It Pays to Pay in Bi-Matrix Games: a Rational Explanation for Bribery

We discuss bribery as a rational behaviour in two player bi-matrix games in game settings, where one player can assign the strategies to the other player. This can be observed as leader (or: Stackelberg) equilibria, where a leader assigns the strategy to herself and to the other player, who follows this lead unless he has an incentive not to. We make the rational assumption that a leader can further incentivise decisions of her follower, by bribing him with a small payoff value, and show that she can improve her gain this way. This results in an asymmetric equilibrium for a strategy profile: the incentive equilibrium. By ’asymmetric equilibrium’, we refer to the strategy profile where a leader might benefit from deviation, while her follower does not. We observe that this concept is strong enough to obtain social optimum in the classic example of the prisoners’ dilemma. We show that computing such incentive equilibria is no more expensive than computing leader equilibria: as opposed to Nash equilibria, they are both tractable. We evaluated our techniques on a large set of benchmarks (100,000 bi-matrix games) and provide the experimental results for incentive equilibrium.