Generalized Incremental Mechanisms for Scheduling Games

We study the problem of devising truthful mechanisms for cooperative cost sharing games that realize (approximate) budget balance and social cost. Recent negative results show that group-strategyproof mechanisms can only achieve very poor approximation guarantees for several fundamental cost sharing games. Driven by these limitations, we consider cost sharing mechanisms that realize the weaker notion of weak groupstrategyproofness. Mehta et al. [Games and Economic Behavior, 67:125–155, 2009] recently introduced the broad class of weakly group-strategyproof acyclic mechanisms and show that several primal-dual approximation algorithms naturally give rise to such mechanisms with attractive approximation guarantees. In this paper, we provide a simple yet powerful approach that enables us to turn any r-approximation algorithm into a r-budget balanced acyclic mechanism. We demonstrate the applicability of our approach by deriving weakly group-strategyproof mechanisms for several fundamental scheduling problems that outperform the best possible approximation guarantees of Moulin mechanisms. The mechanisms that we develop for completion time scheduling problems are the first mechanisms that achieve constant budget balance and social cost approximation factors. Interestingly, our mechanisms belong to the class of generalized incremental mechanisms proposed by Moulin [Social Choice and Welfare, 16:279–320, 1999]

An Online Cost Allocation Model for Horizontal Supply Chains

65A0533 TO 18.1The problem we study in this report focuses on routing in real time a fleet of capacitated vehicles to satisfy requests submitted by a set of customers while assigning the service cost fairly among the requested customers. During each operation, only a subset of the customers request service with some of them known at the beginning of the operation and the rest arriving dynamically during the day. The exact time points of these dynamic requests are unknown at the beginning of the day. We propose a Hybrid Proportional Online Cost Sharing (HPOCS) mechanism to tackle the cost sharing problem and analyze its performance using simulation instances. Although HPOCS does satisfy the desirable properties, namely online fairness, budget balance, immediate response, individual rationality and ex-post incentive compatibility, it has certain drawbacks when the number of dynamic customers is small and does not give sufficient incentive for customers to request early. Therefore, we make two extensions to HPOCS: 1) we extend it to introduce the idea of discounts to encourage customers to submit their request in advance to better facilitate efficient vehicle routing; 2) we extend it to incorporate a dynamic vehicle routing framework that periodically re-optimizes the current vehicle routes. Both extensions include performance analysis and the tradeoff between the performance and the loss of certain desirable properties. In general, our proposed mechanism, along with its extensions can generate efficient cost sharing solutions that satisfy desirable properties, reduce overall operating cost (mainly vehicle miles travelled) and provide sufficient incentives to customers to request service early in support of horizontal cooperation