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~institution:"ESRC Centre for Economic Learning and Social Evolution (ELSE), Department of Economics"
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Greenberg works in an extensive-form context
1
Kreps and Levine (1987)
1
Rubinstein and Wolinksy consider strategic-form games and general "signal fictions". We should make clear from the outset that
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a key issue is what sort of prior itiormation about payoffs should be considered. It is well known that predictions based on common certainty of payoffs are not robust to even a small amount of uncertainty. Following Fudenberg
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although this paper is motivated by the learning-theoretic approach to equilibrium in games
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and players observe only the outcomes in their own matches
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and that this difference corresponds to the distinction between SCE and RSCE.8 Papers by Rubinstein and Wolinksy [1994] and Greenberg [1994]
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are based on the idea that players form their forecasts of opponents play using prior information both about the opponents' payoffs and about the realized outcomes when the game is played. Both these papers
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as it is not in most experiments
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both in the real world and in the laboratory
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but it is consistent with an (approximate
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but may be mistaken about the way that opponents would respond to deviations. Intuitively
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but we have not checked the details
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by the last few rounds of the experiment the first movers had stopped contributing
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consider common certainty of rationality
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each player correctly forecasts the actions that opponents will take along the equilibrium path
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each time the game is played
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for example
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heterogeneous) SCE (Fudenberg and Levine [1996] 7 ). Thus these experiments provide evidence that information about other players' payoffs makes a difference
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in addition to almost common certainty of the payoffs
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in section 4 we show that it does correspond to assuming almost common certainty of payoffs and independence. To capture the idea of SCE
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incorporating restrictions on the priors into the steady-state learning model of Fudenberg and Levine [1993 b]
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independence is discussed fi.u-ther in section 6.) Combining these assumptions lead to rationalizable self-confirming equilibrium
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it (like Nash equilibrium) corresponds to a situation in which players have no prior information about the payoff fimctions of their opponents.4 This may be a good approximation of some real-world situations
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it is also the obvious way to model play in game theory experiments in which subjects are given no itiormation about opponents' payoffs. In other cases
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it seems plausible that players do have some prior information about their opponents' payoffs. The goal of this paper is to develop a more restrictive version of SCE that incorporates the effects of such prior information. In carrying out this program
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like ours
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namely that play corresponds to the steady state of a learning process in which the path is observed each time the game is played
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one for each player role in the game. The observations of different agents in the same player role may differ depending on the actions they take. If itiormation about the aggregate distribution of outcomes is not available to the subjects
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or "RSCE." If we think of equilibrium as describing the steady state of a random- matching process of the sort used in most game theory experiments
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players do not use the prior payoff iniiormation to restrict their beliefs about the play of opponents who have already been observed to deviate from expected play. Intuitively
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players observe only the actions played by their opponents (as opposed to the complete specification of the opponents' strategies) so that they need never receive evidence that their forecasts of off-path play are incorrect. 3 Because self- confirming equilibrium (henceforth "SCE") allows beliefs about off-path play to be completely arbitrary
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players were informed of the fimction determining opponents' monetary payoffs. Here
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ract: In a self-confirming equilibrium
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so that the signal refers only to the deviator's payoffs. We discuss the issue of independence in section 6.) We verify in section 3 that this intuition is correct and that this concept is robust
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subjects were not given any irdlormation about the payoffs of their opponents. In this treatment even in the later rounds of the experiment many first movers contributed to the public good. This is not consistent with RSCE
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that the payoffs are determined independently
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the assumption underlying self- confirming equilibrium
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then the appropriate notion of SCE is Fudenberg and Levine's (1993a) notion of a heterogeneous SCE.G The corresponding notion with prior payoff information is a heterogeneous RSCE. Perhaps the best motivation and illustration of our ideas is a pair of experiments by Prasnikar and Roth [1992] on the "best-shot" game. in which two players sequentially decide how much to contribute to a public good. The backwards-induction solution to this game is for player 1 to contribute nothing and player 2 to contribute 4
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then there are many agents
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Dekel, Eddie
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Fudenberg, Drew
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Levine, David K.
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ESRC Centre for Economic Learning and Social Evolution (ELSE), Department of Economics
Fernuniversität <Hagen> / Lehrgebiet Betriebswirtschaftslehre, insbesondere Operations Research
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China Economics and Management Academy, Central University of Finance and Economics (CUFE)
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Volkswirtschaftliche Fakultät, Ludwig-Maximilians-Universität München
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HAL
2
Université Paris-Dauphine (Paris IX)
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C.E.P.R. Discussion Papers
1
Departamento de Economía, Universidad Pablo de Olavide
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Département d'Économie / Department of Economics, Université d'Ottawa / University of Ottawa
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EconWPA
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Econometric Society
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Economics Department, Fordham University
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Economics Department, University of California-Davis
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Groupe de Recherche en Économie Théorique et Appliquée (GREThA), Université de Bordeaux
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Groupement de Recherches Économiques et Sociales (GRES)
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Hubert BONIN (GREThA UMR CNRS 5113 - Institut de Sciences Politique de Bordeaux)
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IESE Business School, Universidad de Navarra
1
Indian Statistical Institute
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Institut d'Économie Industrielle (IDEI), Toulouse School of Economics (TSE)
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Institut for Miljø og Erhvervsøkonomi, Syddansk Universitet
1
Institut für Volkswirtschaftslehre, Wirtschaftswissenschaftliche Fakutät
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Keleti Károly Gazdasági Kar, Óbudai Egyetem
1
OrdnungsPolitisches Portal (OPO)
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Research Institute for Economics and Business Administration, Kobe University
1
Society for Computational Economics - SCE
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Wirtschaftswissenschaftliche Fakultät, Friedrich-Schiller-Universität Jena
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Payoff Information and Self-Confirming Equilibrium
Dekel, Eddie
;
Fudenberg, Drew
;
Levine, David K.
-
ESRC Centre for Economic Learning and Social Evolution …
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