Cost-sharing Problems Research Articles

Cost Sharing over Combinatorial Domains

We study the problem of designing cost-sharing mechanisms for combinatorial domains. Suppose that multiple items or services are available to be shared among a set of interested agents. The outcome of a mechanism in this setting consists of an assignment, determining for each item the set of players who are granted service, together with respective payments. Although there are several works studying specialized versions of such problems, there has been almost no progress for general combinatorial cost-sharing domains until recently [ 9 ]. Still, many questions about the interplay between strategyproofness, cost recovery, and economic efficiency remain unanswered. The main goal of our work is to further understand this interplay in terms of budget balance and social cost approximation. Towards this, we provide a refinement of cross-monotonicity (which we term trace-monotonicity ) that is applicable to iterative mechanisms. The trace here refers to the order in which players become finalized. On top of this, we also provide two parameterizations (complementary to a certain extent) of cost functions, which capture the behavior of their average cost-shares. Based on our trace-monotonicity property, we design an Iterative Ascending Cost-Sharing Mechanism, which is applicable to the combinatorial cost-sharing setting with symmetric submodular valuations. Using our first cost function parameterization, we identify conditions under which our mechanism is weakly group-strategyproof, \( O(1) \) -budget-balanced, and \( O(H_n) \) -approximate with respect to the social cost. Furthermore, we show that our mechanism is budget-balanced and \( H_n \) -approximate if both the valuations and the cost functions are symmetric submodular; given existing impossibility results, this is best possible. Finally, we consider general valuation functions and exploit our second parameterization to derive a more fine-grained analysis of the Sequential Mechanism introduced by Moulin. This mechanism is budget balanced by construction, but in general, only guarantees a poor social cost approximation of \( n \) . We identify conditions under which the mechanism achieves improved social cost approximation guarantees. In particular, we derive improved mechanisms for fundamental cost-sharing problems, including Vertex Cover and Set Cover.

Accounting for Needs in Cost Sharing

Abstract We introduce basic needs in cost-sharing problems so that agents with higher needs are not penalized, all the while holding them responsible for their consumption. We characterize axiomatically two families of cost-sharing rules, each favoring one aspect—compensation or responsibility—over the other. We also identify specific variants of those rules that protect small users from the cost externality imposed by larger users. Lastly, we show how one can implement these schemes with realistic informational assumptions; i.e., without making explicit interpersonal comparisons of needs and consumption.

The reverse self-dual serial cost-sharing rule

In this study we define a cost-sharing rule for cost-sharing problems. This rule is related to the serial cost-sharing rule defined by Moulin and Shenker (Econometrica 60:1009–1037, 1992). We give some formulas and axiomatic characterizations for the new rule. The axiomatic characterizations are related to some previous ones provided by Moulin and Shenker (J. Econ. Theory 64:178–201, 1994) and Albizuri (Theory Decis. 69:555–567, 2010).

Research on Optimization Model of Taxi-Carpooling Expenses

In order to solve cost-sharing problems for taxi-carpooling passengers, the optimization model of sharing taxi-carpooling expenses was established taking both taxi-driver and passengers’ benefits into fully consideration. Based on the fact that passengers would pay for their own share in proportion, the optimization model was made with the objective function aiming at minimum consumption of time and money. In view of its features, the theoretical model was further developed comparing expenses in theory with that under existing conditions. The results show that this optimization model of sharing taxi-carpooling expenses can meet the need of both passengers and taxi driver. Moreover, the research findings will provide a firm technical support and guarantee for a satisfactory solution to cost-sharing problems on taxi-carpooling.

The [formula omitted]-serial cost-sharing rule

In this paper we present a family of cost-sharing rules for cost-sharing problems. Each rule in this family can be seen as a combination of the serial cost-sharing rule ( Moulin and Shenker, 1992) and the dual serial cost-sharing rule ( Albizuri and Zarzuelo, 2007). The parameter α determines how this combination is obtained. We also provide an axiomatization of this family by using a weaker axiom than the well-known Independence of higher demands axiom ( Moulin and Shenker, 1992).

Quantifying inefficiency in cost-sharing mechanisms

In a cost-sharing problem, several participants with unknown preferences vie to receive some good or service, and each possible outcome has a known cost. A cost-sharing mechanism is a protocol that decides which participants are allocated a good and at what prices. Three desirable properties of a cost-sharing mechanism are: incentive-compatibility, meaning that participants are motivated to bid their true private value for receiving the good; budget-balance, meaning that the mechanism recovers its incurred cost with the prices charged; and economic efficiency, meaning that the cost incurred and the value to the participants are traded off in an optimal way. These three goals have been known to be mutually incompatible for thirty years. Nearly all the work on cost-sharing mechanism design by the economics and computer science communities has focused on achieving two of these goals while completely ignoring the third. We introduce novel measures for quantifying efficiency loss in cost-sharing mechanisms and prove simultaneous approximate budget-balance and approximate efficiency guarantees for mechanisms for a wide range of cost-sharing problems, including all submodular and Steiner tree problems. Our key technical tool is an exact characterization of worst-case efficiency loss in Moulin mechanisms, the dominant paradigm in cost-sharing mechanism design.

The self-dual serial cost-sharing rule

In this study, we present a cost-sharing rule for cost-sharing problems. This rule prescribes the same allocations in a problem and in its dual one. Moreover, in some specific problems it gives the same allocations as the serial cost-sharing rule (Moulin and Shenker, Econometrica, 60, 1009–1037, 1992) does in a related problem. That is why we call it as the self-dual serial cost-sharing rule. We give two axiomatizations of this new rule and another one for the serial cost-sharing rule.

Beyond Moulin mechanisms

The only known general technique for designing truthful and approximately budget-balanced cost-sharing mechanisms with good efficiency or computational complexity properties is due to Moulin [1999. Incremental cost sharing: Characterization by coalition strategy-proofness. Soc. Choice Welfare 16 (2), 279–320]. For many fundamental cost-sharing applications, however, Moulin mechanisms provably suffer from poor budget-balance, poor economic efficiency, or both. We propose acyclic mechanisms, a new framework for designing truthful and approximately budget-balanced cost-sharing mechanisms. Acyclic mechanisms strictly generalize Moulin mechanisms and offer three important advantages. First, it is easier to design acyclic mechanisms than Moulin mechanisms: many classical primal-dual algorithms naturally induce a non-Moulin acyclic mechanism with good performance guarantees. Second, for important classes of cost-sharing problems, acyclic mechanisms have exponentially better budget-balance and economic efficiency than Moulin mechanisms. Finally, while Moulin mechanisms have found application primarily in binary demand games, we extend acyclic mechanisms to general demand games, a multi-parameter setting in which each bidder can be allocated one of several levels of service.

The dual serial cost-sharing rule

In this paper we present a cost-sharing rule for cost-sharing problems. This rule is called the dual serial cost-sharing rule because it prescribes the same allocations as the serial cost-sharing rule in the dual problem. We give two axiomatizations of this new rule, one of them by means of a consistency property. Moreover, we provide a mechanism to implement this rule.