Abstract
In this chapter, the problem of solving infinitely repeated games by means of Nash or sub-Nash equilibria is considered. Using the algebraic form of a logical dynamical system, a strategy with finite memory can be expressed as a logical matrix. The Nash equilibria are then computable, providing Nash solutions to the given game. When the Nash equilibrium does not exist, sub-Nash equilibria and e-tolerance solutions may provide a reasonable solution to the game. Common Nash or sub-Nash equilibria make different memory-length strategies comparable. An optimal or sub-optimal solution can then be obtained. Certain algorithms are proposed. This chapter is based on Cheng et al. (Nash and sub-Nash solutions to infinitely repeated games, 2010; Proc. IEEE CDC’2010, 2010).
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