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Game theoretic equilibria are mathematical expressions of rationality. Rational agents are used to model not only humans and their software representatives, but also organisms, populations, species and genes, interacting with each other and…

We develop a general game-theoretic framework for reasoning about strategic agents performing possibly costly computation. In this framework, many traditional game-theoretic results (such as the existence of a Nash equilibrium) no longer…

Our purpose is to focus attention on a new criterion for quantum schemes by bringing together the notions of quantum game and game isomorphism. A quantum game scheme is required to generate the classical game as a special case. Now, given a…

In this paper we consider symmetric games where a large number of players can be in any one of d states. We derive a limiting mean field model and characterize its main properties. This mean field limit is a system of coupled ordinary…

We study a network formation game where nodes wish to send traffic to other nodes. Nodes can contract bilaterally other nodes to form bidirectional links as well as nodes can break unilaterally contracts to eliminate the corresponding…

This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…

We consider the dynamics, existence and stability of the equilibrium states for large populations of individuals who can play various types of non--cooperative games. The players imitate the most attractive strategies, and the choice is…

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…

A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…

This paper presents an approach that brings together game theory with grammatical inference and discrete abstractions in order to synthesize control strategies for hybrid dynamical systems performing tasks in partially unknown but…

We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the more intuitively obvious definition of globular morphisms as mappings…

Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only…

Game logic is a dynamic modal logic which models strategic two person games; it contains propositional dynamic logic (PDL) as a fragment. We propose an interpretation of game logic based on stochastic effectivity functions. A definition of…

Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…

Rating strategies in a game is an important area of research in game theory and artificial intelligence, and can be applied to any real-world competitive or cooperative setting. Traditionally, only transitive dependencies between strategies…

Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…

The study focuses on strategic-form games extended in the Eisert-Wilkens-Lewenstein scheme by two unitary operations. Conditions are determined under which the pair of unitary operators, along with classical strategies, form a game…