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

We study the memory resources required for near-optimal play in two-player zero-sum stochastic games with the long-run average payoff. Although optimal strategies may not exist in such games, near-optimal strategies always do. Mertens and…

Richman games are zero-sum games, where in each turn players bid in order to determine who will play next [Lazarus et al.'99]. We extend the theory to impartial general-sum two player games called \emph{bidding games}, showing the existence…

Shortest-path games are two-player zero-sum games played on a graph equipped with integer weights. One player, that we call Min, wants to reach a target set of states while minimising the total weight, and the other one has an antagonistic…

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…

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…

In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and…

This paper develops a unified framework for zero-sum games in which both the pure strategies and the payoff matrices contain complex-valued entries. By leveraging a linear isomorphism between complex and real vector spaces, we extend key…

This short note demonstrates how one can define a transformation of a non-zero sum game into a zero sum, so that the optimal mixed strategy achieving equilibrium always exists. The transformation is equivalent to introduction of a passive…

We revisit classic algorithmic search and optimization problems from the perspective of competition. Rather than a single optimizer minimizing expected cost, we consider a zero-sum game in which an optimization problem is presented to two…

Which classes can be learned properly in the online model? -- that is, by an algorithm that at each round uses a predictor from the concept class. While there are simple and natural cases where improper learning is necessary, it is natural…

In this article, we generalize Unbounded Minimax, the state-of-the-art search algorithm for zero sums two-player games with perfect information to the framework of multiplayer games with perfect information. We experimentally show that this…

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the…

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a…

We explore a version of the minimax theorem for two-person win-lose games with infinitely many pure strategies. In the countable case, we give a combinatorial condition on the game which implies the minimax property. In the general case, we…

We consider approximating the minmax value of a multi-player game in strategic form. Tightening recent bounds by Borgs et al., we observe that approximating the value with a precision of epsilon log n digits (for any constant epsilon>0 is…

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…

In large-scale games, approximating the opponent's strategy space with a small portfolio of representative strategies is a common and powerful technique. However, the construction of these portfolios often relies on domain-specific…

In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…

Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among $n$ discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at…