Every two person repeated game of symmetric incomplete information, in which the signals sent at each stage to both players are identical and generated by a state and moves dependent probability distribution on a given finite alphabet, has an equilibrium payoff.

We examine incentive-compatible mechanisms for fair financing and efficient selection of a public budget (or public good). A mechanism selects the level of the public budget and imposes taxes on individuals. Individuals’ preferences are quasilinear. Fairness is expressed as weak monotonicity...

One way to express bounded rationality of a player in a game theoretic models is by specifying a set of feasible strategies for that player. In dynamic game models with finite automata and bounded recall strategies, for example, feasibility of strategies is determined via certain complexity...

This chapter studies the theory of value of games with infinitely many players.Games with infinitely many players are models of interactions with many players. Often most of the players are individually insignificant, and are effective in the game only via coalitions. At the same time there may...

We prove here the existence of a value (of norm 1) on the spaces 'NA and even 'AN, the closure in the variation distance of the linear space spanned by all games f o \mu, where \mu is a non-atomic, non-negative finitely additive measure of mass 1 and f a real-valued function on [0, 1] which...

In a repeated game with perfect monitoring, correlation among a group of players may evolve in the common course of play (online correlation). Such a correlation may be concealed from a boundedly rational player. The feasibility of such “online concealed correlation” is quantified by the...

We prove that games with absorbing states with compact action sets have a value.

Every simple monotonic game in bv'NA is a weighted majority game. Every game v \in bv'NA has a representation v=u+\sum_{i=1}^{\infty}f_i o \mu_i where u \in pNA, \mu_i \in NA^1 and f_i is a sequence of bv' functions with \sum_{i=1}^{\infty}||f_i||<\infty. Moreover, the representation is unique if we require f_i to be singular and that for every i <> j, \mu_i <>\mu_j.

The asymptotic value, introduced by Kannai in 1966, is an asymptotic approach to the notion of the Shapley value for games with infinitely many players. A vector measure game is a game v where the worth v(S) of a coalition S is a function f of ?(S) where ? is a vector measure. Special classes of...

The existence of a value and optimal strategies is proved for the class of twoperson repeated games where the state follows a Markov chain independently of players’ actions and at the beginning of each stage only player one is informed about the state. The results apply to the case of standard...