Mark and Anthony are participating in a trust game. Mark is given a locked box containing five $100 bills and a key. He can either unlock the box himself or he can give it to Anthony
Anthony can either unlock the box himself or return it to the moderator of the game. If Mark unlocks the box himself, he will get $200 and Anthony will get $100 while the rest will be taken back. If Anthony unlocks the box, they will receive $250 each. If Anthony returns the box to the moderator, he will receive $300, while Mark will not get any money. What will the equilibrium outcome of this game be?
In equilibrium, Mark will choose to unlock the box himself. He will take this decision using the method of backward induction. If he gives the box and the key to Anthony, he is likely to hand them over to the moderator, in which case he will receive $300 but Mark will not get any money. Given this information, Mark will choose to unlock it himself as he will earn $200.
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