EXISTENCE OF EQUILIBRIUM FOR GAMES WITH UPPER SEMICONTINUOUS CORRESPONDENCES, UNDER UNCERTAINTY

In this paper we prove the existence of equilibrium pairs for the new model of a Bayesian free abstract economy which extends Kim and Lee's deterministic model of a free abstract economy (2006). Our existence theorems are proved for the case of upper semicontinuous correspondences. We also define a model of a general Bayesian abstract economy and introduce the new notion of equilibrium pair. We prove the existence of equilibrium pair and equilibrium for this type of abstract economy.

Equilibrium existence under generalized convexity

We introduce, in the first part, the notion of weakly convex pair of correspondences, we give its economic interpretation, we state a fixed point and a selection theorem. Then, by using a tehnique based on a continuous selection, we prove existence theorems of quilibrium for an abstract economy. In the second part, we define the weakly biconvex correspondences, we prove a selection theorem and we also demonstrate the existence of equilibrium for a generalized quasi-game (2003 Kim's model). In the last part of the paper, we give other applications in the game theory, finding equilibrium for abstract economies having correspondences with weakly convex graph. We show that the equilibrium exists without continuity assumptions.

A Bayesian Abstract Economy with a Measure Space of Agents

We define the model of an abstract economy with differential (asymmetric) information and a measure space of agents. We generalize N. C. Yannelis's result (2007), considering that each agent is characterised by a random preference correspondence instead of having a random utility function. We establish two different equilibrium existence results.