发帖
雷达卡
Overlapping Generations
There is a long sequence of players. One player is born in each period t, and he lives for periods t and t+1. Thus, two players are alive in any one period, a youngster and an oldster. Each player is born with one unit of chocolate, which cannot be stored. Utility is increasing in chocolate consumption, and a player is very unhappy if he consumes less than 0.2 units of chocolate in a period: the per-period utility functions are U(C) = −1 for C < 0.2 and U(C) = C for C ≥ 0.2, where C is consumption. Players can give away their chocolate, but, since chocolate is the only good, they cannot sell it. A player’s action is to consume X units of chocolate as a youngster and give away 1 −X to some oldster. Every person’s actions in the previous period are common knowledge, and so can be used to condition strategies upon.
a. If there is finite number of generations, what is the unique Nash equilibrium?
b. If there are an infinite number of generations, what are two Pareto-ranked perfect equilibria?
c. If there is a probability θ at the end of each period (after consumption takes place) that barbarians will invade and steal all the chocolate (leaving the civilized people with payoffs of -1 for any X), what is the highest value of θ that still allows for an equilibrium with X = 0.5?
提升卡
置顶卡
沉默卡
变色卡
抢沙发
千斤顶
显身卡
京公网安备 11010802022788号
