Asymmetric Abstractions for Adversarial Settings

In multiagent domains, an agent's beliefs about how other agents will or could act plays a significant role in their own behaviour. In large domains where it is infeasible to uniquely represent every possible decision an agent will face, abstraction is often used to collapse the state and action space to make the problem tractable. By abstracting other agents' views of the environment, the agent makes assumptions about how other agents act. Incorrect abstraction choices can yield less than ideal performance as other agents may, in reality, use coarser or finer abstraction than they were modelled with. The standard approach when abstracting is to use symmetric abstraction: where all agents are assumed to distinguish states in the same way. This work examines the benefits and potential pitfalls of using asymmetric abstractions in two-player zero- sum extensive-form games. Using the domain of two-player limit Texas hold'em poker, we investigate the performance of strategies using both symmetric and asymmetric abstractions in terms of in-game utility and worst-case utility in the real game. Furthermore, we show that combining asymmetric abstractions with robust counter-strategy techniques can produce counter-strategies which dominate their symmetric abstraction counterparts in terms of both exploitative power and worst-case utility.