Mechanism Design in Max-Flows
Shengyuan Huang, Wenjun Mei, Xiaoguang Yang, Zhigang Cao
TL;DR
This work addresses revenue allocation in max-flow games with privately owned edge capacities. It proves that core-selection mechanisms cannot guarantee truthful reporting and introduces five desirable mechanism properties: DSIC, SIR, SP, MP, and CM. The Shapley value mechanism is DSIC and SIR but fails SP, MP, and CM, motivating a minimal-cut based mechanism (MC) that satisfies all five properties by allocating stand-alone values to $s$-$t$ edges and distributing the remainder across minimal cuts with proportional edge shares. The MC mechanism thus offers a robust, structure-aware approach to truthful revenue sharing in flow networks, with discussion of CM implications and computational considerations for minimal cuts.
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.