In a computer network with discrete transmission time slots, three agents want to transmit their(unlimited amount of) information without a predefined protocol. Assume that the agents are synchronized and each has the option to attempt to attempt to transmit (or to not transmit) a packet in each time slot. Each successfully transmitted packet is worth 2 units of utility to the transmitting agent, each transmission attempt costs energy equivalent to 1 unit of utility, and if two agents try to transmit in the same time slot the transmission fails. If an agent does not attempt a transmission, its payoff is 0 since no energy is spent and no transmission payoff is obtained.
I have built a payoff matrix for the stage game but how can I use folk theorem to derive a trigger strategy Nash Equilibrium for an infintely repeating game?
If I understand your description of the stage game properly, there are three pure strategy NE to the stage game, each involving a transmission by one and only one player. What kind of behavior are you trying to support with trigger strategies?