Zero-determinant Strategies for Multi-player Multi-action Iterated Games

Zero-determinant (ZD) strategies that allow a player to unilaterally control the linear combinations of its own and other players' expected rewards in iterated games have recently found wide applications. However, existing ZD strategies mainly focus on some specific scenarios with restrictions on the number of players or actions a player can take. Targeting wider applications and better performance, the ZD strategies along with corresponding existence conditions for general multi-player multi-action iterated games are developed in this work, including existing ones as special cases. In addition, an interesting fact that every player can have at most one master player (that can control the expected reward of the given player) is revealed.