Two players are playing a game. Player 1 is given $100 and is asked to offer a certain share of the money to Player 2. Player 2 can then choose to accept or reject the offer

If he accepts the offer, the money will be split between the two players in the ratio as decided by Player 1. If he rejects the offer, neither of the players will get anything. a) Assume that both players prefer more money to less. How would Player 1 choose his optimal strategy in this case? b) If Player 2 prefers fairness to money, how will his decision change?

a) This is an example of an ultimatum game, and Player 1 should choose his optimal strategy using the process of backward induction, that is, by considering Player 2's decision first. If Player 1 offers a certain percentage of money to Player 2, Player 1 will definitely accept the offer because he prefers more money to less. Therefore, Player 1's optimal strategy is to offer the minimum possible amount to Player 2.
b) If Player 2 prefers fairness to money, he will not accept the offer in case Player 1 offers the lowest possible amount. If Player 1 knows that Player 2 prefers fairness to money, he will figure out that Player 2 will not accept the offer if he offers the lowest possible amount, leaving each of them with $0. Therefore, Player 1 will choose to offer a fair deal.