167:
For example, when faced with a choice between $ 40 with certainty and a coin toss that pays $ 100 if the outcome is guessed correctly and $ 0 otherwise, not only does the certain payment alternative minimizes the risk but also the possibility of regret, since typically the coin will not be tossed (and thus the uncertainty not resolved) while if the coin toss is chosen, the outcome that pays $ 0 will induce regret. If the coin is tossed regardless of the chosen alternative, then the alternative payoff will always be known and then there is no choice that will eliminate the possibility of regret.
176:
experience greater regret if they missed a train by 1 minute more than missing a train by 5 minutes, for example, but commuters who actually missed their train by 1 or 5 minutes experienced (equal and) lower amounts of regret. Commuters appeared to overestimate the regret they would feel when missing the train by a narrow margin, because they tended to underestimate the extent to which they would attribute missing the train to external causes (e.g., missing their wallet or spending less time in the shower).
163:
been able to make a profit and how much could it have been (a participant that has a valuation of $ 50, bids $ 30 and finds out the winning bid was $ 35 will also learn that he or she could have earned as much as $ 15 by bidding anything over $ 35.) This in turn allows for the possibility of regret and if bidders correctly anticipate this, they would tend to bid higher than in the case where no feedback on the winning bid is provided in order to decrease the possibility of regret.
147:
failure or omitting an opportunity that we seek to avoid. Regret, feeling sadness or disappointment over something that has happened, can be rationalized for a certain decision, but can guide preferences and can lead people astray. This contributes to the spread of disinformation because things are not seen as one's personal responsibility.
204:
in 1951. The aim of this is to perform as closely as possible to the optimal course. Since the minimax criterion applied here is to the regret (difference or ratio of the payoffs) rather than to the payoff itself, it is not as pessimistic as the ordinary minimax approach. Similar approaches have been
162:
show that by manipulating the feedback the participants expect to receive, significant differences in the average bids are observed. In particular, "Loser's regret" can be induced by revealing the winning bid to all participants in the auction, and thus revealing to the losers whether they would have
359:
choice based on returns would be to invest in the money market, ensuring a return of at least 1. However, if interest rates fell then the regret associated with this choice would be large. This would be 11, which is the difference between the 12 which could have been received if the outcome had been
166:
In decisions over lotteries, experiments also provide supporting evidence of anticipated regret. As in the case of first price auctions, differences in feedback over the resolution of the uncertainty can cause the possibility of regret and if this is anticipated, it may induce different preferences.
446:
Therefore, using a minimax choice based on regret, the best course would be to invest in bonds, ensuring a regret of no worse than 5. A mixed investment portfolio would do even better: 61.1% invested in stocks, and 38.9% in the money market would produce a regret no worse than about 4.28.
175:
Anticipated regret tends to be overestimated for both choices and actions over which people perceive themselves to be responsible. People are particularly likely to overestimate the regret they will feel when missing a desired outcome by a narrow margin. In one study, commuters predicted they would
146:
Regret aversion is not only a theoretical economics model, but a cognitive bias occurring as a decision has been made to abstain from regretting an alternative decision. To better preface, regret aversion can be seen through fear by either commission or omission; the prospect of committing to a
122:
which depends negatively on the realized outcome and positively on the best alternative outcome given the uncertainty resolution. This regret term is usually an increasing, continuous and non-negative function subtracted to the traditional utility index. These type of preferences always violate
2450:, whose payoffs depend on a state of nature known only by the Agent. The Principal commits to a policy, then the agent responds, and then the state of nature is revealed. They assume that the principal and agent interact repeatedly, and may learn over time from the state history, using
566:. Also, since the estimator is restricted to be linear, the zero MSE cannot be achieved in the latter case. In this case, the solution of a convex optimization problem gives the optimal, minimax regret-minimizing linear estimator, which can be seen by the following argument.
225:
One benefit of minimax (as opposed to expected regret) is that it is independent of the probabilities of the various outcomes: thus if regret can be accurately computed, one can reliably use minimax regret. However, probabilities of outcomes are hard to estimate.
2319:
1510:
130:
For independent lotteries and when regret is evaluated over the difference between utilities and then averaged over the all combinations of outcomes, the regret can still be transitive but for only specific form of regret functional. It is shown that only
1087:
1112:
it cannot be minimized directly. Instead, the concept of regret can be used in order to define a linear estimator with good MSE performance. To define the regret here, consider a linear estimator that knows the value of the parameter
360:
known in advance and the 1 received. A mixed portfolio of about 11.1% in stocks and 88.9% in the money market would have ensured a return of at least 2.22; but, if interest rates fell, there would be a regret of about 9.78.
1855:
2825:
2794:
2033:
249:
Suppose an investor has to choose between investing in stocks, bonds or the money market, and the total return depends on what happens to interest rates. The following table shows some possible returns:
1711:
2084:
1278:
184:
Besides the traditional setting of choices over lotteries, regret aversion has been proposed as an explanation for the typically observed overbidding in first price auctions, and the
2376:
1231:
1270:
808:
897:
694:
1920:
1575:
645:
905:
764:
1887:
1542:
2420:
2396:
2076:
2056:
1595:
1171:
1151:
1131:
1110:
871:
851:
831:
737:
717:
668:
607:
587:
564:
544:
524:
497:
477:
115:. Regret theory models choice under uncertainty taking into account the effect of anticipated regret. Subsequently, several other authors improved upon it.
2893:
Gilbert, Daniel T.; Morewedge, Carey K.; Risen, Jane L.; Wilson, Timothy D. (2004-05-01). "Looking
Forward to Looking Backward The Misprediction of Regret".
2465:
Collina, Roth and Shao improve their mechanism both in running-time and in the bounds for regret (as a function of the number of distinct states of nature).
1725:
135:
function will maintain this property. This form of regret inherits most of desired features, such as holding right preferences in face of first order
3042:
Fogel, S. O. C.; Berry, T. (2006). "The disposition effect and individual investor decisions: the roles of regret and counterfactual alternatives".
3104:
Eldar, Y. C.; Ben-Tal, A.; Nemirovski, A. (2004). "Linear
Minimax regret estimation of deterministic parameters with bounded data uncertainties".
2058:. In practice this MSE cannot be achieved, but it serves as a bound on the optimal MSE. The regret of using the linear estimator specified by
3264:
1928:
2701:
526:
centered at zero. The regret is defined to be the difference between the MSE of the linear estimator that doesn't know the parameter
2600:
3313:
1603:
2378:
This will allow a performance as close as possible to the best achievable performance in the worst case of the parameter
52:
is often experienced, and can be measured as the value of difference between a made decision and the optimal decision.
2435:
2314:{\displaystyle R(x,G)=MSE-MSE^{o}=Tr(GC_{w}G^{*})+x^{*}(I-GH)^{*}(I-GH)x-{\frac {x^{*}x}{1+x^{*}H^{*}C_{w}^{-1}Hx}}.}
3339:
2621:
1505:{\displaystyle MSE^{o}=E\left(||{\hat {x}}^{o}-x||^{2}\right)=Tr(G(x)C_{w}G(x)^{*})+x^{*}(I-G(x)H)^{*}(I-G(x)H)x.}
3334:
356:
108:
3344:
3147:
Eldar, Y. C.; Merhav, Neri (2004). "A Competitive
Minimax Approach to Robust Estimation of Random Parameters".
2758:
2489:
363:
The regret table for this example, constructed by subtracting actual returns from best returns, is as follows:
67:
regret and thus incorporate in their choice their desire to eliminate or reduce this possibility. Regret is a
2529:
Loomes, G.; Sugden, R. (1982). "Regret theory: An alternative theory of rational choice under uncertainty".
2509:
459:. In this example, the problem is to construct a linear estimator of a finite-dimensional parameter vector
155:
Several experiments over both incentivized and hypothetical choices attest to the magnitude of this effect.
2327:
1179:
2902:
2451:
2439:
1717:
3288:
Collina, Natalie; Roth, Aaron; Shao, Han (2023). "Efficient Prior-Free
Mechanisms for No-Regret Agents".
3190:
Eldar, Y. C.; Merhav, Neri (2005). "Minimax MSE-Ratio
Estimation with Signal Covariance Uncertainties".
2474:
100:
479:
from its noisy linear measurement with known noise covariance structure. The loss of reconstruction of
3199:
3156:
3113:
2402:
and in particular a numerical solution can be efficiently calculated. Similar ideas can be used when
136:
68:
2907:
1239:
2826:"Consequences of regret aversion 2: Additional evidence for effects of feedback on decision making"
2399:
775:
238:
159:
124:
2699:
Bardakhchyan, V.; Allahverdyan, A. (2023). "Regret theory, Allais' paradox, and Savage's omelet".
2454:. They assume that the agent is driven by regret-aversion. In particular, the agent minimizes his
3289:
3270:
3242:
3215:
3172:
3129:
3059:
2987:
2936:
2872:
2775:
2756:
Filiz-Ozbay, E.; Ozbay, E. Y. (2007). "Auctions with anticipated regret: Theory and experiment".
2710:
2638:
2546:
2479:
500:
209:
185:
876:
673:
3260:
2979:
2971:
2928:
2920:
2596:
2423:
1082:{\displaystyle MSE=E\left(||{\hat {x}}-x||^{2}\right)=Tr(GC_{w}G^{*})+x^{*}(I-GH)^{*}(I-GH)x.}
112:
1892:
1547:
75:
component, and is central to how humans learn from experience and to the human psychology of
3252:
3207:
3164:
3121:
3086:
3051:
3022:
3014:
2963:
2912:
2864:
2837:
2806:
2767:
2720:
2679:
2669:
2630:
2573:
2538:
2459:
697:
615:
455:
What follows is an illustration of how the concept of regret can be used to design a linear
119:
2954:
Sevdalis, Nick; Harvey, Nigel (2007-08-01). "Biased
Forecasting of Postdecisional Affect".
742:
2484:
1863:
1518:
132:
31:
3203:
3160:
3117:
2795:"Consequences of regret aversion: Effects of expected feedback on risky decision making"
3317:
3005:
Engelbrecht-Wiggans, R. (1989). "The effect of regret on optimal bidding in auctions".
2405:
2381:
2061:
2041:
1580:
1156:
1136:
1116:
1095:
856:
836:
816:
722:
702:
653:
592:
572:
549:
529:
509:
482:
462:
201:
140:
84:
3328:
3274:
3063:
2967:
2916:
2876:
2494:
104:
76:
3219:
3176:
3133:
2779:
2738:
2642:
3090:
2991:
3234:
2940:
3256:
3055:
2504:
1850:{\displaystyle G(x)={\frac {1}{1+x^{*}H^{*}C_{w}^{-1}Hx}}xx^{*}H^{*}C_{w}^{-1}.}
88:
39:
237:
between outcomes, and thus requires interval or ratio measurements, as well as
2868:
2724:
2634:
2324:
The minimax regret approach here is to minimize the worst-case regret, i.e.,
214:
200:
regret approach is to minimize the worst-case regret, originally presented by
72:
17:
2975:
2924:
3211:
3168:
3125:
504:
456:
219:
27:
Measure of value difference between best possible decision and made decision
2983:
2932:
2855:
Somasundaram, J.; Diecidue, E. (2016). "Regret theory and risk attitudes".
2841:
2810:
3018:
2771:
2619:
Diecidue, E.; Somasundaram, J. (2017). "Regret Theory: A New
Foundation".
2577:
3239:
2020 IEEE 61st Annual
Symposium on Foundations of Computer Science (FOCS)
80:
2793:
Zeelenberg, M.; Beattie, J.; Van der Pligt, J.; de Vries, N. K. (1996).
2684:
2550:
2499:
197:
139:, risk averseness for logarithmic utilities and the ability to explain
3027:
2038:
This is the smallest MSE achievable with a linear estimate that knows
83:
that transcends regret from the emotional realm—often modeled as mere
48:
35:
3233:
Camara, Modibo K.; Hartline, Jason D.; Johnsen, Aleck (2020-11-01).
2542:
3294:
3247:
2715:
2564:
Bell, D. E. (1982). "Regret in decision making under uncertainty".
2028:{\displaystyle MSE^{o}={\frac {x^{*}x}{1+x^{*}H^{*}C_{w}^{-1}Hx}}.}
2674:
2657:
127:
in the traditional sense, although most satisfy a weaker version.
2398:. Although this problem appears difficult, it is an instance of
229:
This differs from the standard minimax approach in that it uses
3077:
Savage, L. J. (1951). "The Theory of
Statistical Decision".
739:
is a zero mean random vector with a known covariance matrix
3235:"Mechanisms for a No-Regret Agent: Beyond the Common Prior"
42:—should information about the best course of action arrive
1706:{\displaystyle G(x)=xx^{*}H^{*}(C_{w}+Hxx^{*}H^{*})^{-1}.}
503:(MSE). The unknown parameter vector is known to lie in an
2739:"Why do we anticipate regret before we make a decision?"
63:
proposes that when facing a decision, individuals might
46:
taking a fixed decision—the human emotional response of
2408:
2384:
2330:
2087:
2064:
2044:
1931:
1895:
1866:
1728:
1606:
1583:
1550:
1521:
1281:
1242:
1182:
1159:
1139:
1119:
1098:
908:
879:
859:
839:
819:
778:
745:
725:
705:
676:
656:
618:
595:
575:
552:
532:
512:
485:
465:
2830:
Organizational
Behavior and Human Decision Processes
2799:
Organizational Behavior and Human Decision Processes
91:
choice behavior that is modeled in decision theory.
2614:
2612:
2414:
2390:
2370:
2313:
2070:
2050:
2027:
1914:
1881:
1849:
1705:
1589:
1569:
1536:
1504:
1264:
1225:
1165:
1145:
1125:
1104:
1081:
891:
865:
845:
825:
802:
758:
731:
711:
688:
662:
639:
601:
581:
569:According to the assumptions, the observed vector
558:
538:
518:
491:
471:
546:, and the MSE of the linear estimator that knows
2332:
3079:Journal of the American Statistical Association
589:and the unknown deterministic parameter vector
899:matrix. The MSE of this estimator is given by
79:. Conscious anticipation of regret creates a
8:
171:Anticipated regret versus experienced regret
1597:and the derivative is equated to 0 getting
3293:
3246:
3026:
2906:
2714:
2683:
2673:
2458:. Based on this assumption, they develop
2407:
2383:
2335:
2329:
2290:
2285:
2275:
2265:
2244:
2237:
2207:
2182:
2166:
2156:
2131:
2086:
2063:
2043:
2004:
1999:
1989:
1979:
1958:
1951:
1942:
1930:
1906:
1894:
1865:
1835:
1830:
1820:
1810:
1785:
1780:
1770:
1760:
1744:
1727:
1691:
1681:
1671:
1652:
1639:
1629:
1605:
1582:
1561:
1549:
1520:
1463:
1429:
1413:
1394:
1355:
1350:
1344:
1332:
1321:
1320:
1314:
1309:
1292:
1280:
1256:
1245:
1244:
1241:
1196:
1185:
1184:
1181:
1158:
1138:
1118:
1097:
1049:
1024:
1008:
998:
968:
963:
957:
940:
939:
934:
929:
907:
878:
858:
838:
818:
780:
779:
777:
750:
744:
724:
704:
675:
655:
617:
594:
574:
551:
531:
511:
484:
464:
365:
252:
2521:
2462:that minimize the principal's regret.
2888:
2886:
2371:{\displaystyle \sup _{x\in E}R(x,G).}
1226:{\displaystyle {\hat {x}}^{o}=G(x)y.}
118:It incorporates a regret term in the
7:
2824:Zeelenberg, M.; Beattie, J. (1997).
2656:Bikhchandani, S.; Segal, U. (2011).
1092:Since the MSE depends explicitly on
205:used in a variety of areas such as:
103:simultaneously developed in 1982 by
2593:The Foundations of Expected Utility
2434:Camara, Hartline and Johnsen study
241:(ranking), as in standard minimax.
2702:Journal of Mathematical Psychology
2430:Regret in principal-agent problems
2422:is random with uncertainty in the
1577:is differentiated with respect to
451:Example: Linear estimation setting
25:
2595:. Theory & Decision Library.
2968:10.1111/j.1467-9280.2007.01958.x
2917:10.1111/j.0956-7976.2004.00681.x
3314:"TUTORIAL G05: Decision theory"
2857:Journal of Risk and Uncertainty
3091:10.1080/01621459.1951.10500768
2456:counterfactual internal regret
2362:
2350:
2228:
2213:
2204:
2188:
2172:
2146:
2103:
2091:
1876:
1870:
1738:
1732:
1688:
1645:
1616:
1610:
1531:
1525:
1493:
1487:
1481:
1469:
1460:
1453:
1447:
1435:
1419:
1410:
1403:
1387:
1381:
1375:
1351:
1345:
1326:
1315:
1310:
1265:{\displaystyle {\hat {x}}^{o}}
1250:
1214:
1208:
1190:
1070:
1055:
1046:
1030:
1014:
988:
964:
958:
945:
935:
930:
785:
1:
3044:Journal of Behavioral Finance
803:{\displaystyle {\hat {x}}=Gy}
609:are tied by the linear model
3257:10.1109/focs46700.2020.00033
2440:incomplete-information games
99:Regret theory is a model in
3056:10.1207/s15427579jpfm0702_5
2442:between two players called
71:with a powerful social and
3361:
3241:. IEEE. pp. 259–270.
3192:IEEE Trans. Signal Process
3149:IEEE Trans. Signal Process
3106:IEEE Trans. Signal Process
2622:Journal of Economic Theory
2869:10.1007/s11166-017-9268-9
2725:10.1016/j.jmp.2023.102807
2635:10.1016/j.jet.2017.08.006
1153:can explicitly depend on
892:{\displaystyle m\times n}
689:{\displaystyle n\times m}
2759:American Economic Review
2591:Fishburn, P. C. (1982).
2490:Info-gap decision theory
2436:principal-agent problems
813:be a linear estimate of
3212:10.1109/TSP.2005.843701
3169:10.1109/TSP.2004.828931
3126:10.1109/TSP.2004.831144
1915:{\displaystyle MSE^{o}}
1570:{\displaystyle MSE^{o}}
87:—into the realm of the
2842:10.1006/obhd.1997.2730
2811:10.1006/obhd.1996.0013
2452:reinforcement learning
2416:
2392:
2372:
2315:
2072:
2052:
2029:
1916:
1883:
1851:
1718:Matrix Inversion Lemma
1707:
1591:
1571:
1538:
1506:
1266:
1227:
1167:
1147:
1127:
1106:
1083:
893:
867:
847:
827:
804:
760:
733:
713:
690:
664:
641:
640:{\displaystyle y=Hx+w}
603:
583:
560:
540:
520:
499:is measured using the
493:
473:
3019:10.1287/mnsc.35.6.685
2956:Psychological Science
2895:Psychological Science
2772:10.1257/aer.97.4.1407
2662:Theoretical Economics
2578:10.1287/opre.30.5.961
2475:Regret-free mechanism
2417:
2393:
2373:
2316:
2073:
2053:
2030:
1917:
1884:
1852:
1708:
1592:
1572:
1539:
1507:
1267:
1228:
1168:
1148:
1128:
1107:
1084:
894:
868:
848:
828:
805:
761:
759:{\displaystyle C_{w}}
734:
714:
691:
665:
642:
604:
584:
561:
541:
521:
494:
474:
111:, David E. Bell, and
101:theoretical economics
2510:Wald's maximin model
2406:
2382:
2328:
2085:
2062:
2042:
1929:
1893:
1882:{\displaystyle G(x)}
1864:
1726:
1604:
1581:
1548:
1537:{\displaystyle G(x)}
1519:
1515:To find the optimal
1279:
1240:
1180:
1157:
1137:
1117:
1096:
906:
877:
857:
837:
817:
776:
743:
723:
703:
674:
654:
616:
593:
573:
550:
530:
510:
483:
463:
239:ordinal measurements
160:first price auctions
137:stochastic dominance
3204:2005ITSP...53.1335E
3161:2004ITSP...52.1931E
3118:2004ITSP...52.2177E
2658:"Transitive Regret"
2566:Operations Research
2400:convex optimization
2298:
2012:
1843:
1793:
1133:, i.e., the matrix
378:Interest rates fall
372:Interest rates rise
265:Interest rates fall
259:Interest rates rise
3007:Management Science
2480:Competitive regret
2412:
2388:
2368:
2346:
2311:
2281:
2068:
2048:
2025:
1995:
1912:
1879:
1860:Substituting this
1847:
1826:
1776:
1703:
1587:
1567:
1534:
1502:
1262:
1223:
1163:
1143:
1123:
1102:
1079:
889:
863:
843:
823:
800:
756:
729:
709:
686:
660:
637:
599:
579:
556:
536:
516:
501:mean-squared error
489:
469:
210:Hypothesis testing
186:disposition effect
61:anticipated regret
3340:Optimal decisions
3266:978-1-7281-9621-3
2424:covariance matrix
2415:{\displaystyle x}
2391:{\displaystyle x}
2331:
2306:
2071:{\displaystyle G}
2051:{\displaystyle x}
2020:
1801:
1590:{\displaystyle G}
1329:
1253:
1193:
1166:{\displaystyle x}
1146:{\displaystyle G}
1126:{\displaystyle x}
1105:{\displaystyle x}
948:
866:{\displaystyle G}
846:{\displaystyle y}
826:{\displaystyle x}
788:
732:{\displaystyle w}
712:{\displaystyle m}
663:{\displaystyle H}
602:{\displaystyle x}
582:{\displaystyle y}
559:{\displaystyle x}
539:{\displaystyle x}
519:{\displaystyle E}
492:{\displaystyle x}
472:{\displaystyle x}
444:
443:
353:
352:
113:Peter C. Fishburn
16:(Redirected from
3352:
3335:Choice modelling
3321:
3316:. Archived from
3300:
3299:
3297:
3285:
3279:
3278:
3250:
3230:
3224:
3223:
3198:(4): 1335–1347.
3187:
3181:
3180:
3155:(7): 1931–1946.
3144:
3138:
3137:
3112:(8): 2177–2188.
3101:
3095:
3094:
3074:
3068:
3067:
3039:
3033:
3032:
3030:
3002:
2996:
2995:
2951:
2945:
2944:
2910:
2890:
2881:
2880:
2852:
2846:
2845:
2821:
2815:
2814:
2790:
2784:
2783:
2766:(4): 1407–1418.
2753:
2747:
2746:
2743:The Decision Lab
2735:
2729:
2728:
2718:
2696:
2690:
2689:
2687:
2677:
2653:
2647:
2646:
2616:
2607:
2606:
2588:
2582:
2581:
2561:
2555:
2554:
2531:Economic Journal
2526:
2421:
2419:
2418:
2413:
2397:
2395:
2394:
2389:
2377:
2375:
2374:
2369:
2345:
2320:
2318:
2317:
2312:
2307:
2305:
2297:
2289:
2280:
2279:
2270:
2269:
2253:
2249:
2248:
2238:
2212:
2211:
2187:
2186:
2171:
2170:
2161:
2160:
2136:
2135:
2077:
2075:
2074:
2069:
2057:
2055:
2054:
2049:
2034:
2032:
2031:
2026:
2021:
2019:
2011:
2003:
1994:
1993:
1984:
1983:
1967:
1963:
1962:
1952:
1947:
1946:
1921:
1919:
1918:
1913:
1911:
1910:
1888:
1886:
1885:
1880:
1856:
1854:
1853:
1848:
1842:
1834:
1825:
1824:
1815:
1814:
1802:
1800:
1792:
1784:
1775:
1774:
1765:
1764:
1745:
1716:Then, using the
1712:
1710:
1709:
1704:
1699:
1698:
1686:
1685:
1676:
1675:
1657:
1656:
1644:
1643:
1634:
1633:
1596:
1594:
1593:
1588:
1576:
1574:
1573:
1568:
1566:
1565:
1543:
1541:
1540:
1535:
1511:
1509:
1508:
1503:
1468:
1467:
1434:
1433:
1418:
1417:
1399:
1398:
1365:
1361:
1360:
1359:
1354:
1348:
1337:
1336:
1331:
1330:
1322:
1318:
1313:
1297:
1296:
1271:
1269:
1268:
1263:
1261:
1260:
1255:
1254:
1246:
1232:
1230:
1229:
1224:
1201:
1200:
1195:
1194:
1186:
1172:
1170:
1169:
1164:
1152:
1150:
1149:
1144:
1132:
1130:
1129:
1124:
1111:
1109:
1108:
1103:
1088:
1086:
1085:
1080:
1054:
1053:
1029:
1028:
1013:
1012:
1003:
1002:
978:
974:
973:
972:
967:
961:
950:
949:
941:
938:
933:
898:
896:
895:
890:
872:
870:
869:
864:
852:
850:
849:
844:
832:
830:
829:
824:
809:
807:
806:
801:
790:
789:
781:
765:
763:
762:
757:
755:
754:
738:
736:
735:
730:
718:
716:
715:
710:
698:full column rank
695:
693:
692:
687:
669:
667:
666:
661:
646:
644:
643:
638:
608:
606:
605:
600:
588:
586:
585:
580:
565:
563:
562:
557:
545:
543:
542:
537:
525:
523:
522:
517:
498:
496:
495:
490:
478:
476:
475:
470:
366:
253:
188:, among others.
120:utility function
69:negative emotion
21:
3360:
3359:
3355:
3354:
3353:
3351:
3350:
3349:
3345:Decision theory
3325:
3324:
3320:on 3 July 2015.
3312:
3309:
3304:
3303:
3287:
3286:
3282:
3267:
3232:
3231:
3227:
3189:
3188:
3184:
3146:
3145:
3141:
3103:
3102:
3098:
3076:
3075:
3071:
3041:
3040:
3036:
3004:
3003:
2999:
2953:
2952:
2948:
2908:10.1.1.492.9980
2892:
2891:
2884:
2854:
2853:
2849:
2823:
2822:
2818:
2792:
2791:
2787:
2755:
2754:
2750:
2737:
2736:
2732:
2698:
2697:
2693:
2655:
2654:
2650:
2618:
2617:
2610:
2603:
2590:
2589:
2585:
2563:
2562:
2558:
2543:10.2307/2232669
2528:
2527:
2523:
2518:
2485:Decision theory
2471:
2432:
2404:
2403:
2380:
2379:
2326:
2325:
2271:
2261:
2254:
2240:
2239:
2203:
2178:
2162:
2152:
2127:
2083:
2082:
2060:
2059:
2040:
2039:
1985:
1975:
1968:
1954:
1953:
1938:
1927:
1926:
1902:
1891:
1890:
1862:
1861:
1816:
1806:
1766:
1756:
1749:
1724:
1723:
1687:
1677:
1667:
1648:
1635:
1625:
1602:
1601:
1579:
1578:
1557:
1546:
1545:
1517:
1516:
1459:
1425:
1409:
1390:
1349:
1319:
1308:
1304:
1288:
1277:
1276:
1243:
1238:
1237:
1183:
1178:
1177:
1155:
1154:
1135:
1134:
1115:
1114:
1094:
1093:
1045:
1020:
1004:
994:
962:
928:
924:
904:
903:
875:
874:
855:
854:
835:
834:
815:
814:
774:
773:
746:
741:
740:
721:
720:
701:
700:
672:
671:
652:
651:
614:
613:
591:
590:
571:
570:
548:
547:
528:
527:
508:
507:
481:
480:
461:
460:
453:
247:
194:
182:
173:
158:Experiments in
153:
133:hyperbolic sine
97:
57:regret aversion
32:decision theory
28:
23:
22:
15:
12:
11:
5:
3358:
3356:
3348:
3347:
3342:
3337:
3327:
3326:
3323:
3322:
3308:
3307:External links
3305:
3302:
3301:
3280:
3265:
3225:
3182:
3139:
3096:
3085:(253): 55–67.
3069:
3050:(2): 107–116.
3034:
3013:(6): 685–692.
2997:
2962:(8): 678–681.
2946:
2901:(5): 346–350.
2882:
2847:
2816:
2805:(2): 148–158.
2785:
2748:
2730:
2691:
2648:
2608:
2601:
2583:
2572:(5): 961–981.
2556:
2537:(4): 805–824.
2520:
2519:
2517:
2514:
2513:
2512:
2507:
2502:
2497:
2492:
2487:
2482:
2477:
2470:
2467:
2431:
2428:
2411:
2387:
2367:
2364:
2361:
2358:
2355:
2352:
2349:
2344:
2341:
2338:
2334:
2322:
2321:
2310:
2304:
2301:
2296:
2293:
2288:
2284:
2278:
2274:
2268:
2264:
2260:
2257:
2252:
2247:
2243:
2236:
2233:
2230:
2227:
2224:
2221:
2218:
2215:
2210:
2206:
2202:
2199:
2196:
2193:
2190:
2185:
2181:
2177:
2174:
2169:
2165:
2159:
2155:
2151:
2148:
2145:
2142:
2139:
2134:
2130:
2126:
2123:
2120:
2117:
2114:
2111:
2108:
2105:
2102:
2099:
2096:
2093:
2090:
2067:
2047:
2036:
2035:
2024:
2018:
2015:
2010:
2007:
2002:
1998:
1992:
1988:
1982:
1978:
1974:
1971:
1966:
1961:
1957:
1950:
1945:
1941:
1937:
1934:
1909:
1905:
1901:
1898:
1878:
1875:
1872:
1869:
1858:
1857:
1846:
1841:
1838:
1833:
1829:
1823:
1819:
1813:
1809:
1805:
1799:
1796:
1791:
1788:
1783:
1779:
1773:
1769:
1763:
1759:
1755:
1752:
1748:
1743:
1740:
1737:
1734:
1731:
1714:
1713:
1702:
1697:
1694:
1690:
1684:
1680:
1674:
1670:
1666:
1663:
1660:
1655:
1651:
1647:
1642:
1638:
1632:
1628:
1624:
1621:
1618:
1615:
1612:
1609:
1586:
1564:
1560:
1556:
1553:
1533:
1530:
1527:
1524:
1513:
1512:
1501:
1498:
1495:
1492:
1489:
1486:
1483:
1480:
1477:
1474:
1471:
1466:
1462:
1458:
1455:
1452:
1449:
1446:
1443:
1440:
1437:
1432:
1428:
1424:
1421:
1416:
1412:
1408:
1405:
1402:
1397:
1393:
1389:
1386:
1383:
1380:
1377:
1374:
1371:
1368:
1364:
1358:
1353:
1347:
1343:
1340:
1335:
1328:
1325:
1317:
1312:
1307:
1303:
1300:
1295:
1291:
1287:
1284:
1259:
1252:
1249:
1234:
1233:
1222:
1219:
1216:
1213:
1210:
1207:
1204:
1199:
1192:
1189:
1162:
1142:
1122:
1101:
1090:
1089:
1078:
1075:
1072:
1069:
1066:
1063:
1060:
1057:
1052:
1048:
1044:
1041:
1038:
1035:
1032:
1027:
1023:
1019:
1016:
1011:
1007:
1001:
997:
993:
990:
987:
984:
981:
977:
971:
966:
960:
956:
953:
947:
944:
937:
932:
927:
923:
920:
917:
914:
911:
888:
885:
882:
862:
842:
822:
811:
810:
799:
796:
793:
787:
784:
753:
749:
728:
708:
685:
682:
679:
659:
648:
647:
636:
633:
630:
627:
624:
621:
598:
578:
555:
535:
515:
488:
468:
452:
449:
442:
441:
436:
433:
430:
427:
423:
422:
417:
414:
411:
408:
404:
403:
398:
395:
392:
389:
385:
384:
379:
376:
373:
370:
351:
350:
345:
340:
335:
329:
328:
323:
320:
317:
314:
310:
309:
304:
301:
298:
295:
291:
290:
285:
282:
279:
276:
272:
271:
266:
263:
260:
257:
246:
243:
223:
222:
217:
212:
202:Leonard Savage
193:
192:Minimax regret
190:
181:
178:
172:
169:
152:
149:
141:Allais paradox
96:
93:
85:human behavior
55:The theory of
26:
24:
18:Minimax regret
14:
13:
10:
9:
6:
4:
3:
2:
3357:
3346:
3343:
3341:
3338:
3336:
3333:
3332:
3330:
3319:
3315:
3311:
3310:
3306:
3296:
3291:
3284:
3281:
3276:
3272:
3268:
3262:
3258:
3254:
3249:
3244:
3240:
3236:
3229:
3226:
3221:
3217:
3213:
3209:
3205:
3201:
3197:
3193:
3186:
3183:
3178:
3174:
3170:
3166:
3162:
3158:
3154:
3150:
3143:
3140:
3135:
3131:
3127:
3123:
3119:
3115:
3111:
3107:
3100:
3097:
3092:
3088:
3084:
3080:
3073:
3070:
3065:
3061:
3057:
3053:
3049:
3045:
3038:
3035:
3029:
3024:
3020:
3016:
3012:
3008:
3001:
2998:
2993:
2989:
2985:
2981:
2977:
2973:
2969:
2965:
2961:
2957:
2950:
2947:
2942:
2938:
2934:
2930:
2926:
2922:
2918:
2914:
2909:
2904:
2900:
2896:
2889:
2887:
2883:
2878:
2874:
2870:
2866:
2863:(2–3): 1–29.
2862:
2858:
2851:
2848:
2843:
2839:
2835:
2831:
2827:
2820:
2817:
2812:
2808:
2804:
2800:
2796:
2789:
2786:
2781:
2777:
2773:
2769:
2765:
2761:
2760:
2752:
2749:
2744:
2740:
2734:
2731:
2726:
2722:
2717:
2712:
2708:
2704:
2703:
2695:
2692:
2686:
2681:
2676:
2675:10.3982/TE738
2671:
2668:(1): 95–108.
2667:
2663:
2659:
2652:
2649:
2644:
2640:
2636:
2632:
2628:
2624:
2623:
2615:
2613:
2609:
2604:
2602:90-277-1420-7
2598:
2594:
2587:
2584:
2579:
2575:
2571:
2567:
2560:
2557:
2552:
2548:
2544:
2540:
2536:
2532:
2525:
2522:
2515:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2495:Loss function
2493:
2491:
2488:
2486:
2483:
2481:
2478:
2476:
2473:
2472:
2468:
2466:
2463:
2461:
2457:
2453:
2449:
2445:
2441:
2437:
2429:
2427:
2425:
2409:
2401:
2385:
2365:
2359:
2356:
2353:
2347:
2342:
2339:
2336:
2308:
2302:
2299:
2294:
2291:
2286:
2282:
2276:
2272:
2266:
2262:
2258:
2255:
2250:
2245:
2241:
2234:
2231:
2225:
2222:
2219:
2216:
2208:
2200:
2197:
2194:
2191:
2183:
2179:
2175:
2167:
2163:
2157:
2153:
2149:
2143:
2140:
2137:
2132:
2128:
2124:
2121:
2118:
2115:
2112:
2109:
2106:
2100:
2097:
2094:
2088:
2081:
2080:
2079:
2065:
2045:
2022:
2016:
2013:
2008:
2005:
2000:
1996:
1990:
1986:
1980:
1976:
1972:
1969:
1964:
1959:
1955:
1948:
1943:
1939:
1935:
1932:
1925:
1924:
1923:
1907:
1903:
1899:
1896:
1873:
1867:
1844:
1839:
1836:
1831:
1827:
1821:
1817:
1811:
1807:
1803:
1797:
1794:
1789:
1786:
1781:
1777:
1771:
1767:
1761:
1757:
1753:
1750:
1746:
1741:
1735:
1729:
1722:
1721:
1720:
1719:
1700:
1695:
1692:
1682:
1678:
1672:
1668:
1664:
1661:
1658:
1653:
1649:
1640:
1636:
1630:
1626:
1622:
1619:
1613:
1607:
1600:
1599:
1598:
1584:
1562:
1558:
1554:
1551:
1528:
1522:
1499:
1496:
1490:
1484:
1478:
1475:
1472:
1464:
1456:
1450:
1444:
1441:
1438:
1430:
1426:
1422:
1414:
1406:
1400:
1395:
1391:
1384:
1378:
1372:
1369:
1366:
1362:
1356:
1341:
1338:
1333:
1323:
1305:
1301:
1298:
1293:
1289:
1285:
1282:
1275:
1274:
1273:
1257:
1247:
1220:
1217:
1211:
1205:
1202:
1197:
1187:
1176:
1175:
1174:
1160:
1140:
1120:
1099:
1076:
1073:
1067:
1064:
1061:
1058:
1050:
1042:
1039:
1036:
1033:
1025:
1021:
1017:
1009:
1005:
999:
995:
991:
985:
982:
979:
975:
969:
954:
951:
942:
925:
921:
918:
915:
912:
909:
902:
901:
900:
886:
883:
880:
860:
840:
820:
797:
794:
791:
782:
772:
771:
770:
767:
751:
747:
726:
706:
699:
683:
680:
677:
657:
634:
631:
628:
625:
622:
619:
612:
611:
610:
596:
576:
567:
553:
533:
513:
506:
502:
486:
466:
458:
450:
448:
440:
437:
434:
431:
428:
426:Money market
425:
424:
421:
418:
415:
412:
409:
406:
405:
402:
399:
396:
393:
390:
387:
386:
383:
380:
377:
374:
371:
368:
367:
364:
361:
358:
349:
346:
344:
341:
339:
336:
334:
331:
330:
327:
324:
321:
318:
315:
313:Money market
312:
311:
308:
305:
302:
299:
296:
293:
292:
289:
286:
283:
280:
277:
274:
273:
270:
267:
264:
261:
258:
255:
254:
251:
244:
242:
240:
236:
232:
227:
221:
218:
216:
213:
211:
208:
207:
206:
203:
199:
191:
189:
187:
179:
177:
170:
168:
164:
161:
156:
150:
148:
144:
142:
138:
134:
128:
126:
121:
116:
114:
110:
109:Robert Sugden
106:
105:Graham Loomes
102:
94:
92:
90:
86:
82:
81:feedback loop
78:
77:risk aversion
74:
70:
66:
62:
58:
53:
51:
50:
45:
41:
37:
33:
19:
3318:the original
3283:
3238:
3228:
3195:
3191:
3185:
3152:
3148:
3142:
3109:
3105:
3099:
3082:
3078:
3072:
3047:
3043:
3037:
3010:
3006:
3000:
2959:
2955:
2949:
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382:Worst regret
381:
375:Static rates
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306:
287:
269:Worst return
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262:Static rates
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234:
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183:
180:Applications
174:
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145:
129:
125:transitivity
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29:
2505:Swap regret
1922:, one gets
1236:The MSE of
670:is a known
333:Best return
231:differences
95:Description
40:uncertainty
3329:Categories
3295:2311.07754
3248:2009.05518
3028:2142/28707
2716:2301.02447
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2516:References
2460:mechanisms
1889:back into
355:The crude
215:Prediction
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2976:0956-7976
2925:0956-7976
2903:CiteSeerX
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873:is some
853:, where
151:Evidence
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3200:Bibcode
3157:Bibcode
3114:Bibcode
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2500:Minimax
388:Stocks
357:maximin
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38:under
3290:arXiv
3271:S2CID
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