Related papers: Lipschitz Games

In this paper, we present a new development of inspection games in a mean field setting. In our dynamic version of an inspection game, there is one inspector and a large number N interacting inspectees with a finite state space. By applying…

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…

We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward…

We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…

Two-player stochastic games are games with two 2 players and a randomised entity called "nature". A natural question to ask in this framework is the existence of strategies that ensure that an event happens with probability 1 (almost-sure…

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega\subset \mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a…

In a zero-sum stochastic game, at each stage, two adversary players take decisions and receive a stage payoff determined by them and by a controlled random variable representing the state of nature. The total payoff is the normalized…

In two-player zero-sum stochastic games, where two competing players make decisions under uncertainty, a pair of optimal strategies is traditionally described by Nash equilibrium and computed under the assumption that the players have…

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…

We consider finite two-player normal form games with random payoffs. Player A's payoffs are i.i.d. from a uniform distribution. Given p in [0, 1], for any action profile, player B's payoff coincides with player A's payoff with probability p…

A Dynkin game is a zero-sum, stochastic stopping game between two players where either player can stop the game at any time for an observable payoff. Typically the payoff process of the max-player is assumed to be smaller than the payoff…

In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play Nash…

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 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 consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…

We consider 2-players, 2-values minimization games where the players' costs take on two values, $a,b$, $a<b$. The players play mixed strategies and their costs are evaluated by unimodal valuations. This broad class of valuations includes…

We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…

We study pure-strategy Nash equilibria in multi-player concurrent deterministic games, for a variety of preference relations. We provide a novel construction, called the suspect game, which transforms a multi-player concurrent game into a…

In this paper we consider strong Nash equilibria, in mixed strategies, for finite games. Any strong Nash equilibrium outcome is Pareto efficient for each coalition. First, we analyze the two--player setting. Our main result, in its simplest…

In an $\epsilon$-Nash equilibrium, a player can gain at most $\epsilon$ by unilaterally changing his behaviour. For two-player (bimatrix) games with payoffs in $[0,1]$, the best-known$\epsilon$ achievable in polynomial time is 0.3393. In…