Question

Hint: Consider the last round and work backwards. Consider a centipede game, where there

are two players P1 and P2. The game starts by P1's decision of take or wait. If P1 takes,

P1 earns $1 while P2 earns nothing, and the game ends. If P1 waits, then P2 can choose

between take or wait, and if P2 takes P2 earns $2 while P1 earns nothing and the game

ends, while if P2 waits it becomes P1's turn to choose again. If they keep waiting the reward

grows by $1 each round, until P2's choice of taking $20 or waiting, when the game will end

no matter what. Both of P1 and P2 want to maximize their rewards, and behave as perfect

logicians. Argue that P1 should take $1 in the very first round.

Answer 1