Related papers: O'Neill's Theorem for Games

This short note establishes positionality of mean-payoff games over infinite game graphs by constructing a well-founded monotone universal graph.

We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using…

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…

A Nash equilibrium has become important solution concept for analyzing the decision making in Game theory. In this paper, we consider the problem of computing Nash equilibria of a subclass of generic finite normal form games. We define…

In this report, some properties of the set of Nash equilibria (NEs) of $2 \times 2$ zero-sum games are reviewed. In particular, the cardinality of the set of NEs is given in terms of the entries of the payoff matrix. Moreover, closed-form…

We introduce the class of pay or play games, which captures scenarios in which each decision maker is faced with a choice between two actions: one with a fixed payoff and an- other with a payoff dependent on others' selected actions. This…

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…

We study the performance of Fictitious Play, when used as a heuristic for finding an approximate Nash equilibrium of a 2-player game. We exhibit a class of 2-player games having payoffs in the range [0,1] that show that Fictitious Play…

We analyse the strategy equilibrium of dilemma games considering a payoff matrix affected by small and random perturbations on the off-diagonal. Notably, a recent work [1] reported that, while cooperation is sustained by perturbations…

We establish the existence and uniqueness of distributed equilibria to possibly nonsymmetric $N$ player differential games with interactions through controls under displacement semimonotonicity assumptions. Surprisingly, the nonseparable…

The game in which acts of participants don't have an adequate description in terms of Boolean logic and classical theory of probabilities is considered. The model of the game interaction is constructed on the basis of a non-distributive…

A new concept of an equilibrium in games is introduced that solves an open question posed by A. Neyman.

This paper is concerned with a Stackelberg stochastic differential game on a finite horizon in feedback information pattern. A system of parabolic partial differential equations is obtained at the level of Hamiltonian to give the…

In this paper, we prove the existence of the equilibrium in choice for games in choice form. These games have recently been introduced by A. Stefanescu, M. Ferrara and M. V. Stefanescu. Our results link the recent research to the older…

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…

Cooperation through repetition is an important theme in game theory. In this regard, various celebrated ``folk theorems'' have been proposed for repeated games in increasingly more complex environments. There has, however, been insufficient…

We study multi-player games with perfect information and general payoff function, where the set of stages is the set of non-positive integers $\{\ldots,-2,-1,0\}$. We define two related equilibrium concepts: one considering only deviations…

In this paper, we introduce the concept of infinitely split Nash equilibrium in repeated games in which the profile sets are chain-complete posets. Then by using a fixed point theorem on posets in [8], we prove an existence theorem. As an…

Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…