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.
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.Showthatplayer1sends$10toplayer2ifp>1 andsendszeroifp<1.
c. Briefly, how could this explain why high trust countries have higher standards of living?