This project extends the investigators' research on the solution theory of cooperative games in which binding agreements can be implemented with a large number of players and nontransferable utility games. It consists of four parts. Part I deals with the Harsanyi non-transferable utility value for which payoffs to players are both egalitarian and utilitarian. It studies the relation between these values and Walrasian equilibria in perfectly competitive economies. Part II investigates the non- cooperative foundations for cooperative solutions. In a non- cooperative setup, binding agreements are not possible. But this does not rule out cooperation among the participants if it is in the interest of everyone to follow the agreement rather than defect. Since non-cooperative behavior is the more basic and primitive concept and cooperation could arise only if it is supported by non-cooperative behavior, it is important to understand and look for non-cooperative foundations to cooperative solutions. Part III deals with models of incomplete information and cheap talk - communication that is "free." The research seeks to characterize what is achievable by the simplest form of communication that requires no external devices such as binding agreements and mediators. Part IV proposes to study several topics in incomplete markets theory: the existence problem of equilibria when there is a continuum of states, the determinacy problem when there are too many equilibria and the efficiency problem of an incomplete market equilibrium. This project covers a wide spectrum of important issues in equilibrium analysis. These analyses will lead to a much better understanding of various solution concepts, and of the interplay of communication and strategic interaction among agents. It will provide a strong foundation from which many important questions concerning cooperative and non-cooperative behavior can be addressed.
