In strategic games such as the prisoner's dilemma, allowing players to make binding offers of utility transfers before play has been shown to alter incentives and potentially support cooperative outcomes. These preplay exchange mechanisms reshape payoffs by transferring utility while being contingent on actions; however, they typically require side payments that can reduce individual benefits relative to joint cooperation. In this paper, we extend the analysis to a finite $n$-player prisoner's dilemma with ordered strategy sets, defined such that any restriction of strategies by any subset of players still yields a prisoner's dilemma. To achieve a robust cooperative outcome that resists group deviations, we introduce a novel class of mechanisms: $\textit{losing contracts}$. Unlike transfer-based preplay mechanisms, losing contracts require players to irrevocably reduce their own utility if they defect, thereby aligning individual incentives with cooperation without inter-player payments. With appropriately chosen loss amounts, losing contracts induce joint cooperation as the unique strong Nash equilibrium in the modified game and in every restricted game within it, ensuring that cooperative incentives persist even under possible external constraints on strategy sets. We show that our contracts can be constructively defined, reducing the preplay stage to a simple and binary decision for each player: whether to sign the contract or not. Furthermore, if the losing contract is only executed when all players sign, signing is a strictly dominant strategy for all. Finally, we extend these results to certain public goods games.

翻译：在囚徒困境这类策略博弈中，允许参与者在行动前做出具有约束力的效用转移承诺，已被证明可以改变激励结构并可能支持合作结果。这些预博弈交换机制通过以行动为条件转移效用重塑收益，但通常需要附带支付，这可能导致相对于联合合作而言减少个体收益。本文将该分析扩展至具有有序策略集的有限$n$人囚徒困境，该博弈定义为：任何子集的策略限制仍构成囚徒困境。为抵御群体偏离以实现稳健的合作结果，我们引入一类新型机制：$\textit{失约}$。与基于转移的预博弈机制不同，失约要求参与者若背叛则不可撤销地降低自身效用，从而在没有参与者间支付的情况下协调个体激励与合作。通过适当选择的损失额度，失约在修正博弈及其所有受限子博弈中诱导联合合作成为唯一的强纳什均衡，确保即使在可能的策略集外部约束下合作激励仍能持续。我们证明此类合约可被建设性定义，将预博弈阶段简化为每个参与者的简单二元决策：是否签署合约。此外，若失约仅在全体签署时生效，则签署对所有参与者均为严格占优策略。最后，我们将这些结果拓展至特定公共物品博弈。