Bargaining Mechanisms for One-Way Games

TL;DR

This paper introduces one-way games where some players' payoffs depend solely on their own actions, explores the limitations of traditional mechanisms in such games, and proposes a privacy-preserving bargaining mechanism to improve efficiency.

Contribution

It defines one-way games, analyzes the limitations of existing mechanisms, and proposes a novel privacy-preserving bargaining mechanism that enhances efficiency.

Findings

Equilibrium outcomes can be far from the social optimum in one-way games.

No mechanism can be simultaneously incentive-compatible, budget-balanced, and efficient in this setting.

A single-offer bargaining mechanism improves efficiency while satisfying key incentive and rationality constraints.

Abstract

We introduce one-way games, a framework motivated by applications in large-scale power restoration, humanitarian logistics, and integrated supply-chains. The distinguishable feature of the games is that the payoff of some player is determined only by her own strategy and does not depend on actions taken by other players. We show that the equilibrium outcome in one-way games without payments and the social cost of any ex-post efficient mechanism, can be far from the optimum. We also show that it is impossible to design a Bayes-Nash incentive-compatible mechanism for one-way games that is budget-balanced, individually rational, and efficient. To address this negative result, we propose a privacy-preserving mechanism that is incentive-compatible and budget-balanced, satisfies ex-post individual rationality conditions, and produces an outcome which is more efficient than the equilibrium without payments. The mechanism is based on a single-offer bargaining and we show that a randomized multi-offer extension brings no additional benefit.