On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications

Games of incomplete information and myopic equilibria

We consider a finitely defined game where the payoff for each player at each terminal point of the game is not a fixed quantity but varies according to probability distributions on the terminal points induced by the strategies chosen. We prove that if these payoffs have an upper-semi- continuous and convex valued structure then the game has an equilibrium. For this purpose the concept of a myopic equilibrium is introduced, a con- cept that generalizes that of a Nash equilibrium and applies to the games we consider. We answer in the affirmative a question posed by A. Neyman: if the payoffs of an infinitely repeated game of incomplete information on one side are a convex combination of the undiscounted payoffs and payoffs from a finite number of initial stages, does the game have an equilibrium

Equilibrium existence and topology in some repeated games with incomplete information

This article proves the existence of an equilibrium in any infinitely repeated, un-discounted two-person game of incomplete information on one side where the uninformed player must base his behavior strategy on state-dependent information generated stochastically by the moves of the players and the informed player is capable of sending nonrevealing signals. This extends our earlier result stating that an equilibrium exists if additionally the information is standard. The proof depends on applying new topological properties of set-valued mappings. Given a set-valued mapping F on a compact convex set P subset of R-n, we give further conditions which imply that every point p(0) is an element of P belongs to the convex hull of a finite subset P-0 of the domain of F satisfying boolean AND(xis an element ofP0) F(x) not equal empty set