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Continuous games are multiplayer games in which strategy sets are compact and utility functions are continuous. These games typically have a highly complicated structure of Nash equilibria, and numerical methods for the equilibrium…
In this work, we introduce graphical modelsfor multi-player game theory, and give powerful algorithms for computing their Nash equilibria in certain cases. An n-player game is given by an undirected graph on n nodes and a set of n local…
We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…
Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in…
This note is devoted to study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by minimisation of some cost related to Optimal Transport. In particular we focus on the case of an Optimal…
In multi-agent autonomous systems, deception is a fundamental concept which characterizes the exploitation of unbalanced information to mislead victims into choosing oblivious actions. This effectively alters the system's long term…
We present a new, distributed method to compute approximate Nash equilibria in bimatrix games. In contrast to previous approaches that analyze the two payoff matrices at the same time (for example, by solving a single LP that combines the…
Quantum game theory has emerged as a promising candidate to further the understanding of quantum correlations. Motivated by this, it is demonstrated that pure strategy Nash equilibria can be utilised as a mechanism to witness and determine…
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…
Quantitative games are two-player zero-sum games played on directed weighted graphs. Total-payoff games (that can be seen as a refinement of the well-studied mean-payoff games) are the variant where the payoff of a play is computed as the…
In this paper, a multi-cluster game with high-order players is investigated. Different from the well-known multi-cluster games, the dynamics of players are taken into account in our problem. Due to the high-order dynamics of players,…
Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…
In this paper we show that, given $k\geq 3$, there exist $k$-player quantum XOR games for which the entangled bias can be arbitrarily larger than the bias of the game when the players are restricted to separable strategies. In particular,…
Every real algebraic variety is isomorphic to the set of totally mixed Nash equilibria of some three-person game, and also to the set of totally mixed Nash equilibria of an $N$-person game in which each player has two pure strategies. From…
We compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with pre-fixed structure. Using this representation, we show conditions under which a game has the maximum possible number of this…
Games involving quantum strategies often yield higher payoff. Here, we study a practical realization of the three-player dilemma game using the superconductivity-based quantum processors provided by IBM Q Experience. We analyze the…
This paper examines the convergence behaviour of simultaneous best-response dynamics in random potential games. We provide a theoretical result showing that, for two-player games with sufficiently many actions, the dynamics converge quickly…
An open problem in linear quadratic (LQ) games has been characterizing the Nash equilibria. This problem has renewed relevance given the surge of work on understanding the convergence of learning algorithms in dynamic games. This paper…
We will discuss the generalization of entropic uncertainty principles in terms of a game. The game involves k-players, each measuring one of k possible observables. The question is, what is the maximum number of players that can play such…