Final answer:
In game theory, a repeated game is a scenario where the same game is played multiple times by the same players, with each round offering an opportunity to adjust strategies based on prior outcomes. The Prisoner's Dilemma is a famous example of how repeated games can lead to different strategies than one-shot games. The correct answer to the student's question is 'a) that recurs more than once between two players.'
Step-by-step explanation:
In game theory, a repeated game refers to a scenario where the same game (with the same payoff matrix) is played multiple times by the same participants. Each round of the game offers the players a chance to adjust their strategies based on the outcomes of prior rounds, leading to potentially different decisions and results each time. This concept contrasts with one-shot games, where players interact just once and then the game ends.
One of the classic examples of a repeated game in game theory is the Prisoner's Dilemma. In the Prisoner's Dilemma, two criminals are arrested but the authorities lack sufficient evidence for a specific crime. Held in separate cells, they can't communicate with each other. The authorities offer each prisoner a bargain: betray the other by testifying that the other committed the crime, or cooperate with the other by remaining silent. The dilemma arises because while mutual cooperation would lead to the best collective outcome, self-interest could encourage them to betray each other, leading to a worse situation.
Bringing us back to the student's question, we can now confidently say that the correct option is: a) that recurs more than once between two players. Repeated games are significant in game theory as they provide insight into how cooperation and trust can evolve over time, as players have the opportunity to reward or punish past behavior, steering the game towards different equilibria than a one-shot game might predict.