A New Approach to Incomplete Information Games

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We consider two new approaches to incomplete information games.In the first approach, we propose the use of Bayesian potential games as models of informationally decentralized organizations in order to study the efficient use of information. Applying techniques in team decision problems by Radner (1962), we characterize Bayesian Nash equilibria in terms of Bayesian potentials and demonstrates by examples that Bayesian potentials are useful tools in studying the efficient use of information in organizations.In the second approach, we present a model of incomplete information games with sets of priors. Upon arrival of private information, each player updates by the Bayes rule each of priors in this set to construct the set of posteriors consistent with the arrived piece of information. Then the player uses a possibly proper subset of this set of posteriors to form beliefs about the opponents' strategic choices. And finally the player evaluates his actions by the most pessimistic posterio … More r beliefs a la Gilboa and Schmeidler (1989). So each player's preferences may exhibit non-linearity in probabilities which can be interpreted as the player's aversion to ambiguity or uncertainty. In this setup, we define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players' views on uncertainty about the environment affect the strategic outcomes.We also present a general framework to understand the possibility of a purely speculative trade under asymmetric information, where the decision making rule of each agent conforms to the multiple priors model : the agents are interested in the minimum of the conditional expected value of trade where the minimum is taken over the set of posteriors. In this framework, we derive a necessary and sufficient condition on the sets of posteriors, thus implicitly on the updating rules adopted by the agents, for non-existence of trade such that it is always common knowledge that every agent expects a positive gain. Less