91Ó°ÊÓ

EXERCISE 207.1 (Timing claims on an investment) An amount of money is accumulating; in period \(t(=1,2, \ldots, T)\) its size is $$\$ 2 t .$$ In each period two people simultaneously decide whether to claim the money. If only one person does so, she gets all the money; if both people do so, they split the money equally; and if neither person does so, both people have the opportunity to do so in the next period. If neither person claims the money in period \(T\), each person obtains $$\$ T$$. Each person cares only about the amount of money she obtains. Formulate this situation as an extensive game with perfect information and simultaneous moves, and find its subgame perfect equilibria). (Start by considering the cases \(T=1\) and \(T=2 .)\)