An Existence Result for Discontinuous Games

We introduce a notion of upper semicontinuity, weak upper semicontinuity, adn show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games.

Doubly Strong Equilibrium

We present a new concept for (generalized) strategic form games, called \emph{doubly strong equilibrium}, and give an existence result when the players have non-ordered and discontinuous preferences. Since a doubly strong equilibrium is a strong equilibrium in the sense of Aumann, we get the existence of strong equilibria in discontinuous games. The result has been obtained by using the \emph{quasi-Ky Fan minimax inequality}. Applications to exchange economies are given. We prove the existence of \emph{doubly strong allocations}, which maximize consumers' preferences on the set of feasible allocations. The doubly strong allocations belong to the core of the economy. When consumers' preferences are selfish, we have that the doubly strong allocations are fair in the sense of Schmeidler and Yaari. So, we get the existence of fair allocations in the setting of non-ordered and discontinuous preferences.

Doubly Strong Equilibrium

We present a new concept for (generalized) strategic form games, called \emph{doubly strong equilibrium}, and give an existence result when the players have non-ordered and discontinuous preferences. Since a doubly strong equilibrium is a strong equilibrium in the sense of Aumann, we get the existence of strong equilibria in discontinuous games. The result has been obtained by using the \emph{quasi-Ky Fan minimax inequality}. Applications to exchange economies are given. We prove the existence of \emph{doubly strong allocations}, which maximize consumers' preferences on the set of feasible allocations. The doubly strong allocations belong to the core of the economy. When consumers' preferences are selfish, we have that the doubly strong allocations are fair in the sense of Schmeidler and Yaari. So, we get the existence of fair allocations in the setting of non-ordered and discontinuous preferences.

A note on a Tarski type fixed-point theorem

AbstractIn this paper we propose a basic fixed-point theorem for correspondences inspired by Tarski's intersection point theorem. This result furnishes an efficient tool to prove the existence of pure strategy Nash equilibria for two player games with possibly discontinuous payoffs functions defined on compact real intervals

Existence of Nash Equilibrium in games with a measure space of players and discontinuous payoff functions

Balder's (2002) model of games with a measure space of players is integrated with the line of research on finite-player games with discontinuous payoff functions which follows Reny (1999). Specifically, we extend the notion of continuous security, introduced by McLennan, Monteiro and Tourky (2011) and Barelli and Meneghel (2012) for finite-players games, to games with a measure space of players and establish the existence of pure strategy Nash equilibrium for such games. A specification of our main existence result is provided which is ready to fit the needs of applications. As an illustration, we consider several optimal income tax problems in the spirit of Mirrlees (1971) and use our game-theoretic result to show the existence of an optimal income tax in each of these problems

Existence of Nash Equilibrium in games with a measure space of players and discontinuous payoff functions

Balder's (2002) model of games with a measure space of players is integrated with the line of research on finite-player games with discontinuous payoff functions which follows Reny (1999). Specifically, we extend the notion of continuous security, introduced by McLennan, Monteiro and Tourky (2011) and Barelli and Meneghel (2012) for finite-players games, to games with a measure space of players and establish the existence of pure strategy Nash equilibrium for such games. A specification of our main existence result is provided which is ready to fit the needs of applications. As an illustration, we consider several optimal income tax problems in the spirit of Mirrlees (1971) and use our game-theoretic result to show the existence of an optimal income tax in each of these problems

Existence of Nash Equilibrium in Discontinuous Games

This paper offers an equilibrium existence theorem in discontinuous games. We introduce a new notion of continuity, called quasi-weak transfer continuity that guarantees the existence of pure strategy Nash equilibrium in compact and quasiconcave games. We also consider possible extensions and improvements of the main result. Our conditions are simple and easy to verify. We present applications to show that our conditions allow for economically meaningful payoff discontinuities

Existence of Nash Equilibrium in Discontinuous Games

This paper offers an equilibrium existence theorem in discontinuous games. We introduce a new notion of continuity, called quasi-weak transfer continuity that guarantees the existence of pure strategy Nash equilibrium in compact and quasiconcave games. We also consider possible extensions and improvements of the main result. Our conditions are simple and easy to verify. We present applications to show that our conditions allow for economically meaningful payoff discontinuities

Communication and equilibrium in discontinuous games of incomplete information

This paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs. Typically, the discontinuities arise from indeterminacies (ties) in the underlying problem. The point of view taken here is that the tie-breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model. A solution is therefore a tie-breaking rule together with strategies satisfying the usual best-response criterion. When information is incomplete, solutions need not exist; that is, there may be no tie-breaking rule that is compatible with the existence of strategy profiles satisfying the usual best-response criteria. It is shown that the introduction of incentive compatible communication (cheap talk) restores existence

Existence of equilibria in countable games: an algebraic approach

Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Wald's pick-the-larger-integer game. Several authors have provided conditions for the existence of equilibria in infinite games. These conditions are typically of topological nature and are rarely applicable to countable games. Here we establish an existence result for the equilibrium of countable games when the strategy sets are a countable group and the payoffs are functions of the group operation. In order to obtain the existence of equilibria, finitely additive mixed strategies have to be allowed. This creates a problem of selection of a product measure of mixed strategies. We propose a family of such selections and prove existence of an equilibrium that does not depend on the selection. As a byproduct we show that if finitely additive mixed strategies are allowed, then Wald's game admits an equilibrium. We also prove existence of equilibria for nontrivial extensions of matching-pennies and rock-scissors-paper. Finally we extend the main results to uncountable games