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RATIONAL BELIEF HIERARCHIES
"... We consider agents whose language can only express probabilistic beliefs that attach a rational number to every event. We call these probability measures rational. We introduce the notion of a rational belief hierarchy, where the first order beliefs are described by a rational measure over the fund ..."
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We consider agents whose language can only express probabilistic beliefs that attach a rational number to every event. We call these probability measures rational. We introduce the notion of a rational belief hierarchy, where the first order beliefs are described by a rational measure over the fundamental space of uncertainty, the second order beliefs are described by a rational measure over the product of the fundamental space of uncertainty and the opponent’s first order rational beliefs, and so on. Then, we derive the corresponding (rational) type space model, thus providing a Bayesian representation of rational belief hierarchies. Our first main result shows that this typebased representation violates our intuitive idea of an agent whose language expresses only rational beliefs, in that there are rational types associated with nonrational beliefs over the canonical state space. We rule out these types by focusing on the rational types that satisfy common certainty in the event that everybody holds rational beliefs over the canonical state space. We call these types universally rational and show that they are characterized by a bounded rationality condition which restricts the agents’ computational capacity. Moreover, the universally rational types form a dense subset of the universal type space. Finally, we show that the strategies rationally played under common universally rational belief in rationality generically coincide with those satisfying correlated rationalizability.
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 twoplayer games, the equilibrium counterpart is obtained by taking the associated rationalizability concept and adding the following correct beliefs assumption: (a) a player ..."
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Abstract In the literature on static and dynamic games, most rationalizability concepts have an equilibrium counterpart. In twoplayer 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 extensiveform rationalizability (Pearce (1984), Battigalli (1997)), epistemically characterized by common strong belief in rationality (Battigalli and Siniscalchi JEL Classi…cation: C72 I thank Christian Bach for some very valuable comments on this paper.
A revealedpreference theory of strategic counterfactuals
, 2011
"... Preliminary: comments welcome The analysis of extensiveform games involves assumptions concerning players ’ beliefs at histories off the predicted path of play. However, the revealedpreference interpretation of such assumptions is unclear: how does one elicit probabilities conditional upon events ..."
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Preliminary: comments welcome The analysis of extensiveform games involves assumptions concerning players ’ beliefs at histories off the predicted path of play. However, the revealedpreference interpretation of such assumptions is unclear: how does one elicit probabilities conditional upon events that have zero exante probability? This paper addresses this issue by proposing and axiomatizing a novel choice criterion for an individual who faces a general dynamic decision problem. The individual’s preferences are characterized by a Bernoulli utility function and a conditional probability system Myerson (1986a). At any decision point, preferences are determined by conditional expected payoffs at the current node, as well as at all subsequent nodes. Thus, prior preferences contain enough information to identify all conditional beliefs. Furthermore, preferences are dynamically consistent, so prior preferences also determine behavior at subsequent decision nodes, including those that have zero exante probability. In particular, the proposed criterion is consistent with, and indeed inspired by the gametheoretic notion of sequential rationality.