Mechanism Design in Max-Flows

TL;DR

This paper investigates truthful mechanism design in max-flow games with private capacities, revealing limitations of core-selection mechanisms and proposing a new minimal cut-based mechanism that satisfies multiple desirable properties.

Contribution

It introduces a novel mechanism based on minimal cuts that satisfies five key properties, improving upon existing Shapley value mechanisms.

Findings

Core-selection mechanisms are not truthful in max-flow games.

The Shapley value mechanism satisfies some properties but not all.

The proposed minimal cut-based mechanism satisfies all five desirable properties.

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.