Rationalizability in General Games

Master'sMASTER OF SOCIAL SCIENCE

Iterated elimination procedures

We study the existence and uniqueness (i.e.,order independence) of any arbitrary form of iterated elimination procedures in an abstract environment. By allowing for a transfinite elimination, we show a general existence of the iterated elimination procedure. Inspired by the seminal work of Gilboa, Kalai and Zemel (1990), we identify a fairly weak suffcient condition of Monotonicity* for the order independence of iterated elimination procedure. Monotonicity* requires a monotonicity property along any elimination path. Our approach is applicable to different forms of iterated elimination procedures used in (in)finite games, for example, iterated elimination of strictly dominated strategies, iterated elimination of weakly dominated strategies, rationalizability, and soon. We introduce a notion of CD* games, which incorporates Jackson's (1992) idea of "boundedness", and show the iterated elimination procedure is order independent in the class of CD* games. In finite games, we also formulate and show an "outcome" order-independence result suitable for Marx and Swinkels's (1997) notion of nice weak dominance

THREE ESSAYS ON GAME THEORY

Ph.DDOCTOR OF PHILOSOPH

Strategic interdependence, hypothetical bargaining, and mutual advantage in non-cooperative games

One of the conceptual limitations of the orthodox game theory is its inability to offer definitive theoretical predictions concerning the outcomes of noncooperative games with multiple rationalizable outcomes. This prompted the emergence of goal-directed theories of reasoning – the team reasoning theory and the theory of hypothetical bargaining. Both theories suggest that people resolve non-cooperative games by using a reasoning algorithm which allows them to identify mutually advantageous solutions of non-cooperative games. The primary aim of this thesis is to enrich the current debate on goaldirected reasoning theories by studying the extent to which the principles of the bargaining theory can be used to formally characterize the concept of mutual advantage in a way which is compatible with some of the conceptually compelling principles of orthodox game theory, such as individual rationality, incentive compatibility, and non-comparability of decision-makers’ personal payoffs. I discuss two formal characterizations of the concept of mutual advantage derived from the aforementioned goal-directed reasoning theories: A measure of mutual advantage developed in collaboration with Jurgis Karpus, which is broadly in line with the notion of mutual advantage suggested by Sugden (2011, 2015), and the benefit-equilibrating bargaining solution function, which is broadly in line with the principles underlying Conley and Wilkie’s (2012) solution for Pareto optimal point selection problems with finite choice sets. I discuss the formal properties of each solution, as well as its theoretical predictions in a number of games. I also explore each solution concept’s compatibility with orthodox game theory. I also discuss the limitations of the aforementioned goal-directed reasoning theories. I argue that each theory offers a compelling explanation of how a certain type of decision-maker identifies the mutually advantageous solutions of non-cooperative games, but neither of them offers a definitive answer to the question of how people coordinate their actions in non-cooperative social interactions

(Bayesian) Coalitional Rationalizability *

Abstract We extend Ambrus's [QJE, 2006] concept of "coalitional rationalizability (c-rationalizability)" to situations where, in seeking mutual beneficial interests, players in groups (i) make use of Bayes rule in expectation calculations and (ii) contemplate various deviations -i.e. the validity of deviation is checked against any arbitrary sets of strategies, not only against restricted subsets of strategies. In this paper we offer an alternative notion of c-rationalizability suitable for such complicated interactions. More specifically, following Bernheim's [Econometrica 52(1984), 1007-1028] and Pearce's [Econometrica 52(1984), 1029-1051] approach, we define c-rationalizability by the terminology "coalitional rationalizable set (CRS)". Roughly speaking, a CRS is a product set of pure strategies from which no group of player(s) would like to deviate. We show that this notion of c-rationalizability possesses nice properties similar to those of conventional rationalizability. We also provide its epistemic foundation. JEL Classification: C70, C72, D8

Bayesian coalitional rationalizability

In this paper we extend Ambrus's [A. Ambrus, Coalitional rationalizability, Quart. J. Econ. 121 (2006) 903-929] concept of "coalitional rationalizability (c-rationalizability)" to situations where, in seeking mutually beneficial interests, players in groups (i) make use of Bayes' rule in expectation calculations and (ii) contemplate various deviations, i.e., the validity of deviation is checked against any arbitrary sets of strategies, and not just only against restricted subsets of strategies. We offer an alternative notion of Bayesian c-rationalizability suitable for such complex social interactions. We show that Bayesian c-rationalizability possesses nice properties similar to those of conventional rationalizability.Bayesian c-rationalizability Iterated c-dominance

Bayesian coalitional rationalizability

10.1016/j.jet.2008.03.004Journal of Economic Theory1441248-263JECT