We examine normal-form games in which players may \emph{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 \emph{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 $\Gamma$ with a non-degenerate Nash equilibrium $\vec{\sigma}$, this protocol implements every welfare-maximizing payoff profile that \emph{strictly} Pareto-improves $\vec{\sigma}$. Thus, gradual and bounded commitments restore the full efficiency potential of side payments while avoiding the inefficiencies identified by Jackson and Wilkie.

翻译：本文研究正规形式博弈中参与者在选择行动前可预先承诺结果导向转移支付的情形。在该模型的一次性版本中，Jackson与Wilkie证明附带契约可能产生反效果：即使存在帕累托最优纳什均衡的博弈，在允许无限制同步承诺后也可能退化为低效均衡。其根本原因在于囚徒困境效应——每位参与者均可利用其承诺权力重塑对自身有利的均衡，从而损害整体福利。为规避此问题，我们提出分阶段承诺协议：参与者仅可在多轮次中以小额上限递增方式承诺转移支付，且每阶段需经全体同意方可延续。我们证明，从任意具有非退化纳什均衡$\vec{\sigma}$的有限博弈$\Gamma$出发，该协议能实现所有严格帕累托改进$\vec{\sigma}$的社会福利最大化收益配置。因此，渐进且有界的承诺机制在恢复附带支付完全效率潜力的同时，避免了Jackson与Wilkie所指出的效率损失问题。