Minimax regret and strategic uncertainty

This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004)).Minimax regret, rationality, conjectures, price dispersion, auction

Minimax regret and strategic uncertainty

This paper introduces a new solution concept, a minimax regret equilibrium, which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents. We provide several applications of our concept. In particular, we consider pricesetting environments and show that optimal pricing policy follows a non-degenerate distribution. The induced price dispersion is consistent with experimental and empirical observations (Baye and Morgan (2004)).minimax regret; rationality; conjectures; price dispersion; auction

Mechanism Design With Ambiguous Communication Devices

This paper considers mechanism design problems in environments with ambiguity-sensitive individuals. The novel idea is to introduce ambiguity in mechanisms so as to exploit the ambiguity sensitivity of individuals. Deliberate engineering of ambiguity, through ambiguous mediated communication, can allow (partial) implementation of social choice functions that are not incentive compatible with respect to prior beliefs. We provide a complete characterization of social choice functions partially implementable by ambiguous mechanisms

Compromise, don't optimize:Generalizing perfect Bayesian equilibrium to allow for ambiguity

We introduce a solution concept for extensive-form games of incomplete information in which players can have multiple priors. Players’ choices are based on the notions of complaints and compromises. Complaints come from hypothetical assessors who have different priors and evaluate the choices of the players. Compromises are choices that aim to make these complaints small. The resulting solution concept is called perfect compromise equilibrium and generalizes perfect Bayesian equilibrium. We use this concept to provide insights into how ambiguity influences Cournot and Bertrand markets, public good provision, markets for lemons, job market signaling, bilateral trade with common value, and forecasting

One for all, all for one---von Neumann, Wald, Rawls, and Pareto

Applications of the maximin criterion extend beyond economics to statistics, computer science, politics, and operations research. However, the maximin criterion---be it von Neumann's, Wald's, or Rawls'---draws fierce criticism due to its extremely pessimistic stance. I propose a novel concept, dubbed the optimin criterion, which is based on (Pareto) optimizing the worst-case payoffs of tacit agreements. The optimin criterion generalizes and unifies results in various fields: It not only coincides with (i) Wald's statistical decision-making criterion when Nature is antagonistic, (ii) the core in cooperative games when the core is nonempty, though it exists even if the core is empty, but it also generalizes (iii) Nash equilibrium in $n$-person constant-sum games, (iv) stable matchings in matching models, and (v) competitive equilibrium in the Arrow-Debreu economy. Moreover, every Nash equilibrium satisfies the optimin criterion in an auxiliary game

Rationality, uncertainty aversion and equilibrium concepts in normal and extensive form games

This thesis contributes to a re-examination and extension of the equilibrium concept in normal and extensive form games. The equilibrium concept is a solution concept for games that is consistent with individual rationality and various assumptions about players' knowledge about the nature of their strategic interaction. The thesis argues that further consistency conditions can be imposed on a rational solution concept. By its very nature, a rational solution concept implicitly defines which strategies are non-rational. A rational player's beliefs about play by non-rational opponents should be consistent with this implicit definition of non-rational play. The thesis shows that equilibrium concepts that satisfy additional consistency requirements can be formulated in Choquet-expected utility theory, i.e. non-expected utility theory with non-additive or set-valued beliefs, together with an empirical assumption about players' attitude toward uncertainty. Chapter 1 introduces the background of this thesis. We present the conceptual problems in the foundations of game theory that motivate our approach. We then survey the decision-theoretic foundations of Choquet-expected utility theory and game-theoretic applications of Choquet-expected utility theory that are related to the present approach. Chapter 2 formulates this equilibrium concept for normal form games. This concept, called Choquet-Nash Equilibrium, is shown to be a generalization of Nash Equilibrium in normal form games. We establish an existence result for finite games, derive various properties of equilibria and establish robustness results for Nash equilibria. Chapter 3 extends the analysis to extensive games. We present the equivalent of subgame-perfect equilibrium, called perfect Choquet Equilibrium, for extensive games. Our main finding here is that perfect Choquet equilibrium does not generalize, but is qualitatively different from subgame-perfect equilibrium. Finally, in chapter 4 we examine the centipede game. It is shown that the plausible assumption of bounded uncertainty aversion leads to an 'interior' equilibrium of the centipede game

Acknowledgement Misspecification in Macroeconomic Theory

We explore methods for confronting model misspecification in macroeconomics. We construct dynamic equilibria in which private agents and policy makers recognize that models are approximations. We explore two generalizations of rational expectations equilibria. In one of these equilibria, decision makers use dynamic evolution equations that are imperfect statistical approximations, and in the other misspecification is impossible to detect even from infinite samples of time-series data. In the first of these equilibria, decision rules are tailored to be robust to the allowable statistical discrepancies. Using frequency domain methods, we show that robust decision makers treat model misspecification like time-series econometricians.

Decisions under Risk, Uncertainty and Ambiguity: Theory and Experiments

I combine theory, experiments and econometrics to undertake the task of disentangling the subtleties and implications of the distinction between risk, uncertainty and ambiguity. One general conclusion is that the elements of this methodological trilogy are not equally advanced. For example, new experimental tools must be developed to adequately test the predictions of theory. My dissertation is an example of this dynamic between theoretical and applied economics