Related papers: Monotonicity and Bracketing in Games

We analyze the robustness of (pure strategy) Nash equilibria for network games against perturbations of the players' utility functions. We first derive a simple characterization of the margin of robustness, defined as the minimum magnitude…

It is known that the generalized Nash equilibrium problem can be reformulated as a quasivariational inequality. Our aim in this work is to introduce a variational approach to study the existence of solutions for generalized ordinal Nash…

Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…

Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…

Mean field games are limit models for symmetric $N$-player games with interaction of mean field type as $N\to\infty$. The limit relation is often understood in the sense that a solution of a mean field game allows to construct approximate…

We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…

We consider solutions of normal form games that are invariant under strategic equivalence. We consider additional properties that can be expected (or be desired) from a solution of a game, and we observe the following: - Even the weakest…

In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A…

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…

Quantum games with incomplete information can be studied within a Bayesian framework. We analyze games quantized within the EWL framework [Eisert, Wilkens, and Lewenstein, Phys Rev. Lett. 83, 3077 (1999)]. We solve for the Nash equilibria…

We study the problem of computing all Nash equilibria of a subclass of finite normal form games. With algebraic characterization of the games, we present a method for computing all its Nash equilibria. Further, we present a method for…

We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…

We identify structural assumptions which provide solvability of the Nash system arising from a linear-quadratic closed-loop game, with stable properties with respect to the number of players. In a setting of interactions governed by a…

If a game has a unique Nash equilibrium, then this equilibrium is arguably the solution of the game from the refinement's literature point of view. However, it might be that for almost all initial conditions, all strategies in the support…

Computing Nash equilibria for strategic multi-agent systems is challenging for expensive black box systems. Motivated by the ubiquity of games involving exploitation of common resources, this paper considers the above problem for potential…

We study the asymptotic organization among many optimizing individuals interacting in a suitable "moderate" way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player…

We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are ``weakly'' stable: irrationality propagates and amplifies through players'…

We consider a stochastic tournament game in which each player is rewarded based on her rank in terms of the completion time of her own task and is subject to cost of effort. When players are homogeneous and the rewards are purely rank…

For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…