game theory at a high school level, tysm to whomever helps me!!

Question

Peter, while studying game theory, came across a game where a couple of rational agents find a machine that delivers three coins to one of them when the other deposits a coin into it. So each agent has to choose to deposit (cooperate) or not (cheat) a coin in the machine during each round. The game consists of at least 10 rounds, agents do not know which round will be the last, each agent is aware of the other's choice in previous rounds but not in the present one, and the total utility of each is the sum of its results in each round.

Agent A / Agent B - Cooperate - Cheat

Cooperate 2 / 2 -1 / 3

0 3 / -1 0 / 0

a) If an agent is selfish, he will always cheat, regardless of the strategy adopted by the other.

b) The two agents cheating and cooperating alternately, in one round A cooperates and B cheats and in the other A cheats and B cooperates, would be a rational strategy.

c) If an agent is altruistic, valuing the other's utility with a multiplicative factor of 0.3, it will always cooperate regardless of the other's strategy.

d) A rational and selfish agent may decide to cooperate in order to obtain gains in the following rounds.

e) After around where both cooperated, each agent has an incentive to be the first to cheat.

Answer 1