Related papers: Game Dynamics and Nash Equilibria
We present a unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and…
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…
While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash…
Recently, a new model extending the standard replicator equation to a finite set of players connected on an arbitrary graph was developed in evolutionary game dynamics. The players are interpreted as subpopulations of multipopulations…
In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
Nash equilibrium is a key concept in game theory fundamental for elucidating the equilibrium state of strategic interactions, finding applications in diverse fields such as economics, political science, and biology. However, the Nash…
We study the query complexity of approximate notions of Nash equilibrium in games with a large number of players $n$. Our main result states that for $n$-player binary-action games and for constant $\varepsilon$, the query complexity of an…
Various social contexts ranging from public goods provision to information collection can be depicted as games of strategic interactions, where a player's well-being depends on her own action as well as on the actions taken by her…
Nash equilibria provide a principled framework for modeling interactions in multi-agent decision-making and control. However, many equilibrium-seeking methods implicitly assume that each agent has access to the other agents' objectives and…
We analyze, using a dynamical systems approach, the replicator dynamics for the asymmetric Hawk-Dove game in which there is a set of four pure strategies with arbitrary payoffs. We give a full account of the equilibrium points and their…
Whilst network coordination games and network anti-coordination games have received a considerable amount of attention in the literature, network games with coexisting coordinating and anti-coordinating players are known to exhibit more…
Dynamic games are powerful tools to model multi-agent decision-making, yet computing Nash (generalized Nash) equilibria remains a central challenge in such settings. Complexity arises from tightly coupled optimality conditions, nested…
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…
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…
This is a short introduction to the subject of strategic games. We focus on the concepts of best response, Nash equilibrium, strict and weak dominance, and mixed strategies, and study the relation between these concepts in the context of…
Game theory studies situations in which strategic players can modify the state of a given system, due to the absence of a central authority. Solution concepts, such as Nash equilibrium, are defined to predict the outcome of such situations.…
We study the connection between the evolutionary replicator dynamics and the number of Nash equilibria in large random bi-matrix games. Using techniques of disordered systems theory we compute the statistical properties of both, the fixed…
Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the…
This paper presents a general closed graph property for (randomized strategy) Nash equilibrium correspondence in large games. In particular, we show that for any large game with a convergent sequence of fiinite-player games, the limit of…