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Stabilizing Welfare-Maximizing Decisions via Endogenous Transfers

Joshua Kavner

TL;DR

This work develops a transferable-utility framework for decentralized social choice with endogenous, outcome-contingent transfers, enabling agents to contract before voting to stabilize welfare-maximizing decisions. By formalizing utilities as $U_i(a)=u_i(a)+\tau_i(a)$ with contracts $c_{i\to j}(a)$ and budget balance, it shows that IR-SNE exist under the consensus AMR rule and can be constructed efficiently, implementing welfare-maximizing outcomes. For broader AMR rules, the authors derive tight necessary conditions for profitable coalitional deviations, thereby sharply limiting destabilizing coalitions. Conceptually, the framework bridges cooperative and noncooperative perspectives, demonstrating that transferable utility can achieve core-like stability and restore efficiency and budget balance even in the presence of classical impossibility results. These results offer a practical, robust mechanism for coordinating large-scale strategic multiagent systems.

Abstract

Many multiagent systems rely on collective decision-making among self-interested agents, which raises deep questions about coalition formation and stability. We study social choice with endogenous, outcome-contingent transfers, where agents voluntarily form contracts that redistribute utility depending on the collective decision, allowing fully strategic, incentive-aligned coalition formation. We show that under consensus rules, individually rational strong Nash equilibria (IR-SNE) always exist, implementing welfare-maximizing outcomes with feasible transfers, and provide a simple, efficient algorithm to construct them. For more general anonymous, monotonic, and resolute rules, we identify necessary conditions for profitable deviations, sharply limiting destabilizing coalitions. By bridging cooperative and noncooperative perspectives, our approach shows that transferable utility can achieve core-like stability, restoring efficiency and budget balance even where classical impossibility results apply. Overall, this framework offers a practical and robust way to coordinate large-scale strategic multiagent systems.

Stabilizing Welfare-Maximizing Decisions via Endogenous Transfers

TL;DR

This work develops a transferable-utility framework for decentralized social choice with endogenous, outcome-contingent transfers, enabling agents to contract before voting to stabilize welfare-maximizing decisions. By formalizing utilities as with contracts and budget balance, it shows that IR-SNE exist under the consensus AMR rule and can be constructed efficiently, implementing welfare-maximizing outcomes. For broader AMR rules, the authors derive tight necessary conditions for profitable coalitional deviations, thereby sharply limiting destabilizing coalitions. Conceptually, the framework bridges cooperative and noncooperative perspectives, demonstrating that transferable utility can achieve core-like stability and restore efficiency and budget balance even in the presence of classical impossibility results. These results offer a practical, robust mechanism for coordinating large-scale strategic multiagent systems.

Abstract

Many multiagent systems rely on collective decision-making among self-interested agents, which raises deep questions about coalition formation and stability. We study social choice with endogenous, outcome-contingent transfers, where agents voluntarily form contracts that redistribute utility depending on the collective decision, allowing fully strategic, incentive-aligned coalition formation. We show that under consensus rules, individually rational strong Nash equilibria (IR-SNE) always exist, implementing welfare-maximizing outcomes with feasible transfers, and provide a simple, efficient algorithm to construct them. For more general anonymous, monotonic, and resolute rules, we identify necessary conditions for profitable deviations, sharply limiting destabilizing coalitions. By bridging cooperative and noncooperative perspectives, our approach shows that transferable utility can achieve core-like stability, restoring efficiency and budget balance even where classical impossibility results apply. Overall, this framework offers a practical and robust way to coordinate large-scale strategic multiagent systems.
Paper Structure (23 sections, 18 theorems, 54 equations, 1 algorithm)

This paper contains 23 sections, 18 theorems, 54 equations, 1 algorithm.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. A model of endogenous transfers in social choice.
  4. Strong Nash equilibrium under consensus rules.
  5. Necessary conditions for deviations in general.
  6. A bridge between cooperative and noncooperative social choice.
  7. Related Work
  8. Preliminaries
  9. Model.
  10. Contracts.
  11. Strategic Voting.
  12. Coalitional Deviation.
  13. Main Results
  14. Truthful Considerations and Observable Participation
  15. IR–SNE for Consensus
  16. ...and 8 more sections

Key Result

Lemma 1

Given base utilities $u$, consider states $(P, \tau, S)$ and $(P', \tau', S')$. If there exists an alternative $a \in \mathcal{A}$ such that either (1) $\tau_i(a) \le 0$ and $\tau'_i(a) < \tau_i(a)$, or (2) $\tau_i(a) \ge 0$ and $\tau'_i(a) < 0$, then $i \in S'$.

Theorems & Definitions (38)

  • Definition 1: Coalitional Deviation
  • Definition 2: Individually Rational Deviation
  • Definition 3: Strong Nash Equilibrium
  • Example 1
  • Lemma 1: Observable Participation
  • proof
  • Proposition 1: Non-Welfare-Maximizing States Are Not SNE
  • Definition 4: Fully Covered
  • Proposition 2: Truthful State Is SNE Under Consensus
  • Lemma 2
  • ...and 28 more