"Zero-determinant strategies and their extensions"Ichinose, GenkiIn repeated games of game theory, direct reciprocity has been studied for many years, in which one can expect cooperation from the opponent later by behaving cooperatively in the present. In related research fields, Zero-Determinant (ZD) strategies, discovered in 2012 by Press & Dyson [1], have attracted much attention because they include unbeatable strategies called Extortion and the strategies which fix the opponent payoff to a specific value called Equalizer in a one-to-one competition as a subset. These characteristics come from the property that ZD strategies can enforce a linear payoff relationship between themselves and their opponents, regardless of the opponents’ strategies. Inspired by the discovery of the ZD strategy, many researchers in this field have made various extensions to the ZD strategies. In the past few years, we have also developed the theory of ZD strategy with realistic factors such as observation error and discount factor. In this talk, I first explain what ZD strategies are in detail. Then, I mathematically derive the ZD strategies. Finally, I introduce our discoveries in ZD strategies. Our extensions include a discount factor and observation errors. I also discuss the existence of ZD strategies in such situations. These studies expand the importance of ZD strategies in more realistic situations. [1] W. H. Press and F. J. Dyson, Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent, Proc. Natl. Acad. Sci. USA, 109:10409–10413, 2012. |
« back