Worst-case control via linear programming: applications to truncation selection and partially malicious players

TL;DR

This paper explores how linear programming can be used to analyze worst-case scenarios in game theory, including truncation selection in large populations and dealing with malicious opponents, providing computational methods and numerical results.

Contribution

It introduces novel linear programming approaches for predicting outcomes in truncation dynamics and for strategic defense against partially malicious players in game theory.

Findings

Linear programming effectively predicts truncation selection outcomes.

Strategies outperform maximin in malicious opponent scenarios.

Numerical results validate the proposed methods.

Abstract

The connection between game theory, convex optimization, and geometry is deep. There are many applications of linear programming methods and polyhedral representation conversion methods in game theory. In this paper, we discuss two more scenarios where such methods can be useful. The first scenario is predicting the results of independent truncation dynamics under the large population assumption. The second scenario is when a player's opponent in a normal form game is not completely rational but shows some degree of malice. We show how one can compute a more profitable defensive play compared to simply playing a maximin strategy. We provide detailed computation procedure and numerical results for both scenarios.