How discontinuous is Computing Nash Equilibria?

TL;DR

This paper examines how sensitive various game theory solution concepts, including Nash, pure, and correlated equilibria, are to small changes in game data, providing insights into their stability and continuity properties.

Contribution

It offers a detailed analysis of the discontinuity levels of multiple equilibrium concepts in two-player games, extending results to n-player scenarios and solving related linear inequality systems.

Findings

Nash equilibria exhibit significant discontinuity in certain cases

Pure and correlated equilibria also show notable discontinuity behavior

The discontinuity degree of solving linear inequalities is characterized

Abstract

We investigate the degree of discontinuity of several solution concepts from non-cooperative game theory. While the consideration of Nash equilibria forms the core of our work, also pure and correlated equilibria are dealt with. Formally, we restrict the treatment to two player games, but results and proofs extend to the n-player case. As a side result, the degree of discontinuity of solving systems of linear inequalities is settled.