Presentation Information
[SS19-03]On the existence of zero-determinant strategies in repeated asymmetric games
*GENKI ICHINOSE1 (1. Shizuoka University (Japan))
Keywords:
Asymmetric repeated game,Discount factor,Zero-determinant strategies,Cooperation,Direct reciprocity
Zero-determinant (ZD) strategies represent a class of memory-one strategies that allow a player to unilaterally enforce a linear relationship between their own payoff and that of their opponent in repeated games, providing a novel perspective on the emergence of cooperation through direct reciprocity. While previous studies have extensively examined ZD strategies in symmetric games, in many cases, payoffs are not symmetric. Furthermore, in repeated interactions, future payoffs are often discounted, reflecting realistic decision-making processes. Despite these important considerations, the existence conditions of ZD strategies in asymmetric repeated games with discounting remain less explored. In this study, we systematically investigate the existence conditions of ZD strategies in repeated asymmetric games by incorporating a discount factor. Specifically, we focus on two key subclasses of ZD strategies: equalizer strategies and multiplicative strategies (which include extortionate strategies as a special case). We derive the conditions under which equalizer strategies exist, determine the payoff range they impose on the opponent, and identify the minimum discount factor required to sustain them. Additionally, we analyze the feasibility of multiplicative ZD strategies, characterizing the range of multiplicative factors that allow a player to enforce a cooperative relationship between the net payoffs. Our results provide new insights into the role of discounting in asymmetric repeated interactions.