Consider the following model of overlapping generations. In each period t = 1,2...., an agent is...

 

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Consider the following model of overlapping generations. In each period t = 1,2...., an agent is born and lives for two periods. Agent t (i.e. the person born at t) is young in period t and old in period t + 1. There is also an old agent in period 1. So in every period, there are two agents alive, a young agent and an old agent. A young agent is endowed with two loaves of bread. An old agent has nothing. Bread is a perishable good, and cannot be stored for future consumption. A young agent may transfer one loaf of bread to the old agent in the current period or she may transfer nothing, i.e. her action set is {0, 1), where a denotes her transfer. An old agent has no choices to make. Agent t observes the entire history of transfers, h = (a, a2.....-1) made by all previous agents. Each agent only cares about her own consumption over the two periods of her lifetime. Her utility is u(x, y) where r is her consumption when young and y is her consumption when old. Assume that u(2.1) > u(1,1)> u(2.0) > u(1.0) (a) Consider the strategy profile where each young agent chooses at = 0 at every history h. That is, for every t and every he, s(he) = 0. Show that this is a subgame perfect equilibrium. (b) Show that the allocation where each young agent transfers 1 unit to the old agent is feasible, and that it Pareto-dominates the outcome in (a). (c) Construct a subgame perfect equilibrium where the outcome in (b) is an equilibrium outcome. (Hint: construct this along the lines of the grim trigger strategy). (d) Can you construct a subgame perfect equilibrium that supports the outcome in (b), such that if some agent at date t deviates from the equilibrium, the agents from t + 1 onwards are not adversely affected as compared to the outcome in the equilibrium? (e) Suppose now that for every t > 1, the player at date t only observes the action at-1 taken by the player at date t-1, and does not observe the actions taken by previous players. 1 Consider the following model of overlapping generations. In each period t = 1,2...., an agent is born and lives for two periods. Agent t (i.e. the person born at t) is young in period t and old in period t + 1. There is also an old agent in period 1. So in every period, there are two agents alive, a young agent and an old agent. A young agent is endowed with two loaves of bread. An old agent has nothing. Bread is a perishable good, and cannot be stored for future consumption. A young agent may transfer one loaf of bread to the old agent in the current period or she may transfer nothing, i.e. her action set is {0, 1), where a denotes her transfer. An old agent has no choices to make. Agent t observes the entire history of transfers, h = (a, a2.....-1) made by all previous agents. Each agent only cares about her own consumption over the two periods of her lifetime. Her utility is u(x, y) where r is her consumption when young and y is her consumption when old. Assume that u(2.1) > u(1,1)> u(2.0) > u(1.0) (a) Consider the strategy profile where each young agent chooses at = 0 at every history h. That is, for every t and every he, s(he) = 0. Show that this is a subgame perfect equilibrium. (b) Show that the allocation where each young agent transfers 1 unit to the old agent is feasible, and that it Pareto-dominates the outcome in (a). (c) Construct a subgame perfect equilibrium where the outcome in (b) is an equilibrium outcome. (Hint: construct this along the lines of the grim trigger strategy). (d) Can you construct a subgame perfect equilibrium that supports the outcome in (b), such that if some agent at date t deviates from the equilibrium, the agents from t + 1 onwards are not adversely affected as compared to the outcome in the equilibrium? (e) Suppose now that for every t > 1, the player at date t only observes the action at-1 taken by the player at date t-1, and does not observe the actions taken by previous players. 1

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a To show that the strategy profile where each young agent chooses to transfer 0 units to the old agent at every history h t is a subgame perfect equilibrium we need to show that this strategy is a be... View the full answer