Game Theory of Asking and Granting Forgiveness
Referenced article: https://www.psychologytoday.com/blog/one-among-many/201507/game-forgiveness
Forgiveness is widely viewed in a positive light. It is one of the six cardinal virtues in Hinduism, and in Buddhism it is believed to be necessary for protecting one’s mental well-being. In Christianity, it is a duty to forgive even when the receiver is undeserving, and there is even research that demonstrates the benefits of forgiveness. However, despite that forgiveness is often seen to be beneficial to the forgiver, we don’t always forgive.
It seems silly that we would ever refuse to forgive when viewing forgiveness in this frame of mind, but the article encourages us to view forgiveness as a decision like any other. Assume that a potential forgiver wants to forgive if the seeker is worthy, but wishes to withhold forgiveness if the seeker is unworthy. Then there are four cases to be examined, the first of which is a Hit (H), where the potential forgive grants forgiveness to a worthy seeker. The second is the case of the Correct Rejection (CR), where the giver withholds forgiveness from an unworthy seeker. In either of these cases, the giver makes the “correct” decision. But then, there also exist cases where the giver makes the “wrong” decision. Consider the case of the False Alarm (FA), where the giver grants forgiveness to an unworthy seeker, as well as the Miss (M), where the giver refuses forgiveness to a worthy seeker. The article assumes that the preference of the giver lies in the following order: H > CR > M > FA. Here, decision theory reveals that it is not always in the giver’s best interest to forgive, which is not always apparent without a methodical case by case analysis.
Now, we consider the issue from a game theory perspective, analyzing the relationship between the two decision makers of the game: the giver and the seeker. Both the giver and the seeker have the choice to either cooperate or defect, as defined by the article. The seeker has the choice to ask for forgiveness (cooperation) or not to ask (defection), and the giver may either forgive (cooperation) or refuse to forgive (defection). Hence, there are four possible cases: (A) the case where the seeker asks for forgiveness and the giver grants it, (B) the case where the seeker does not ask for forgiveness and the giver does not grant it, (C) the case where the giver forgives without being asked, and (D) the case where the giver refuses to forgive after being asked. The article asserts that the giver prefers the cases in the order A > B > D > C while the seeker prefers the cases in the order C > A > B > D.
Assigning arbitrary payoffs from 1 to 4 for the giver and seeker, we obtain the following payoff matrix:
| Ask forgiveness | Refuse to ask | |
| Forgive | 4, 3 | 1, 4 |
| Refuse forgiveness | 2, 1 | 2, 3 |
From the matrix, we see that regardless of the giver’s decision, the seeker will have a higher payoff if he refuses to ask for forgiveness. As such is the case, the giver would theoretically assume that the seeker will not ask. Thus the giver will choose to withhold forgiveness. In this problem concerning granting and asking forgiveness, the payoff matrix of the game shows that the seeker will not ask for forgiveness, and neither will the giver grant forgiveness.