We study the existence of different notions of value in two-person zero-sum repeated games where the state evolves and players receive signals. We provide some examples showing that the limsup value (and the uniform value) may not exist in general. Then we show the existence of the value for any Borel payoff function if the players observe a public signal including the actions played. We also p...

Modern game theory was born in 1928, when John von Neumann published his Minimax Theorem. Inter alia, this theorem ascribes to all two-person zero-sum games a value—what rational players should expect to get. Almost 80 years later, strategic game theory has not gotten beyond that initial point, insofar as the basic question of value is concerned. To be sure, we do have equilibrium theories: the...

Recently, the list of solved two-person zero-sum games with perfect information has increased. The state of current knowledge is that many games are a win for the ®rst player, some games are draws, and only a few games are a win for the second player. For games with three outcomes (won, drawn, lost) a game is commonly de®ned as fair if the theoretical value of the game is drawn. For these games...

We show that in zero-sum polymatrix games, a multiplayer generalization of two-person zerosum games, Nash equilibria can be found efficiently with linear programming. We also show that the set of coarse correlated equilibria collapses to the set of Nash equilibria. In contrast, other important properties of two-person zero-sum games are not preserved: Nash equilibrium payoffs need not be unique...

This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustr...

The central innovation introduced by game theory is its strategic dimension. A player’s environment is not neutral, and she expects that other players will try to out-guess her plans. Reasoning about such expectations and strategizing one’s own response accordingly constitutes the main logical challenge of game theory. Evaluation games have been long used by logicians to define the semantics of...