We examine normal-form games in which players may pre-commit to outcome-contingent transfers before choosing their actions. In the one-shot version of this model, Jackson and Wilkie showed that side contracting can backfire: even a game with a Pareto-optimal Nash equilibrium can devolve into inefficient equilibria once unbounded, simultaneous commitments are allowed. The root cause is a prisoner's dilemma effect, where each player can exploit her commitment power to reshape the equilibrium in her favor, harming overall welfare. To circumvent this problem we introduce a staged-commitment protocol. Players may pledge transfers only in small, capped increments over multiple rounds, and the phase continues only with unanimous consent. We prove that, starting from any finite game Γ with a non-degenerate Nash equilibrium σ, this protocol implements every welfare-maximizing payoff profile that strictly Pareto-improves σ. Thus, gradual and bounded commitments restore the full efficiency potential of side payments while avoiding the inefficiencies identified by Jackson and Wilkie.
Geffner et al. (Sun,) studied this question.