In this paper we study the complexity of finding approximate Nash equilibria in multi-player normal-form games. First, for any constant number n, we present a polynomial-time algorithm for computing a relative ( 1− 1 1+(n−1)n ) -Nash equilibrium in arbitrary nplayer games and a relative ( 1− 1 1+(n−1)n−1 ) -Nash equilibrium in symmetric n-player games. Next, we show that there is an additive ε-...

Generalized Nash equilibrium problems have become very important as a modeling tool during the last decades. The aim of this survey paper is twofold. It summarizes recent advances in the research on computational methods for generalized Nash equilibrium problems and points out current challenges. The focus of this survey is on algorithms and their convergence properties. Therefore, we also pres...

In a Nash equilibrium, each player selects a strategy that is optimal with respect to the strategies of other players. This definition does not mention the process by which players reach a Nash equilibrium. The topic of learning in games seeks to address this issue in that it explores how simplistic learning/adaptation rules can lead to Nash equilibrium. This article presents a selective sampli...

We auction scarce rights to play the Proposer and Responder positions in ultimatum games. As a control treatment, we randomly allocate these rights and charge exogenous participation fees. These participation fee sequences match the auction price sequence from a session of the original treatment. With endogenous selection via auctions, we find that play converges to a session-specific Nash equi...