Related papers: Matrix Games, Mixed Strategies, and Statistical Me…

Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…

In classical game theory, optimal strategies are determined for games with complete information; this requires knowledge of the opponent's goals. We analyze games when a player is mistaken about their opponents goals. For definitiveness, we…

Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditional game theory studies the equilibria of simple games. But is traditional game theory applicable if the game is…

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely…

For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, one shows that the optimal strategy of the informed player can be computed through an auxiliary optimization problem over some…

This paper investigates mixed strategies in dynamic games with perfect information. We present an example to show that a player may obtain higher payoff by playing mixed strategy. By contrast, the main result of the paper shows that every…

When modeling robot interactions as Nash equilibrium problems, it is desirable to place coupled constraints which restrict these interactions to be safe and acceptable (for instance, to avoid collisions). Such games are continuous with…

We introduce the study of search games between a mobile Searcher and an immobile Hider in a new setting in which the Searcher has some potentially erroneous information, i.e., a prediction on the Hider's position. The objective is to…

Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…

Repeated games are difficult to analyze, especially when agents play mixed strategies. We study one-memory strategies in iterated prisoner's dilemma, then generalize the result to k-memory strategies in repeated games. Our result shows that…

Two-player zero-sum repeated games are well understood. Computing the value of such a game is straightforward. Additionally, if the payoffs are dependent on a random state of the game known to one, both, or neither of the players, the…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

A new solution concept for two-player zero-sum matrix games with multi-dimensional payoff is introduced. It is based on extensions of vector orders in K-dimensional spaces to order relations in their power sets, so-called set relations, and…

Given a skew-symmetric matrix, the corresponding two-player symmetric zero-sum game is defined as follows: one player, the row player, chooses a row and the other player, the column player, chooses a column. The payoff of the row player is…

In multi-agent settings, game theory is a natural framework for describing the strategic interactions of agents whose objectives depend upon one another's behavior. Trajectory games capture these complex effects by design. In competitive…

Strategy iteration is a technique frequently used for two-player games in order to determine the winner or compute payoffs, but to the best of our knowledge no general framework for strategy iteration has been considered. Inspired by…

The notions of symmetry and anonymity in strategic games have been formalized in different ways in the literature. We propose a combinatorial framework to analyze these notions, using group actions. Then, the same framework is used to…

We study the problem of finding equilibrium strategies in multi-agent games with incomplete payoff information, where the payoff matrices are only known to the players up to some bounded uncertainty sets. In such games, an ex-post…

We consider multiplayer stochastic games in which the payoff of each player is a bounded and Borel-measurable function of the infinite play. By using a generalization of the technique of Martin (1998) and Maitra and Sudderth (1998), we show…

Von Neumann's Min-Max Theorem guarantees that each player of a zero-sum matrix game has an optimal mixed strategy. This paper gives an elementary proof that each player has a near-optimal mixed strategy that chooses uniformly at random from…