Problem 1 - Overlapping Generations Consider an overlapping generations model (OLG) as follows. Each player lives for two pe- riods in the first of which he is referred to as being "young" and in the second "old." As an old generation dies a new one of equal size is born. At date 1 there are N young and N old players. At date 2 there is a new generation of N young players to replace the now deceased old players of the preceding generation and the young of date 1 become the old of date 2, and so on, ad infinitum. Each old player is randomly matched with one of the young play- ers to play a prisoners' dilemma game with strategies "Cooperate" (C) and "Defect" (D) and payoffs C D C 2,2 -1,3 D 3,-1 0,0 Assume that each new generation knows the entire history of play. 1 A player who is young seeks to maximize the undiscounted sum of his (two-period) lifetime payoffs. It turns out that some cooperation can be sustained in this world of finitely lived agents. Explain how (commenting briefly on why finitely was italicized), carefully specifying a subgame perfect Nash equilibrium in which each player's total lifetime payoffs equals two units. Recall that a strategy must specify behavior after all histories. Note that this overlapping generation model can be viewed as a toy model of the social security system. Explain how. Hint: Consider the payoffs and incentives of the young separately.