From the Editor’s Desk
22nd July 2023

Game Theory models the strategic interaction between at least two players in a situation with set rules and outcomes which helps predict, understand, and explain activities. The players in Game Theory do not know what the other party could do, but they are aware of what actions they can take. Moreover, one party’s choices will influence the outcome for the other, which means that the parties are interdependent.

This article explores the use of Mathematics in an area of law called mediation. Mediation is not like adjudication before a judge in a court of law, but parties have the opportunity to present their ideas and views to an objective mediator who will guide the parties to achieve a common solution in line with their goals. The process of mediation could be likened to a game, where the outcome of the mediation depends on the actions of the parties, with a payoff received by each party after a certain outcome, and parties receive a set of common information.

A key concept in Game Theory is the Nash equilibrium, when both parties cannot independently change their strategy without ending up in a less desirable position. To illustrate this concept, consider the Nash Equilibrium within the Prisoner’s Dilemma, where both the prisoners confess to reduce the risk of the worst possible outcome, when maintaining their innocence would have landed them both in better consequences.

In the Prisoner’s Dilemma, there are two criminals who are being interrogated separately. The state lacks the evidence to convict them of the crime they have committed – only the evidence to convict both on a lesser charge, resulting in each spending 1 year in jail. The prosecutor wants to convict each criminal on the more serious charge and incentivises each criminal to confess and implicate the other. He tells each criminal that if he confesses but his partner does not, he will go free, and his partner will be locked up for 10 years. If both confess, they will be put away for 3 years, but if neither confess, both will be let go. The dilemma lies in whether both prisoners will refuse to confess without communicating with each other, or whether they will cheat.

Game Theory can be applied to the mediation process as with proper communication facilitated by an observant mediator, parties can avoid Nash equilibriums and strive for better outcomes. The Nash Equilibrium is a valuable strategy for mediators as they can gauge the parties’ understanding of the mediation process and their plans to walk away from it with a desirable outcome. The Nash Equilibrium is highly relevant during reframing as the mediators must avoid a situation where the parties “trap” themselves within a Nash Equilibrium by refusing to compromise and communicate.

In the Prisoner’s Dilemma, both criminals want to reduce the risk of the worst possible outcome and confess although staying silent would have been best for both. The Nash Equilibrium arose due to the prisoners’ inability to communicate. By acting out of self-interest while trying to guess at the other party’s decision, the parties in mediation could similarly trap themselves in a Nash Equilibrium as their actions are based on what they think the other party would do.

In mediation, law students who are aspiring to be mediators could view mediation in the Game Theory lens – that each party is an agent who makes certain decisions based on certain cues. Good mediators will then facilitate communication and attempt to defuse the tension between parties so that parties do not act rashly, trapping them in a cycle of decisions which would leave them worse off than before.