
3554:
3525:
3502:
3498:
3469:
3440:
3411:
3388:
3384:
3361:
3357:
3344:
3340:
3326:
3300:
3296:
3292:
3287:
3283:
3279:
3276:
3256:
3253:
3247:
3240:
3237:
3233:
3230:
3224:
3218:
3215:
3208:
3191:
3187:
3183:
3178:
3174:
3166:
3165:
3164:
3146:
3143:
3135:
3131:
3127:
3122:
3118:
3110:
3107:
3101:
3097:
3093:
3085:
3081:
3077:
3072:
3068:
3061:
3054:
3039:
3036:
3028:
3024:
3020:
3015:
3011:
3003:
3000:
2994:
2990:
2986:
2978:
2974:
2970:
2965:
2961:
2954:
2947:
2946:
2945:
2929:
2925:
2902:
2898:
2875:
2871:
2867:
2859:
2855:
2851:
2846:
2842:
2835:
2813:
2809:
2805:
2797:
2793:
2789:
2784:
2780:
2773:
2751:
2747:
2743:
2721:
2717:
2713:
2701:
2699:
2682:
2679:
2671:
2668:
2665:
2659:
2653:
2648:
2643:
2639:
2635:
2630:
2625:
2621:
2617:
2614:
2594:
2572:
2568:
2558:
2541:
2538:
2533:
2530:
2527:
2521:
2516:
2512:
2489:
2485:
2481:
2476:
2472:
2449:
2445:
2422:
2418:
2414:
2409:
2405:
2401:
2396:
2392:
2371:
2364:) and price (
2351:
2343:
2338:
2324:
2304:
2278:
2273:
2269:
2262:
2256:
2253:
2248:
2245:
2242:
2236:
2231:
2227:
2219:
2203:
2198:
2194:
2188:
2182:
2179:
2174:
2171:
2168:
2162:
2157:
2153:
2145:
2144:
2143:
2127:
2123:
2119:
2114:
2110:
2099:
2085:
2082:
2074:
2044:
2014:
1945:
1922:
1919:
1916:
1913:
1908:
1904:
1900:
1897:
1894:
1889:
1885:
1881:
1878:
1875:
1872:
1864:
1860:
1846:
1842:
1838:
1833:
1829:
1820:
1802:
1788:
1785:
1782:
1779:
1774:
1770:
1766:
1763:
1758:
1754:
1750:
1747:
1744:
1741:
1738:
1730:
1726:
1712:
1708:
1704:
1699:
1695:
1686:
1668:
1667:
1666:
1647:
1643:
1636:
1633:
1628:
1624:
1620:
1617:
1612:
1608:
1604:
1601:
1598:
1592:
1584:
1580:
1576:
1571:
1567:
1558:
1546:
1530:
1526:
1519:
1516:
1511:
1507:
1503:
1500:
1495:
1491:
1487:
1484:
1481:
1475:
1467:
1463:
1459:
1454:
1450:
1441:
1429:
1428:
1427:
1410:
1404:
1395:
1379:
1375:
1371:
1368:
1363:
1359:
1355:
1352:
1349:
1346:
1343:
1323:
1320:
1317:
1314:
1311:
1308:
1286:
1282:
1278:
1273:
1269:
1265:
1262:
1242:
1217:
1213:
1209:
1206:
1201:
1197:
1190:
1184:
1181:
1175:
1167:
1155:
1139:
1135:
1131:
1128:
1123:
1119:
1112:
1106:
1103:
1097:
1089:
1077:
1076:
1075:
1060:
1038:
1034:
1030:
1027:
1019:
1015:
1008:
986:
982:
961:
938:
935:
932:
926:
923:
901:
897:
876:
867:
859:
854:
852:
845:
843:
841:
836:
832:
827:
823:
816:
814:
811:
807:
793:
771:
767:
744:
740:
736:
731:
727:
723:
720:
697:
691:
688:
685:
665:
645:
622:
616:
596:
576:
567:
553:
543:
541:
530:
527:
526:independently
519:
512:
495:
489:
466:
459:
456:
432:
425:
422:
418:
415:
409:
403:
380:
374:
371:
348:
342:
339:
330:
326:
325:of its price.
309:
303:
283:
273:
271:
267:
258:
249:
247:
243:
242:Joan Robinson
239:
235:
231:
220:
215:
211:
209:
205:
200:
198:
197:Irving Fisher
194:
190:
183:
179:
177:
175:
169:
166:
165:best response
162:
158:
154:
150:
142:
135:
133:
124:
122:
120:
116:
100:
87:
83:
80:
77:
74:
70:
67:
63:
60:
56:
53:
49:
48:
47:
45:
41:
36:
32:
19:
6495:Peyton Young
6490:Paul Milgrom
6405:Hervé Moulin
6345:Amos Tversky
6287:Folk theorem
6215:
5998:-player game
5995:
5920:Grim trigger
5577:
5553:
5550:Tirole, Jean
5540:
5512:
5498:
5493:December 13,
5491:. Retrieved
5482:
5463:
5451:
5442:, quoted by
5417:
5411:
5405:
5396:, quoted in
5390:December 13,
5372:
5362:
5353:, quoted by
5351:Cournot 1897
5346:
5339:Cournot 1897
5334:
5324:December 13,
5322:. Retrieved
5306:
5300:
5287:
5280:Cournot 1897
5275:
5266:, quoted by
5233:
5224:
5215:, quoted by
5198:
5194:
5175:Cournot 1897
5170:
5161:
5141:
5130:Robert, Paul
5124:
5114:December 13,
5112:. Retrieved
5103:(1): 31–46.
5100:
5096:
5042:
5036:
5023:
4994:
4990:
4965:. Retrieved
4949:
4945:
4932:
4922:December 13,
4920:. Retrieved
4900:
4895:
4885:
4861:
4824:
4755:
4752:competition.
4748:
4746:
4739:
4733:
4728:
4722:
4712:
4593:
4352:
4062:
3827:
3629:
3517:is equal to
3348:
3318:
3162:
2705:
2559:
2339:
2296:
2100:
1937:
1664:
1396:
1234:
863:
849:
830:
828:
824:
820:
812:
808:
568:
544:
536:
525:
523:
331:
328:
275:
269:
265:
263:
226:
217:
213:
201:
186:
181:
170:
152:
147:
140:
131:
129:
91:
73:market power
30:
29:
6612:Coopetition
6415:Jean Tirole
6410:John Conway
6390:Eric Maskin
6186:Blotto game
6171:Pirate game
5980:Global game
5950:Tit for tat
5885:Bid shading
5875:Appeasement
5725:Equilibrium
5705:Solved game
5640:Determinacy
5623:Definitions
5616:game theory
5519:, cited by
5517:Fisher 1898
5503:, cited by
5479:Molk, Jules
5313:: 623–656.
5205:: 329–414.
5071:, cited by
5049:: 119–138.
5001:: 172–174.
4967:January 22,
4956:: 174–192.
4790:Game theory
658:is written
204:game theory
189:LĂ©on Walras
71:Firms have
52:homogeneous
6662:Categories
6256:Trust game
6241:Kuhn poker
5910:Escalation
5905:Deterrence
5895:Cheap talk
5867:Strategies
5685:Preference
5614:Topics of
5424:: 80–105.
5388:Retrieved
5254:B0000CKANF
5138:Rey, Alain
4876:0393927024
4840:References
3928:is 0, but
210:explains:
182:Recherches
6688:Oligopoly
6440:John Nash
6146:Stag hunt
5890:Collusion
5568:Huw Dixon
5438:154081349
5015:154319304
4893:(1897) .
4859:(2006) .
4407:−
2868:⋅
2806:⋅
2702:Example 2
2672:χ
2669:−
2649:∗
2631:∗
2573:∗
2534:χ
2531:−
2517:∗
2450:∗
2423:∗
2352:χ
2325:χ
2263:−
2249:χ
2246:−
2189:−
2175:χ
2172:−
2075:−
1917:χ
1914:−
1895:−
1879:−
1857:∂
1817:Π
1813:∂
1783:χ
1780:−
1764:−
1745:−
1723:∂
1683:Π
1679:∂
1637:χ
1634:−
1618:−
1602:−
1555:Π
1520:χ
1517:−
1501:−
1485:−
1438:Π
1369:−
1353:−
1318:−
1210:χ
1207:−
1164:Π
1132:χ
1129:−
1086:Π
1061:χ
1031:χ
927:∈
860:Example 1
846:Collusion
835:Edgeworth
66:collusion
6581:Lazy SMP
6275:Theorems
6226:Deadlock
6081:Checkers
5962:of games
5729:concepts
5471:(1911).
5370:(1881).
5262:58-14221
5238:New York
5232:(1959).
5203:Elsevier
5091:(2000).
5031:(1898).
4999:Springer
4954:Elsevier
4905:New York
4764:See also
4647:′
4431:′
4373:against
4315:′
4257:′
4096:′
3789:′
3269:, where
3241:′
3111:′
3004:′
2766:, i.e.,
2607:will be
1053:, where
833:price".
713:, where
460:′
426:′
396:, i.e.,
137:—
119:monopoly
35:economic
6333:figures
6116:Chicken
5970:Auction
5960:Classes
5481:(ed.).
5066:1882115
954:, firm
866:duopoly
840:Shapiro
540:Shapiro
270:demande
157:duopoly
125:History
55:product
44:duopoly
5436:
5381:London
5260:
5252:
5154:
5063:
5013:
4873:
4735:Pareto
4719:Walras
916:where
132:stable
115:demand
33:is an
6071:Chess
6058:Games
5487:Paris
5434:S2CID
5420:(1).
5377:(PDF)
5309:(3).
5297:(PDF)
5162:débit
5061:JSTOR
5045:(2).
5011:S2CID
4997:(2).
4952:(2).
4942:(PDF)
4899:[
4816:Notes
4749:price
266:débit
5752:Core
5495:2022
5392:2022
5326:2022
5258:LCCN
5250:ASIN
5242:N.Y.
5152:ISBN
5116:2022
4969:2023
4924:2022
4871:ISBN
4164:via
3649:>
3376:and
2828:and
2736:and
2464:for
2015:>
759:and
240:and
6331:Key
5566:by
5545:PDF
5426:doi
5315:doi
5207:doi
5105:doi
5051:doi
5003:doi
4958:doi
4913:hdl
4721:'s
3743:and
3206:and
3052:and
831:his
511:).
6664::
6066:Go
5576:,
5552:.
5543:,
5539:.
5497:.
5432:.
5418:42
5416:.
5383::
5379:.
5307:24
5305:.
5299:.
5256:.
5248:.
5244::
5240:,
5236:.
5201:.
5197:.
5182:^
5160:.
5150:.
5136:;
5132:;
5101:37
5099:.
5095:.
5080:^
5059:.
5043:12
5041:.
5035:.
5009:.
4995:26
4993:.
4977:^
4950:30
4948:.
4944:.
4911:.
4907::
4848:^
4760:.
4124:.
3627:.
3560:ll
3475:ll
3339:.
2698:.
2557:.
2079:MR
2071:MC
2049:MR
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2019:MR
2011:MC
1989:MR
1967:MC
1394:.
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5428::
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5317::
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4971:.
4960::
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4692:p
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