In a trust game, player 1 is given $10. She can send any fraction of that money to player 2. Player 1 keeps the remainder. Whatever money is sent to player 2 is tripled in the process (e. g. if $6 is sent by player 1, then player 2 receives $18). Player 2 then decides how much of the money she receives to return to player 1. Required:
a. When both players maximize their monetary payoff, what is the subgame perfect equilibrium of this game? Explain why the equilibrium is Pareto inefficient.
b. Player 1 again maximizes his monetary payoff. But now suppose that player 2 can be either a trustworthy type or untrustworthy type. Untrustworthy types maximize their monetary payoff. But trustworthy types always return to player 1 double what player 1 sent. Suppose that player 1 believes that player 2 is a trustworthy type with probability p. Show that player1 sends $10 to player 2 if p >1 and sends zero if p <1.
c. Briefly, how could this explain why high trust countries have higher standards of living?