216:: that "every player knows the payoffs and strategies available to other players," where the word "payoff" is descriptive of behavior—what the player is trying to maximize. If, in the first town, the competitor enters and the monopolist is aggressive, the second competitor has observed that the monopolist is not, from the standpoint of common knowledge of payoffs and strategies, maximizing the assumed payoffs; expecting the monopolist to do so in this town seems dubious.
153:"). If a few do test the chain store early in the game, and see that they are greeted with the aggressive strategy, the rest of the competitors are likely not to test any further. Assuming all 17 are deterred, Player A receives 91 (17Ă—5 + 2Ă—3). Even if as many as 10 competitors enter and test Player A's will, Player A will still receive a payoff of 41 (10Ă—0+ 7Ă—5 + 3Ă—2), which is better than the induction (game theoretically correct) payoff.
1125:
1115:
113:, Player A receives a higher payoff from choosing to cooperate than aggressive, and being the last period of the game, there are no longer any future competitors whom Player A needs to intimidate from the market. Knowing this, the 20th competitor enters the market, and Player A will cooperate (receiving a payoff of 2 instead of 0).
116:
The outcome in the final period is set in stone, so to speak. Now consider period 19, and the potential competitor's decision. He knows that A will cooperate in the next period, regardless of what happens in period 19. Thus, if player 19 enters, an aggressive strategy will not be able to deter player
273:
Depending on which level is selected, the individual begins the decision procedure. The individual then arrives at a (possibly different) decision for each level available (if we have chosen imagination, we would arrive at a routine decision and possible and imagination decision). Selten argues that
144:
This theory states that Player A will be able to get payoff of higher than 40. Suppose Player A finds the induction argument convincing. He will decide how many periods at the end to play such a strategy, say 3. In periods 1–17, he will decide to always be aggressive against the choice of IN. If all
251:
The individual makes a conscious effort to analyze the situation in a rational way, using both past experience and logical thinking. This mode of decision uses simplified models whose assumptions are products of imagination, and is the only method of reasoning permitted and expected by game theory.
219:
If competitors place even a very small probability on the possibility that the monopolist is spiteful, and places intrinsic value on being (or appearing) aggressive, and the monopolist knows this, then even if the monopolist has payoffs as described above, responding to entry in an early town with
161:
If Player A follows the game theory payoff matrix to achieve the optimal payoff, they will have a lower payoff than with the "deterrence" strategy. This creates an apparent game theory paradox: game theory states that induction strategy should be optimal, but it looks like "deterrence strategy" is
274:
individuals can always reach a routine decision, but perhaps not the higher levels. Once the individuals have all their levels of decision, they can decide which answer to use...the Final
Decision. The final decision is made on the routine level and governs actual behavior.
242:
The individual tries to visualize how the selection of different alternatives may influence the probable course of future events. This level employs the routine level within the procedural decisions. This method is similar to a computer simulation.
233:
The individuals use their past experience of the results of decisions to guide their response to choices in the present. "The underlying criteria of similarity between decision situations are crude and sometimes inadequate". (Selten)
204:, is in fact an acceptable idea by the rationality that individuals actually employ. Selten argues that individuals can make decisions of three levels: Routine, Imagination, and Reasoning.
181:. A rational player will not carry out a non-credible threat, but the paradox is that it nevertheless seems to benefit Player A to carry out the threat.
93:
These outcomes lead to two theories for the game, the induction (game theoretically optimal version) and the deterrence theory (weakly dominated theory):
561:
709:
265:
One chooses which method (routine, imagination or reasoning) to use for the problem, and this decision itself is made on the routine level.
452:
70:, he will receive a payoff of either 2 or 0, depending on the response of Player A to his action. Player A, in response to a choice of
1154:
770:
739:
576:
367:
501:
995:
220:
aggression will be optimal if it increases the probability that later competitors place on the monopolist's being spiteful.
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166:
54:(Player A) has branches in 20 towns. He faces 20 potential competitors, one in each town, who will be able to choose
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136:, and Player A always cooperates. A receives a payoff of 40 (2Ă—20) and each competitor receives 2.
145:
of the potential competitors know this, it is unlikely potential competitors 1–17 will bother the
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Consider the decision to be made by the 20th and final competitor, of whether to choose
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62:. They do so in sequential order and one at a time. If a potential competitor chooses
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212:
Game theory is based on the idea that each matrix is modeled with the assumption of
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holds all the way back to the first competitor. Each potential competitor chooses
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32:
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149:, thus risking the safe payout of 1 ("A" will not retaliate if they choose "
86:, both player A and the competitor receive a payoff of 2, and if A chooses
66:, he receives a payoff of 1, while A receives a payoff of 5. If he chooses
27:
might make, where a "deterrence strategy" appears optimal instead of the
462:
395:
330:
193:
314:
430:
426:
Relation of Chain Store
Paradox to Constitutional Politics in Canada
526:
434:
23:
is an apparent game theory paradox describing the decisions a
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469:
117:20 from entering. Player 19 knows this and chooses
196:is to argue that the idea of "deterrence", while
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74:, must choose one of two pricing strategies,
8:
1114:
453:
439:
431:
223:
356:"Reputation and the Chain-Store Paradox"
305:
90:, each player receives a payoff of 0.
7:
380:(1978). "The chain store paradox".
165:The "deterrence strategy" is not a
38:The paradox was first put forth by
771:What the Tortoise Said to Achilles
224:Selten's levels of decision making
14:
1124:
1123:
1113:
362:. Routledge. pp. 247–249.
313:Selten, Reinhard (1978-04-01).
109:. He knows that if he chooses
1:
192:'s response to this apparent
167:Subgame perfect equilibrium
128:Of course, this process of
1171:
294:Unexpected hanging paradox
1155:Decision-making paradoxes
1109:
360:A Political Theory Primer
315:"The chain store paradox"
184:
690:Paradoxes of set theory
256:Decision-making process
157:The chain store paradox
121:. Player A chooses to
238:The imagination level
208:Complete information?
31:strategy of standard
1056:Kavka's toxin puzzle
828:Income and fertility
214:complete information
200:by the standards of
46:The chain store game
715:Temperature paradox
638:Free choice paradox
502:Fitch's knowability
383:Theory and Decision
352:Ordeshook, Peter C.
319:Theory and Decision
247:The reasoning level
171:non-credible threat
169:: It relies on the
21:chain store paradox
16:Game theory paradox
1091:Prisoner's dilemma
777:Heat death paradox
765:Unexpected hanging
730:Chicken or the egg
396:10.1007/BF00131770
331:10.1007/BF00131770
289:Traveler's dilemma
269:The final decision
130:backward induction
29:backward induction
1137:
1136:
808:Arrow information
229:The routine level
185:Selten's response
173:of responding to
162:optimal instead.
140:Deterrence theory
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928:Service recovery
782:Olbers's paradox
482:Buridan's bridge
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378:Selten, Reinhard
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97:Induction theory
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82:. If he chooses
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1016:Decision-making
962:Decision theory
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710:Hilbert's Hotel
643:Grelling–Nelson
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420:Further reading
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261:The predecision
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190:Reinhard Selten
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40:Reinhard Selten
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562:Rule-following
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487:Dream argument
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390:(2): 127–159.
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325:(2): 127–159.
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1001:Buridan's ass
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974:Apportionment
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750:Plato's beard
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648:Kleene–Rosser
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572:Theseus' ship
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532:Mere addition
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470:Philosophical
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369:0-415-90241-X
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284:Repeated game
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36:
34:
30:
26:
22:
1081:Preparedness
1005:
913:Productivity
893:Mandeville's
685:Opposite Day
613:Burali-Forti
608:Bhartrhari's
387:
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37:
20:
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1150:Game theory
1011:Condorcet's
863:Giffen good
823:Competition
577:White horse
552:Omnipotence
202:Game Theory
147:chain store
84:cooperative
76:cooperative
35:reasoning.
33:game theory
25:chain store
1144:Categories
1086:Prevention
1076:Parrondo's
1066:Navigation
1051:Inventor's
1046:Hedgehog's
1006:Chainstore
989:Population
984:New states
918:Prosperity
898:Mayfield's
740:Entailment
720:Barbershop
633:Epimenides
300:References
198:irrational
179:aggressive
88:aggressive
80:aggressive
52:monopolist
1101:Willpower
1096:Tolerance
1071:Newcomb's
1036:Fredkin's
923:Scitovsky
843:Edgeworth
838:Easterlin
803:Antitrust
700:Russell's
695:Richard's
668:Pinocchio
623:Crocodile
542:Newcomb's
512:Goodman's
507:Free will
492:Epicurean
463:paradoxes
412:143946876
404:0040-5833
339:1573-7187
123:cooperate
42:in 1978.
1129:Category
1026:Ellsberg
878:Leontief
858:Gibson's
853:European
848:Ellsberg
818:Braess's
813:Bertrand
791:Economic
725:Catch-22
705:Socratic
547:Nihilism
517:Hedonism
477:Analysis
461:Notable
354:(1992).
278:See also
1031:Fenno's
996:Arrow's
979:Alabama
969:Abilene
948:Tullock
903:Metzler
745:Lottery
735:Drinker
678:Yablo's
673:Quine's
628:Curry's
591:Logical
567:Sorites
557:Preface
537:Moore's
522:Liberal
497:Fiction
194:paradox
938:Thrift
908:Plenty
883:Lerner
873:Jevons
868:Icarus
798:Allais
760:Ross's
598:Barber
582:Zeno's
527:Meno's
410:
402:
366:
337:
1041:Green
1021:Downs
953:Value
888:Lucas
755:Raven
663:No-no
618:Court
603:Berry
408:S2CID
177:with
1119:List
943:Toil
658:Card
653:Liar
400:ISSN
364:ISBN
335:ISSN
19:The
392:doi
327:doi
151:out
107:out
105:or
78:or
64:out
60:out
58:or
1146::
406:.
398:.
386:.
358:.
333:.
321:.
317:.
175:in
134:in
125:.
119:in
111:in
103:in
72:in
68:in
56:in
50:A
773:"
769:"
454:e
447:t
440:v
414:.
394::
388:9
372:.
341:.
329::
323:9
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