Two individuals are playing a trust game that has three rounds. In the first two rounds of the game, they have accumulated $1,000 as a team. In the third round, Player 1 is blindfolded and asked to decide whether he would let Player 2 guide him to a particular destination or opt out of the game. If he lets Player 2 guide him, Player 2 can either guide him to the correct destination or take him elsewhere. If she leads him to the correct destination, each of them will get half of the accumulated money. However, if Player 2 leads him astray, Player 2 will get 75 percent of the accumulated money and Player 1 will get 25 percent. If Player 1 opts out of the game, he will get 30 percent of the accumulated money and Player 2 will get 20 percent.
a) What is the equilibrium outcome in this case?
b) How will the equilibrium change if the players can impose a guilt penalty of 60 percent of the accumulated money on the defecting player?

Question

Quizplus · Accepted Answer

The Answer is a) In equilibrium, Player 1 will choose to opt out of the game. He will make this decision using backward induction. If he lets Player 2 guide him to the destination, Player 2 is likely to lead him astray, because Player 2 would earn 75 percent of the accumulated money by doing so, instead of the 50 percent she would earn by leading Player 1 to the correct destination. Given this information, Player 1 will choose to opt out of the game, as he will earn 30 percent of the accumulated money by doing so, instead of the 25 percent he would earn if Player 2 led him astray.
b) If the players can choose to impose a guilt penalty of 60 percent of the accumulated money, Player 1 will let Player 2 guide him, and Player 2 will guide him to the correct destination. In this case, Player 2 will get only 75 percent − 60 percent = 15 percent of the accumulated money if she leads Player 1 astray, while she will get 50 percent by guiding him to the correct destination. Therefore, she will always choose to guide him to the correct destination. Given this information, Player 1 will choose to be guided by Player 2, as he will get 50 percent of the accumulated money by doing so, instead of 30 percent if he opted out of the game.

Two Individuals Are Playing a Trust Game That Has Three