Related papers: Remarks on existence and uniqueness of Cournot-Nas…
We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out…
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…
We consider a large population dynamic game in discrete time where players are characterized by time-evolving types. It is a natural assumption that the players' actions cannot anticipate future values of their types. Such games go under…
We consider a large population dynamic game in discrete time. The peculiarity of the game is that players are characterized by time-evolving types, and so reasonably their actions should not anticipate the future values of their types. When…
We consider a class of games with continuum of players where equilibria can be obtained by the minimization of a certain functional related to optimal transport as emphasized in [7]. We then use the powerful entropic regularization…
The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of $N$ player games. Analysis of Nash equilibria is however a complex issue when the number of players is large. In this article we…
This paper develops a novel methodology to study robust stability properties of Nash equilibrium points in dynamic games. Small-gain techniques in modern mathematical control theory are used for the first time to derive conditions…
A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement…
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…
We study the existence and computation of Nash equilibria in concave games where the players' admissible strategies are subject to shared coupling constraints. Under playerwise concavity of constraints, we prove existence of Nash…
Methods of exploring Nash equilibrium in quantum games are studied. Analytical conditions of the existence, the uniqueness or the multiplicity of the equilibria are found.
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
We investigate the degree of discontinuity of several solution concepts from non-cooperative game theory. While the consideration of Nash equilibria forms the core of our work, also pure and correlated equilibria are dealt with. Formally,…
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,…
In this paper we consider continuity of the set of Nash equilibria and approximate Nash equilibria for parameterized games. For parameterized games with unique Nash equilibria, the continuity of this equilibrium mapping is well-known.…
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…
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…
A robust game is a distribution-free model to handle ambiguity generated by a bounded set of possible realizations of the values of players' payoff functions. The players are worst-case optimizers and a solution, called robust-optimization…
An heuristic approach to compute strong Nash (Aumann) equilibria is presented. The method is based on differential evolution and three variants of a generative relation for strong Nash equilibria characterization. Numerical experiments…
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…