Dominance Solvability in Random Games

TL;DR

This paper investigates how the likelihood of dominance solvability in random games diminishes as players' actions increase, and how game imbalance affects the simplification process through iterated elimination.

Contribution

It provides new insights into the probability of dominance solvability in large random games and demonstrates the application of combinatorial methods to analyze complex game structures.

Findings

Dominance solvability becomes very rare as the number of actions increases.

The number of iterations to reach Nash equilibrium grows rapidly with larger action sets.

Highly imbalanced games significantly simplify through iterated elimination.

Abstract

We study the effectiveness of iterated elimination of strictly-dominated actions in random games. We show that dominance solvability of games is vanishingly small as the number of at least one player's actions grows. Furthermore, conditional on dominance solvability, the number of iterations required to converge to Nash equilibrium grows rapidly as action sets grow. Nonetheless, when games are highly imbalanced, iterated elimination simplifies the game substantially by ruling out a sizable fraction of actions. Technically, we illustrate the usefulness of recent combinatorial methods for the analysis of general games.