Maximizing Social Welfare with Side Payments

2025-08-09

AI Summary

In standard commitment games, one-shot side payments often induce a prisoner’s dilemma, leading to inefficient equilibria—even when the underlying game admits a Pareto-optimal Nash equilibrium. Method: This paper proposes a phased, capped pre-commitment mechanism that integrates multi-round, outcome-contingent transfer payments with a unanimity rule, enabling gradual implementation of side contracts within a finite number of steps. Contribution: The mechanism avoids strategic abuse inherent in single-stage commitments and, starting from any non-degenerate Nash equilibrium, achieves all strictly Pareto-superior welfare allocations. We formally prove that it guarantees strict Pareto improvements and fully restores the efficiency potential of side payments. By doing so, it provides a feasible and robust institutional design for enhancing aggregate social welfare within a non-cooperative framework.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications
• Security and Privacy: Privacy-enhancing technologies

Abstract

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 $Γ$ with a non-degenerate Nash equilibrium $vecσ$, this protocol implements every welfare-maximizing payoff profile that emph{strictly} Pareto-improves $vecσ$. Thus, gradual and bounded commitments restore the full efficiency potential of side payments while avoiding the inefficiencies identified by Jackson and Wilkie.

Problem

• Preventing inefficiency in games with side payments
• Avoiding prisoner's dilemma in commitment strategies
• Implementing welfare-maximizing payoff profiles gradually

Innovation

• Staged-commitment protocol for side payments
• Capped incremental transfers over multiple rounds
• Unanimous consent required for continuation