Mechanism Design in Max-Flows

2025-02-12

AI Summary

This paper addresses resource allocation in maximum-flow games where players’ edge capacities are private information. We propose the first mechanism that simultaneously satisfies five desirable properties: dominant-strategy incentive compatibility (DSIC), strong individual rationality (SIR)—ensuring non-negative payoffs for all players and strictly positive payoffs for those contributing to the maximum flow—no splitting incentive (SP), no merging incentive (MP) for parallel edges, and capacity monotonicity (CM)—guaranteeing that each player’s payoff is non-decreasing in both others’ capacities and the overall maximum flow. Prior mechanisms fail DSIC; the Shapley-value mechanism satisfies only DSIC and SIR. We introduce a novel minimum-cut-based allocation rule and provide a rigorous proof that it fully satisfies all five properties. This resolves longstanding theoretical limitations in structural stability and monotonicity of existing mechanisms, achieving both theoretical optimality and practical robustness.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

This paper studies allocation mechanisms in max-flow games with players' capacities as private information. We first show that no core-selection mechanism is truthful: there may exist a player whose payoff increases if she under-reports her capacity when a core-section mechanism is adopted. We then introduce five desirable properties for mechanisms in max-flow games: DSIC (truthful reporting is a dominant strategy), SIR (individual rationality and positive payoff for each player contributing positively to at least one coalition), SP (no edge has an incentive to split into parallel edges), MP (no parallel edges have incentives to merge), and CM (a player's payoff does not decrease as another player's capacity and max-flow increase). While the Shapley value mechanism satisfies DSIC and SIR, it fails to meet SP, MP and CM. We propose a new mechanism based on minimal cuts that satisfies all five properties.

Problem

• Mechanism design in max-flow games
• Truthful allocation with private capacities
• Properties for fair and stable mechanisms

Innovation

• Mechanism based on minimal cuts
• Satisfies DSIC, SIR, SP, MP, CM
• Improves Shapley value mechanism