Azrieli, Yaron and Teper, Roee (2009): Uncertainty aversion and equilibrium existence in games with incomplete information.
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Abstract
We consider games with incomplete information a la Harsanyi, where the payoff of a player depends on an unknown state of nature as well as on the profile of chosen actions. As opposed to the standard model, players' preferences over statecontingent utility vectors are represented by arbitrary functionals. The definitions of Nash and Bayes equilibria naturally extend to this generalized setting. We characterize equilibrium existence in terms of the preferences of the participating players. It turns out that, given continuity and monotonicity of the preferences, equilibrium exists in every game if and only if all players are averse to uncertainty (i.e., all the functionals are quasiconcave). We further show that if the functionals are either homogeneous or translation invariant then equilibrium existence is equivalent to concavity of the functionals.
Item Type:  MPRA Paper 

Original Title:  Uncertainty aversion and equilibrium existence in games with incomplete information 
Language:  English 
Keywords:  Games with incomplete information, equilibrium existence, uncertainty aversion, convex preferences. 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty > D81  Criteria for DecisionMaking under Risk and Uncertainty C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  17617 
Depositing User:  Yaron Azrieli 
Date Deposited:  01. Oct 2009 18:21 
Last Modified:  21. Feb 2013 02:30 
References:  [1] P. Artzner, F. Delbaen, J.M. Eber, D. Heath, Coherent measures of risk, Mathematical Finance 9 (1999), 203228. [2] R. J. Aumann, Correlated equilibrium as an expression of Bayesian rationality, Econometrica 55 (1987), 118. [3] S. Bade, Ambiguous act equilibria, (2008) Manuscript. [4] S. Bade, Electoral competition with uncertainty averse parties, (2008) Manuscript. [5] S. Bose, E. Ozdenoren, A. Pape, Optimal auctions with ambiguity, Theoretical Economics 1 (2006), 411438. [6] S. Cerreia, F. Maccheroni, M. Marinacci, L. Montrucchio, Uncertainty averse preferences, (2008) Manuscript. [7] V. Crawford, Equilibrium without independence, Journal of Economic Theorey, 50 (1990), 127154. [8] F. Delbaen, Coherent risk measures on general probability spaces, in: K. Sandmann et al. (Eds.), Advances in Finance and Stochastics (Essays in Honour of Dieter Sondermann), Springer, pp137. [9] D. Ellsberg, Risk, ambiguity, and the Savage axioms, Quarterly Journal of Economics 75 (1961), 643669. [10] L.G. Epstein, A definition of uncertainty aversion, Review of Economic Stusied 66 (1999), 579608. [11] L.G. Epstein, T. Wang, Beliefs about beliefs without probabilities, Econometrica 64 (1996), 1343 1373. [12] H. Fäollmer, A. Scheid, Convex measures of risk and trading constraints, Finance and Stochastics 6 (2002), 429447. [13] P. Ghirardato, M. Marinacci, Ambiguity made precise: A comparative foundation, Journal of Economic Theory 102 (2002), 251289. [14] I. Gilboa, D. Schmeidler, Maxmin expected utility with a nonunique prior, Journal of Mathemat ical Economics 18 (1989), 141153. [15] E. Hanany, P. Klibanoff, Updating ambiguity averse preferences, (2007) Manuscript. [16] J.C. Harsanyi, Games with incomplete information played by Bayesian players IIII, Management Science 14 (1967), 159182, 320334, 486502. [17] A. Kajii, T. Ui, Incomplete information games with multiple priors, Japanese Economic Review 56 (2005), 332351. [18] E. Karni, State{dependent utility, in: P. Anand, P. K. Pattanaik, C. Puppe (Eds.), Handbook of rational and social choice, Oxford University Press, Oxford, Forthcoming. [19] D. Levin, E. Ozdenoren, Auctions with a set of priors: uncertain number of bidders, Journal of Economic Theory 118 (2004), 229251. [20] K.C. Lo, Sealed bid auctions with uncertainty averse bidders, Economic Theory 12 (1998), 120. [21] F. Maccheroni, M. Marinacci, A. Rustichini, Ambiguity aversion, robustness, and the variational representation of preferences, Econometrica 74 (2006), 14471498. [22] A. MasCollel, The recoverability of consumers' preferences from market demand behavior, Econo metrica, 45 (1977), 14091430. [23] P.R. Milgrom, R.J. Weber, Distributional strategies in games with incomplete information, Math ematics of Operations Research 10 (1985), 619632. [24] S. Mukerji, J. M. Tallon, An overview of economic applications of David Schmeidler's models of decision making under uncertainty, in: I. Gilboa (Editor), Uncertainty in Economic Theory: A collection of essays in honor of David Schmeidler's 65 th birthday, Routledge Publishers, London, 2004, pp283302. [25] T. Rader, Theory of Microeconomics, Academic Press, New York, 1972. [26] A. Salo, M. Weber, Ambiguity aversion in firstprice sealedbid auctions, Journal of Risk and Uncertainty 11 (1995), 123137. [27] D. Schmeidler, Subjective probability and expected utility without additivity, Econometrica 57 (1989), 571587. [28] W.R. Shephard, Theory of Cost and Production Functions, Princton University Press, Princeton, NJ., 1970. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/17617 
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