Problem
Research questions and friction points this paper is trying to address.
Zero-determinant strategies
Repeated games
Without discounting
Cesaro average
Performance of Zero-determinant Strategies in Repeated Games without Discounting
🤖 AI Summary
This study addresses the performance analysis of zero-determinant (ZD) strategies in undiscounted repeated games, which has long relied on the Cesàro limit assumption, thereby restricting its theoretical applicability. By integrating game theory with mathematical analysis, this work discards the conventional assumption and directly derives and rigorously proves the asymptotic behavior and performance bounds of ZD strategies without presupposing the convergence of Cesàro-averaged probability distributions. Consequently, the proposed approach yields stronger theoretical guarantees than existing literature, fundamentally broadens the conditions under which ZD strategies are theoretically applicable, and provides a more complete characterization of strategic performance in undiscounted settings.
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Zero-determinant strategies
Repeated games
Cesaro average
Payoff control
Cooperation
🔎 Similar Papers
No similar papers found.
