Preliminary Results for Cooperative Extensions of the Bayesian Game

The descriptive theory of cooperative game with incomplete information developed to date is surveyed. The theory has the potential to provide game-theoretical foundations of economic analysis of the free societies in which organizations (coalitions) as corporations institute a non-market resource allocation mechanism while using the market resource allocation mechanism at the same time. The present-day corporations are interdependent, so the required game theory needs to model an environment in which the feasibility and implications of coordinated strategy choice within a coalition are influenced by the outsiders of strategy choice. The first part of the paper provides the key ingredients. After formulating the basic one-shot model, which synthesizes Harsanyi's Bayesian game and Aumann and Peleg's non-side-payment game (NTU game), and illustrating economic examples, two required conditions on an endogenously determined strategy are discussed: measurability with respect to an information structure, and Bayesian incentive compatibility. Several descriptive solution concepts that have been proposed to date are discussed. The second part addresses six issues studied in the literature: First, the existence of the descriptive solutions in the general setup. Second, explanation of information revelation, that is, a process through which private information turns into public information. Third, definitions of efficiency. Fourth, comparisons of several core concepts. Fifth, the existence results specific only to the Bayesian pure exchange economy, and revival of the core convergence theorem within the framework of the Bayesian pure exchange economy. Sixth, another view on coalition formation, specifically analyses of situations in which coalitional membership is anonymous.89 p