No abstract

Players who have a common interest are engaged in a game with incomplete information. Before playing they get differential signals that stochastically depend on the actual state of nature. These signal not only provide the players with partial information about the state of nature but also serve as a correlation means.Different information structures induce different outcomes. An information structure is better than another, with respect to a certain solution concept, if the highest solution payoff it induces is at least that induced by the latter structure. This paper fully characterizes when one information structure is better than another with respect to various solution concepts. The solution concepts we refer to differ from each other in the scope of communication allowed between the players. The characterizations are phrased in terms of maps that take signals of one structure and (stochastically) translate them to signals of another structure.

JEL classification: C70Real world players often increase their payoffs by voluntarily committing to play a fixed strategy, prior to the start of a strategic game. In fact, the players may further benefit from commitments that are conditional on the commitments of others. This paper proposes a model of conditional commitments that unifies earlier models while avoiding circularities that often arise in such models. A commitment folk theorem shows that the potential of voluntary conditional commitments is essentially unlimited. All feasible and individually rational payoffs of a two-person strategic game can be attained at the equilibria of one (universal) commitment game that uses simple commitment devices. The commitments are voluntary in the sense that each player maintains the option of playing the game without commitment, as originally defined.

We prove that, in dynamic programming framework, uniform convergence of vλ implies uniform convergence of vn and vice versa. Moreover, both have the same limit.