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

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.