Related papers: Simple Strategies for Large Zero-Sum Games with Ap…

For matrix games we study how small nonzero probability must be used in optimal strategies. We show that for nxn win-lose-draw games (i.e. (-1,0,1) matrix games) nonzero probabilities smaller than n^{-O(n)} are never needed. We also…

The equivalence between von Neumann's Minimax Theorem for zero-sum games and the LP Duality Theorem connects cornerstone problems of the two fields of game theory and optimization, respectively, and has been the subject of intense scrutiny…

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…

We define a class of zero-sum games with combinatorial structure, where the best response problem of one player is to maximize a submodular function. For example, this class includes security games played on networks, as well as the problem…

Strategic-form min-max game theory examines the existence, multiplicity, selection of equilibria, and the worst-case computational complexity under perfect rationality. However, in many applications, games are drawn from an ensemble, and…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

A seminal result in game theory is von Neumann's minmax theorem, which states that zero-sum games admit an essentially unique equilibrium solution. Classical learning results build on this theorem to show that online no-regret dynamics…

Many emerging applications - such as adversarial training, AI alignment, and robust optimization - can be framed as zero-sum games between neural nets, with von Neumann-Nash equilibria (NE) capturing the desirable system behavior. While…

We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which Player I has n pure strategies and Player II has an arbitrary number of pure strategies. We assume that for any given…

We consider the problem of maximizing the minimum (weighted) value of all components of a vector over a polymatroid. This is a special case of the lexicographically optimal base problem introduced and solved by Fujishige. We give an…

Extensive-form games with imperfect recall are an important game-theoretic model that allows a compact representation of strategies in dynamic strategic interactions. Practical use of imperfect recall games is limited due to negative…

The minimax theorem for zero-sum games is easily proved from the strong duality theorem of linear programming. For the converse direction, the standard proof by Dantzig (1951) is known to be incomplete. We explain and combine classical…

We prove the almost equivalence of the minimax theorem and the strong duality theorem for a large class of games and conic programs. The previous fundamental results on the equivalence of linear programming and two-player zero-sum games…

The known results regarding two-player zero-sum games are naturally generalized in complex space and are presented through a complete compact theory. The payoff function is defined by the real part of the payoff function in the real case,…

Zero-sum and non-zero-sum (aka general-sum) games are relevant in a wide range of applications. While general non-zero-sum games are computationally hard, researchers focus on the special class of monotone games for gradient-based…

We consider a formulation of a non zero-sum n players game by an n+1 players zero-sum game. We suppose the existence of the n+1-th player in addition to n players in the main game, and virtual subsidies to the n players which is provided by…

We introduce two min-max problems: the first problem is to minimize the supremum of finitely many rational functions over a compact basic semi-algebraic set whereas the second problem is a 2-player zero-sum polynomial game in randomized…

In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases the probability of play…

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 this paper we study how to play (stochastic) games optimally using little space. We focus on repeated games with absorbing states, a type of two-player, zero-sum concurrent mean-payoff games. The prototypical example of these games is…