Theoretical Guarantees for the Retention of Strict Nash Equilibria by Coevolutionary Algorithms

Most methods for finding a Nash equilibrium rely on procedures that operate over the entire action space, making them infeasible for settings with too many actions to be searched exhaustively. Randomised search heuristics such as coevolutionary algorithms offer benefits in such settings, however they lack many of the theoretical guarantees established for exhaustive methods such as zero-regret learning. We address this by developing a method for proving necessary and sufficient conditions for a coevolutionary algorithm to be stable, in the sense that it reliably retains a Nash equilibrium following discovery. As the method provides bounds that are adapted to both application and algorithm instance, it can be used as a practical tool for parameter configuration. We additionally show how bounds on regret may be deduced from our results and undertake corresponding empirical analysis.