In a trust game, player 1 is given dollar 10. She can send any fraction of that

Question

In a trust game, player 1 is given dollar 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 dollar 6 is sent by player 1, then player 2 receives dollar 18). Player 2 then decides how much of the money she receives to return to player 1. When both players maximize their monetary payoff, what is the subgame perfect equilibrium of this game? Explain why the equilibrium is Pareto inefficient. 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 player 1 sends dollar 10 to player 2 if p >1/2 and sends zero if p

Explanation / Answer

Player 1 has $10 thus the maximum that he can lend is $10. But it depends upon the trust level. Now let us assume that player 1 lends x and player 2 receives 3x. Further player 2 returns y. Thus the payoff for player 1 will be 10-x+y and for player 2 it will be 3x-y. Only when y is equal to or greater than x player 1 can trust player 2. So the subgame perfect equilibrium is (10-x+y, 3x-y) so that the benefits of both are maximized. This is pareto inefficient since it is not possible to make any player better off without making the other player worst. Player 1 has $10 thus the maximum that he can lend is $10. But it depends upon the trust level. Now let us assume that player 1 lends x and player 2 receives 3x. Further player 2 returns y. Thus the payoff for player 1 will be 10-x+y and for player 2 it will be 3x-y. Only when y is equal to or greater than x player 1 can trust player 2. Practically y will always be greater to x since player 2 needs to maintain the trust. Thus let us assume his probability to be trust worthy i.e p>1/2. In this event let us assume player 1 lends $10 to player 2. Replacing the value in both equation and assuming that y=x we get the payoff as (10,20) and when he lends $0 then the payoff will be (10,0) when p1/2 player 1 lends $10 and if p

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.