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 he leads him to the correct destination, each of them will get half the accumulated money. On the other hand, if Player 2 can lead him astray, Player 2 will get 75% of the accumulated money and Player 1 will get 25%. If Player 1 opts out of the game, he will get 30% of the accumulated money and Player 2 will get 20%. 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% of the accumulated money on the defecting player?

a) In equilibrium, Player 1 will choose to opt out of the game. He will make this decision using the method of backward induction. If he lets Player 2 guide him to the destination, Player 2 is likely to lead him astray because Player 2 will earn 75% of the accumulated money in that case, while he will earn only 50% 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% of the accumulated money while he will earn only 25% if Player 2 leads him astray.
b) If the players can choose to impose a guilt penalty of 60% 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% - 60% = 15% of the accumulated money if he leads Player 1 astray, while he will get 50% by guiding him to the correct destination. Therefore, he 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% of the accumulated money in that case, while he will get only 30% if he opts out of the game.