Game theory study uncovers secret to taming bullies and extortionists

Game theory is a branch of mathematics that studies strategic interactions. The most famous example is the prisoners' dilemma, in which two separated prisoners must independently decide to cooperate and face minor consequences, or betray the other for potential personal gain, risking severe consequences if both choose betrayal.

A new study from Dartmouth, published in PNAS Nexus, used game theory to develop "unbending strategies" to beat bullies. The strategies in the study, such as memory-one PSO Gambler, WSLS, and Zero Determinant, steer the dynamics toward fairness and cooperation, even when faced with players who try to exploit others.


"Unbending players who choose not to be extorted can resist by refusing to fully cooperate. They also give up part of their own payoff, but the extortioner loses even more," said Chen, who is now an assistant professor at the Beijing University of Posts and Telecommunications.

"Our work shows that when an extortioner is faced with an unbending player, their best response is to offer a fair split, thereby guaranteeing an equal payoff for both parties," she said. "In other words, fairness and cooperation can be cultivated and enforced by unbending players."

"The practical insight from our work is for weaker parties to be unbending and resist being the first to compromise, thereby transforming the interaction into an ultimatum game in which extortioners are incentivized to be fairer and more cooperative to avoid 'lose-lose' situations," Fu said.