Bilevel Entropy based Mechanism Design for Balancing Meta in Video Games

We address a mechanism design problem where the goal of the designer is to maximize the entropy of a player's mixed strategy at a Nash equilibrium. This objective is of special relevance to video games where game designers wish to diversify the players' interaction with the game. To solve this design problem, we propose a bi-level alternating optimization technique that (1) approximates the mixed strategy Nash equilibrium using a Nash Monte-Carlo reinforcement learning approach and (2) applies a gradient-free optimization technique (Covariance-Matrix Adaptation Evolutionary Strategy) to maximize the entropy of the mixed strategy obtained in level (1). The experimental results show that our approach achieves comparable results to the state-of-the-art approach on three benchmark domains "Rock-Paper-Scissors-Fire-Water", "Workshop Warfare" and "Pokemon Video Game Championship". Next, we show that, unlike previous state-of-the-art approaches, the computational complexity of our proposed approach scales significantly better in larger combinatorial strategy spaces.