Safe Exploitative Play with Untrusted Type Beliefs

TL;DR

This paper analyzes how incorrect type beliefs in Bayesian games affect an agent's payoff, establishing bounds on the risk-opportunity tradeoff and providing insights into safe exploitative strategies.

Contribution

It introduces a formal framework for understanding the impact of belief inaccuracies on payoffs and characterizes the tradeoff between risk and opportunity in Bayesian game settings.

Findings

Bounds on the Pareto front for normal-form Bayesian games

Bounds on the Pareto front for stochastic Bayesian games

Numerical results illustrating the tradeoff analysis

Abstract

The combination of the Bayesian game and learning has a rich history, with the idea of controlling a single agent in a system composed of multiple agents with unknown behaviors given a set of types, each specifying a possible behavior for the other agents. The idea is to plan an agent's own actions with respect to those types which it believes are most likely to maximize the payoff. However, the type beliefs are often learned from past actions and likely to be incorrect. With this perspective in mind, we consider an agent in a game with type predictions of other components, and investigate the impact of incorrect beliefs to the agent's payoff. In particular, we formally define a tradeoff between risk and opportunity by comparing the payoff obtained against the optimal payoff, which is represented by a gap caused by trusting or distrusting the learned beliefs. Our main results characterize the tradeoff by establishing upper and lower bounds on the Pareto front for both normal-form and stochastic Bayesian games, with numerical results provided.