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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?

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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?

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  • $\begingroup$ Yes, you are right. There will be 3 Nash Equilibriums. I was thinking if the agent is transferring the data that should defect and if they are waiting then cooperation if that's what you are asking. $\endgroup$ – Yatharth Garg Apr 20 '18 at 2:02
  • $\begingroup$ I don't think trigger strategies get you anywhere here. The static equilibria are efficient so you aren't going to enforce something different with trigger style punishment strategies. $\endgroup$ – ks11469 Apr 20 '18 at 2:15
  • $\begingroup$ That doesn't mean you can't do it. You can support any distribution of payoffs in the convex hull of stage game payoffs where each player feta an average payoff greater than zero in this case. I just mean you don't actually NEED the trigger strategies for this--you can probably do it with a sequence of stage game equilibria. $\endgroup$ – ks11469 Apr 20 '18 at 2:17
  • $\begingroup$ I know I don't need trigger strategies, but that's the question that I am stuck on. It specifically says use folk theorem to derive trigger strategy Nash Equilibrium. Any help would be appreciated. $\endgroup$ – Yatharth Garg Apr 20 '18 at 2:20
  • $\begingroup$ You need to first know what behavior you're trying to support along the path of play. Typically this would be behavior that is not an equilibrium to the stage game (e.g. C,C in the prisoner's dilemma). The trigger strategy will give the minimax payoff to any player that defects (forever as in grim trigger, for one period as in tit for tat, or whatever). The folk theorem tells you whether some such strategy will be part of a spne but doesn't particularly help you construct a strategy. So my first question was what are you trying to get the players to do along the path of play. $\endgroup$ – ks11469 Apr 20 '18 at 2:53

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