arXiv subjects

Enxian Chen

Publications and source records attributed to Enxian Chen.

3 recordsLinked to original sources

arXiv2024

Equilibrium convergence in large games

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 any convergent sequence of Nash equilibria of the corresponding finite-player games can be induced by a Nash equilibrium of the large game. Such a result goes beyond earlier results on the closed graph property for pure strategy Nash equilibrium correspondence in large games in multiple aspects. An application on equilibrium selection in large games is also presented.

math.OC↗

arXiv2021

Robust perfect equilibrium in large games

This paper proposes a new equilibrium concept "robust perfect equilibrium" for non-cooperative games with a continuum of players, incorporating three types of perturbations. Such an equilibrium is shown to exist (in symmetric mixed strategies and in pure strategies) and satisfy the important properties of admissibility, aggregate robustness, and ex post robust perfection. These properties strengthen relevant equilibrium results in an extensive literature on strategic interactions among a large number of agents. Illustrative applications to congestion games and potential games are presented. In the particular case of a congestion game with strictly increasing cost functions, we show that there is a unique symmetric robust perfect equilibrium.

econ.TH↗

arXiv2019

Does randomization matter in dynamic games?

This paper investigates mixed strategies in dynamic games with perfect information. We present an example to show that a player may obtain higher payoff by playing mixed strategy. By contrast, the main result of the paper shows that every two-player dynamic zero-sum game with nature has the no-mixing property, which implies that mixed strategy is useless in this most classical class of games. As for applications, we show the existence of pure-strategy subgame-perfect equilibria in two-player zero-sum games with nature. Based on the main result, we also prove the existence of a universal subgame-perfect equilibrium that can induce all the pure-strategy subgame-perfect equilibria in such games. A generalization of the main result for multiple players and some further results are also discussed.

math.OC↗