EPICENTER Working Paper Series
Andrés Perea: Order Independence in Dynamic Games, EPICENTER Working Paper No. 8 (2017)
In this paper we investigate the order independence of iterated reduction procedures in dynamic games. We distinguish between two types of order independence: with respect to strategies and with respect to outcomes. The first states that the specific order of elimination chosen should not affect the final set of strategy combinations, whereas the second states that it should not affect the final set of reachable outcomes in the game. We provide sufficient conditions for both types of order independence: monotonicity, and monotonicity on reachable histories, respectively.
We use these sufficient conditions to explore the order independence properties of various reduction procedures in dynamic games: the extensive-form rationalizability procedure (Pearce (1984), Battigalli (1997)), the backward dominance procedure (Perea (2014)) and Battigalli and Siniscalchi’s (1999) procedure for jointly rational belief systems (Reny (1993)). We finally exploit these results to prove that every outcome that is reachable under the extensive-form rationalizability procedure is also reachable under the backward dominance procedure.
Christian Bach, Andrés Perea: Incomplete Information and Generalized Iterated Strict Dominance, EPICENTER Working Paper No. 7 (2017)
In games with incomplete information, players face uncertainty about the opponents’ utility functions. We follow Harsanyi’s (1967-68) one-person perspective approach to modelling incomplete information. Moreover, our formal framework is kept as basic and parsimonious as possible, to render the theory of incomplete information accessible to a broad spectrum of potential applications. In particular, we formalize common belief in rationality and provide an algorithmic characterization of it in terms of decision problems, which gives rise to the non-equilibrium solution concept of generalized iterated strict dominance.
Christian Nauerz, Andrés Perea: Local Prior Expected Utility: a basis for utility representations under uncertainty, EPICENTER Working Paper No. 6 (2015)
Abstract: Abstract Models of decision-making under ambiguity are widely used in economics. One stream of such models results from weakening the independence axiom in Anscombe et al. (1963). We identify necessary assumptions on independence to represent the decision maker’s preferences such that he acts as if he maximizes expected utility with respect to a possibly local prior. We call the resulting representation Local Prior Expected Utility, and show that the prior used to evaluate a certain act can be obtained by computing the gradient of some appropriately defined utility mapping. The numbers in the gradient, moreover, can naturally be interpreted as the subjective likelihoods the decision maker assigns to the various states. Building on this result we provide a unified approach to the representation results of Maximin Expected Utility and Choquet Expected Utility and characterize the respective sets of priors.
Andrés Perea: Forward Induction Reasoning versus Equilibrium Reasoning EPICENTER Working Paper No. 5 (2015)
Abstract: In the literature on static and dynamic games, most rationalizability concepts have an equilibrium counterpart. In two-player games, the equilibrium counterpart is obtained by taking the associated rationalizability concept and adding the following correct beliefs assumption: (a) a player believes that the opponent is correct about his beliefs, and (b) a player believes that the opponent believes that he is correct about the opponent’s beliefs. This paper shows that there is no equilibrium counterpart to the forward induction concept of extensive-form rationalizability (Pearce (1984), Battigalli (1997)), epistemically characterized by common strong belief in rationality (Battigalli and Siniscalchi (2002)). The reason is that there are games where the epistemic conditions of common strong belief in rationality are logically inconsistent with the correct beliefs assumption. In fact, we show that this inconsistency holds for “most” dynamic games of interest.
Andrés Perea and Elias Tsakas: Local Reasoning in Dynamic Games EPICENTER Working Paper No.4 (2015)
Abstract: In this paper we introduce a novel framework for modeling the players’ reasoning in a dynamic game: at each history each active player reasons about her opponents’ rationality at certain histories only. As a result we obtain a generalized solution concept, called local common strong belief in rationality, and we characterize the strategy profiles that can be rationally played under our concept by means of a simple elimination procedure. Finally, we show that standard models of reasoning can be embedded as special cases on our framework. In particular, the forward induction concept of common strong belief in rationality (Battigalli and Siniscalchi, 2002) is a special case of our model with the players reasoning about all histories, whereas the backward induction concept of common belief in future rationality (Perea, 2014) is a special case of our model with the players reasoning about future histories only.
Andrés Perea and Arkadi Predtetchinski: An Epistemic Approach to Stochastic Games EPICENTER Working Paper No.3 (2014)
Abstract: In this paper we focus on stochastic games with finitely many states and actions. For this setting we study the epistemic concept of common belief in future rationality, which is based on the condition that players always believe that their opponents will choose rationally in the future. We distinguish two different versions of the concept — one for the discounted case with a fixed discount factor δ, and one for the case of uniform optimality, where optimality is required for “all discount factors close enough to 1″. We show that both versions of common belief in future rationality always yield non-empty predictions for every stochastic game. This is in sharp contrast with the non-existence of subgame perfect equilibrium in many stochastic games under the uniform optimality criterion. We also provide an epistemic characterization of subgame perfect equilibrium for 2-player stochastic games, showing that it is essentially equivalent to common belief in future rationality together with some “correct beliefs assumption”. We finally present a recursive procedure to compute the set of stationary strategies that can be chosen by certain simple types under common belief in future rationality.
Christian Nauerz: Understanding reasoning in games using utility proportional beliefs EPICENTER Working Paper No.2 (2014)
Abstract: Traditionally very little attention has been paid to the reasoning process that underlies a game theoretic solution concept. When modeling bounded rationality in one-shot games, however, the reasoning process can be a great source of insight. The reasoning process itself can provide testable assertions, which provide more insight than the fit to experimental data. Based on Bach and Perea’s (2014) concept of utility proportional beliefs, I analyze the players’ reasoning process and find three testable implications: (1) Players form an initial belief that is the basis for further reasoning. (2) Players reason by alternatingly considering their own and their opponent’s incentives. (3) Players perform only several rounds of deliberate reasoning.
Andrés Perea: When Do Types Induce the Same Belief Hierarchy? EPICENTER Working Paper No.1 (2014)
Abstract: Harsanyi (1967–1968) showed how infinite belief hierarchies can be encoded by means of type structures. Such encodings, however, are far from unique: Two different types — possibly from two different type structures — may generate exactly the same belief hierarchy. In this paper we present a finite recursive procedure, the Type Partitioning Procedure, which verifies whether two types, from two potentially different finite type structures, induce the same belief hierarchy or not. Important is that the procedure does not make explicit reference to belief hierarchies, but operates entirely within the “language” of type structures. In the second part of this paper we relate the procedure to the notion of type morphisms and hierarchy morphisms between type structures.