Iman Shames' Talk on The Attractor of the Replicator Dynamic in Zero-Sum Games

Title: The Attractor of the Replicator Dynamic in Zero-Sum Games

Time, Date, Location: 11:00, Friday, 1 March, 2024, Room 2.02 Seminar Room, Birch Building

Abstract: Abstract: In this work we characterise the long-run behaviour of the replicator dynamic in zero-sum games (symmetric or non-symmetric). Specifically, we prove that every zero-sum game possesses a unique global replicator attractor, which we then characterise. Most urprisingly, this attractor depends only on each player’s preference order over their own strategies and not on the cardinal payoff values, defined by a finite directed graph we call the game’s preference graph. When the game is symmetric, this graph is a tournament whose nodes are strategies; when the game is not symmetric, this graph is the game’s response graph. We discuss the consequences of our results on chain recurrence and Nash equilibria.

This paper is the recipient of the Outstanding paper award from Association for Algorithmic Learning Theory’s Algorithmic Learning Theory 2024.