Zero determinant strategies in repeated games work without discounts
Performance of Zero-determinant Strategies in Repeated Games without Discounting
Multiagent Systems
Summary
Zero-determinant (ZD) strategies let one player control outcomes in repeated games, often helping cooperation. Previous work assumed a specific mathematical limit to explain their effects, but this paper removes that assumption. The authors show that these strategies still work well even without assuming that limit exists. This makes understanding of ZD strategies stronger and more broadly applicable.
What this means in practice
- •For algorithm designers: Develop algorithms for repeated interactions where past actions are not discounted but strategic control over outcomes is needed.
- •For economic modelers: Model long-term social interactions without discounting while predicting cooperative behavior enforced by specific strategies.
A theory result. No direct application yet.
Authors
Masahiko Ueda
Abstract
Zero-determinant (ZD) strategies are a class of strategies in repeated games, which unilaterally control payoffs. It has been shown that several ZD strategies promote cooperation in social dilemma games. It has been widely believed that the performance of ZD strategies is expressed as ``unilaterally enforce linear relations between payoffs''. However, in order to interpret properties of ZD strategies in repeated games without discounting, previous studies assumed that the limit of the Cesaro average of the probability distribution of the action profile exists. Here, we explain the performance of ZD strategies without this assumption, which leads to a stronger result than previous ones.