Solution concepts for games with ambiguous payoffs

Abstract

I consider games with ambiguous payoffs played by non-Expected Utility decision makers. Three equilibrium solutions are studied. Nash equilibrium in which equilibrium mixed strategies must be best responses, Crawford equilibrium in beliefs and pure equilibrium in beliefs in which equilibrium strategies are mixtures of best responses, with the latter restricting best responses to pure actions. I study the interactions between ambiguity preferences on one side and equilibrium properties on the other. I show how the equilibrium concepts differ, computing necessary and sufficient conditions for existence and equivalence. I also show how these solution concepts fare against two fundamental principles of Nash equilibrium in standard games: the principle of indifference and the reduction principle. Given both are central to the computation of Nash equilibrium in games with Expected Utility players, their failure indicates how relaxing the Expected Utility hypothesis may disrupt standard game theoretic results such as the characterization of equilibria in two-player games. KeywordsAmbiguity • Equilibrium in beliefs • Game theory • Nash equilibrium • Non-expected utility B Dorian Beauchêne

Project Net Present Value estimation under uncertainty

“…There are numerous decision rules devoted to decision making under uncertainty (see, for example, Basili 2006;Basili et al 2008;Basili and Chateauneuf 2011;Beauchene 2015;Chassein and Goerigk 2016;Ellsberg 2001;Etner et al 2012;Gaspars-Wieloch 2012, 2013, 2014a, b, c, d, 2015a, b, c, d, e, 2016a, b, 2017aGhirardato et al 2004;Gilboa 2009;Gilboa and Schmeidler 1989;Halpern and Leung 2014;Hayashi 2008;Hurwicz 1952;Ioan and Ioan 2011;Marinacci 2002;Nakamura1996;Perez et al 2015;Piasecki 1990;Savage 1961;Schmeidler 1986;Tversky and Kahneman 1992;Wald 1950), but some of them are based on the probability calculus or do notconsider the DM's nature-thus, they cannot be applied to the aforementioned problem.…”

Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

“…And Bade studies a game‐theoretic framework with the effect of ambiguity aversion on equilibrium outcomes. Moreover, some researchers also discuss the concept of solution to a game with ambiguous payoffs. Although all of these models concern the effect of ambiguity aversion in games, they just focus on part of our payoff types, such as ambiguity lottery or interval payoff.…”

Ambiguous games without a state space and full rationality

“…characterize equilibrium existence in terms of the preferences of the players; the evidence from this paper is s that equilibria exist if and only if agents are ambiguity averse, as ambiguity aversion is deeply related to some form of convexity of preferences 5. There is no evidence in the literature showing that this kind of ambiguity can be properly reconducted to incomplete information gamesà la Harsanyi (that is, with a state space) under multiple priors which, in turn, must be generalized in order to encompass this specific game theoretical issue 6. De Marco and Romaniello (2012) presents the general model, an existence theorem and many motivating examples.…”

“…In previous papers, De Marco and Romaniello (2012, 2013, 2015a introduced and studied the (so called) model of game under ambiguous belief correspondences 6 which provides a rather general tool to study ambiguity in games. The key point of these papers is that, for every player, ambiguity is directly represented by a belief correspondence which maps the set of strategy profiles into the set of all subsets of probability distributions over the outcomes of the game.…”