Design of zero-determinant strategies and its application to networked repeated games

2023/11/13 by Daizhan Cheng, Cheng, Daizhan, Changxi Li +1 · 1 citation
Physics and Astronomy · Social Sciences · #Complex Network Analysis Techniques #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Opinion Dynamics and Social Influence #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2311.07124

openalex publication_date 2023/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using semi-tensor product (STP) of matrices, the profile evolutionary equation (PEE) for repeated finite games is obtained. By virtue of PEE, the zero-determinant (ZD) strategies are developed for general finite games. A formula is then obtained to design ZD strategies for general finite games with multi-player and asymmetric strategies. A necessary and sufficient condition is obtained to ensure the availability of the designed ZD strategies. It follows that player i is able to unilaterally design k_i-1 (one less than the number of her strategies) dominating linear relations about the expected payoffs of all players. Finally, the fictitious opponent player is proposed for networked repeated games (NRGs). A technique is proposed to simplify the model by reducing the number of frontier strategies.

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