Achieving Coordination in Non-Cooperative Joint Replenishment Games

2025-10-12

AI Summary

This paper addresses the design of cost-allocation rules in noncooperative joint replenishment games, aiming to coordinate retailers’ autonomous optimization of replenishment intervals to minimize the system’s long-run average cost. We propose a class of allocation mechanisms that apportion the supplier’s setup cost according to pre-specified weights, proving they satisfy agent-response monotonicity and admit a computationally efficient, payoff-dominant pure-strategy Nash equilibrium. Under an infinite-horizon deterministic model, coordination efficiency is quantified via the Price of Stability (PoS): one rule leveraging retailers’ holding-cost rates achieves PoS = 1.25—nearly optimal; another rule requiring no private information also attains high efficiency. The core contribution is a cost-sharing framework that simultaneously ensures computational tractability, incentive compatibility, and near-optimal system-wide performance.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Coordination and Collaboration
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We analyze an infinite-horizon deterministic joint replenishment model from a non-cooperative game-theoretical approach. In this model, a group of retailers can choose to jointly place an order, which incurs a major setup cost independent of the group, and a minor setup cost for each retailer. Additionally, each retailer is associated with a holding cost. Our objective is to design cost allocation rules that minimize the long-run average system cost while accounting for the fact that each retailer independently selects its replenishment interval to minimize its own cost. We introduce a class of cost allocation rules that distribute the major setup cost among the associated retailers in proportion to their predefined weights. For these rules, we establish a monotonicity property of agent better responses, which enables us to prove the existence of a payoff dominant pure Nash equilibrium that can also be computed efficiently. We then analyze the efficiency of these equilibria by examining the price of stability (PoS), the ratio of the best Nash equilibrium's system cost to the social optimum, across different information settings. In particular, our analysis reveals that one rule, which leverages retailers' own holding cost rates, achieves a near-optimal PoS of 1.25, while another rule that does not require access to retailers' private information also yields a favorable PoS.

Problem

• Designing cost allocation rules for joint retailer replenishment games
• Minimizing long-run system costs with independent retailer decisions
• Analyzing equilibrium efficiency through price of stability metrics

Innovation

• Cost allocation rules distribute major setup costs proportionally
• Monotonicity property ensures existence of Nash equilibrium
• Rules achieve near-optimal price of stability efficiently