Design of zero-determinant alliances in repeated multi-player games

Abstract

The formation of coalitions or alliances is ubiquitous in nature. This paper extends the zero-determinant (ZD) strategies from single players to subsets of players, to which we refer to as the ZD alliances. First, we model the dynamics of repeated multi-player games with a strategic alliance as an equivalent algebraic form and a simple formula is proposed to design a strategic ZD alliance. Thereafter, the modeling and designing methods for synchronous ZD alliance are considered. Finally, we apply the main results to a four-player prisoner's dilemma and analyze the influence of parameters on the probability of alliance cooperation. Our results can not only reduce the computation complexity, but also highlight the importance of coordination to succeed in large groups.