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We study pure Nash equilibria in games on graphs with an imperfect monitoring based on a public signal. In such games, deviations and players responsible for those deviations can be hard to detect and track. We propose a generic epistemic…

We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and…

Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide…

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…

Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…

In a finite two player game consider the matrix of one player's payoff difference between any two consecutive pure strategies. Define the half space induced by a column vector of this matrix as the set of vectors that form an obtuse angle…

The fundamental laws of quantum world upsets the logical foundation of classic physics. They are completely counter-intuitive with many bizarre behaviors. However, this paper shows that they may make sense from the perspective of a general…

In this paper we present a novel generic mapping between Graphical Games and Markov Random Fields so that pure Nash equilibria in the former can be found by statistical inference on the latter. Thus, the problem of deciding whether a…

This paper explores aggregative games in a network of general linear systems subject to external disturbances. To deal with external disturbances, distributed strategy-updating rules based on internal model are proposed for the case with…

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at…

Game-theoretic techniques and equilibria analysis facilitate the design and verification of competitive systems. While algorithmic complexity of equilibria computation has been extensively studied, practical implementation and application…

Weakly acyclic games generalize potential games and are fundamental to the study of game theoretic control. In this paper, we present a generalization of weakly acyclic games, and we observe its importance in multi-agent learning when…

Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…

In this paper, we consider a class of $n$-person noncooperative games, where the utility function of every player is given by a homogeneous polynomial defined by the payoff tensor of that player, which is a natural extension of the bimatrix…

Standard game theory assumes that the structure of the game is common knowledge among players. We relax this assumption by considering extensive games where agents may be unaware of the complete structure of the game. In particular, they…

A model of stochastic games where multiple controllers jointly control the evolution of the state of a dynamic system but have access to different information about the state and action processes is considered. The asymmetry of information…

A classic model to study strategic decision making in multi-agent systems is the normal-form game. This model can be generalised to allow for an infinite number of pure strategies leading to continuous games. Multi-objective normal-form…

A growing body of literature in networked systems research relies on game theory and mechanism design to model and address the potential lack of cooperation between self-interested users. Most game-theoretic models applied to system…

We introduce and study the class of semidefinite games, which generalizes bimatrix games and finite $N$-person games, by replacing the simplex of the mixed strategies for each player by a slice of the positive semidefinite cone in the space…

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with merely monotone and restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method…