2019/05/26 by Ben Amiet, Andrea Collevecchio, Amiet, Ben +5 · 2 citations
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #60K35 #91A06 #91A10 #Combinatorics (math.CO) #Computer Science and Game Theory (cs.GT) #Economic theories and models #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Game Theory and Applications #Opinion Dynamics and Social Influence #Probability (math.PR) #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.1905.10758
openalex publication_date 2019/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In finite games mixed Nash equilibria always exist, but pure equilibria may fail to exist. To assess the relevance of this nonexistence, we consider games where the payoffs are drawn at random. In particular, we focus on games where a large number of players can each choose one of two possible strategies, and the payoffs are i.i.d. with the possibility of ties. We provide asymptotic results about the random number of pure Nash equilibria, such as fast growth and a central limit theorem, with bounds for the approximation error. Moreover, by using a new link between percolation models and game theory, we describe in detail the geometry of Nash equilibria and show that, when the probability of ties is small, a best-response dynamics reaches a Nash equilibrium with a probability that quickly approaches one as the number of players grows. We show that a multitude of phase transitions depend only on a single parameter of the model, that is, the probability of having ties.