How Repeated Games with Unequal Discount Factors Affect the Cooperation Behavior in DF Cooperative Communication Systems

Abstract

In this work, the repeated game model with unequal discount factors is utilized to understand how the players' behavior affect the system performance in a decode-and-forward cooperative communication system. Unlike previous work, in which all free-ridings are illegal, we differentiate the free-riding into the legal free-riding (LFR) and the illegal one (IFR). Taking LFR and IFR into account, the conditions for the case which players cooperate to be a NE and to be the only NE in the proposed repeated games are established as well when the discount factors of players are not equal, which are then confirmed through extensive computer simulations.