Serial Cost Sharing Research Articles

Cost Sharing Mechanisms for Fair Pricing of Resource Usage

We propose a simple and intuitive cost mechanism which assigns costs for the competitive usage of m resources by n selfish agents. Each agent has an individual demand; demands are drawn according to some probability distribution. The cost paid by an agent for a resource it chooses is the total demand put on the resource divided by the number of agents who chose that same resource. So, resources charge costs in an equitable, fair way, while each resource makes no profit out of the agents. We call our model the Fair Pricing model. Its fair cost mechanism induces a non-cooperative game among the agents. To evaluate the Nash equilibria of this game, we introduce the Diffuse Price of Anarchy, as an extension of the Price of Anarchy that takes into account the probability distribution on the demands. We prove: Towards the end, we consider two closely related cost sharing models, namely the Average Cost Pricing and the Serial Cost Sharing models, inspired by Economic Theory. In contrast to the Fair Pricing model, we prove that pure Nash equilibria do exist for both these models.

An experimental comparison of collective choice procedures for excludable public goods

This paper compares three collective choice procedures for the provision of excludable public goods under incomplete information. One, serial cost sharing (SCS), is budget balanced, individually rational, anonymous and strategy proof. The other two are “hybrid” procedures: voluntary cost sharing with proportional rebates (PCS) and with no rebates (NR). PCS satisfies all these properties except strategy proofness, and NR satisfies all the properties except for strategy proofness and budget balance. However, PCS and NR do not exclude any potential users, and they do not require equal cost shares, thereby overcoming the two main sources of inefficiency with SCS. We characterize the Bayesian Nash equilibria (BNE) of the hybrid mechanisms and conduct laboratory experiments to compare the performance of the three mechanisms. We find that PCS produces significantly more efficient allocations than either SCS or NR.

Serial cost sharing in multidimensional contexts

The Serial Cost Sharing Rule was originally conceived for situations where the demands of agents pertain to a homogeneous private good, produced by an unreplicable technology. In this context, it is endowed with a variety of desirable equity and coherency properties. This paper investigates the extension of this rule to the context where agents request many goods that may be public, private or specific to some of them, where aggregation of demands may be very general and where demands may have to be scaled in a non-proportional way, more precisely along paths, in order to compute cost shares. We propose the Path Serial Rule to treat these general problems and we explore its properties and characteristics. Some properties are transposed directly from the single good to the general context. Other properties must be weakened by requiring that they hold only on the paths along which demands must be scaled when needed. This is the case of the serial principle, which we show is incompatible with the basic equal treatment of equals. The resulting weaker Path Serial Principle characterizes the Path Serial Rule together with the Equal Treatment of Equivalent Demands in terms of stand alone costs, a stronger form of Equal Treatment of Equals.

Strategic properties of heterogeneous serial cost sharing

We show that the Serial Cost Sharing method for heterogeneous goods [J. Econ. Theory 87 (1999) 275], and a large number of other cost sharing mechanisms, have the same strong strategic properties as the Serial Cost Sharing method for homogeneous goods [J. Econ. Theory 64 (1992) 178; Econometrica 60 (1992) 1009], including uniqueness of the Nash equilibrium for all utility profiles and cost functions, dominance solvability, solvability in overwhelmed actions, and robustness to coalitional deviations. We describe several applications to cost/surplus sharing and the Internet.

Three Methods to Share Joint Costs or Surplus

We study cost sharing methods with variable demands of heterogeneous goods, additive in the cost function and meeting the dummy axiom. We consider four axioms: scale invariance (SI); demand monotonicity (DM); upper bound for homogeneous goods (UBH) placing a natural cap on cost shares when goods are homogeneous; average cost pricing for homogeneous goods (ACPH). The random order values based on stand alone costs are characterized by SI and DM. Serial costsharing, by DM and UB; the Aumann–Shapley pricing method, by SI and ACPH. No other combination of the four axioms is compatible with additivity and dummy. Journal of Economic Literature Classification Numbers: C71, D62, D63

Decreasing Serial Cost Sharing under Economies of Scale

We consider the problem of cost sharing in the presence of increasing returns to scale and potential strategic behavior on the part of consumers. We show that any smooth and strictly monotonic mechanism for which a Nash equilibrium exists for all profiles of convex and monotonic preferences must be dictatorial. However, we propose a cost sharing mechanism, the decreasing serial mechanism, for which an interesting domain restriction ensures existence of a noncooperative equilibrium for its cost sharing game. A characterization theorem of the mechanism based on the strategic properties of existence, uniqueness, and efficiency of its noncooperative equilibrium is provided.Journal of Economic LiteratureClassification Numbers: C70, C72, D70.

Equitable Nonlinear Price Regulation: An Alternative Approach to Serial Cost Sharing

This paper examines the serial cost share rule from a perspective of nonlinear pricing. The expenditure function concept is introduced to facilitate the modelling of a wide variety of pricing mechanisms including those featuring head taxes, block pricing, or volume discounts. Axioms on equitable price regulation are shown to characterize the serial expenditure function, a pricing mechanism which induces the distribution of serial cost shares. Several such characterizations are offered in a variety of technological contexts.Journal of Economic LiteratureClassification Numbers: D63, C71

Multi-Product Serial Cost Sharing: An Incompatibility with the Additivity Axiom

Previous literature has shown that the serial cost sharing rule is endowed with a variety of desirable incentive and equity features. By definition, applications of this mechanism are essentially constrained to single service facilities. We investigate difficulties that emerge when attempting to extend serial cost sharing to multi-product environments. In particular, we show that such an extension is incompatible with the additivity axiom.Journal of Economic LiteratureClassification Numbers: D63, C71.

Cost Sharing under Increasing Returns: A Comparison of Simple Mechanisms

A technology with decreasing marginal costs is used by agents with equal rights. Each agent demands a quantity of output and costs are divided by means of a fixed formula. Several such mechanisms are compared for the existence of Nash equilibrium demand profiles and for the equity properties of these equilibria. Among three mechanisms, average cost pricing, the Shapley–Shubik cost sharing, and serial cost-sharing, only the latter two possess at least one Nash equilibrium on a reasonable domain of individual preferences. Only the serial cost sharing equilibria pass the equity tests of No Envy and Stand Alone cost.Journal of Economic LiteratureClassification Numbers: C72, D63.

Average Cost Pricing versus Serial Cost Sharing: An Axiomatic Comparison

A finite group of agents share a (one output) production function. A cost sharing rule allocates the total cost among the users for every conceivable profile of output demands. We investigate the space of possible cost sharing rules from an axiomatic perspective. We provide two characterizations of average cost pricing, one based on the axioms of Additivity and Monotonicity (both with respect to the cost function), and the other based on the axioms of Additivity and a version of Consistency. We also provide a characterization of serial cost sharing based, essentially, on Additivity and a Free Lunch axiom. Journal of Economic Literature Classification Numbers: D63, D78, C79.

Cost Sharing Under Increasing Returns: A Comparison of Simple Mechanisms

A technology with decreasing marginal costs is used by agents with equal rights. Each agent demands a quantity of output and costs are divided by means of a fixed formula. Several such mechanisms are compared for the existence of Nash equilibrium demand profiles and for the equity properties of these equilibria. Among three mechanisms, average cost pricing, the Shapley-Shubik cost sharing and serial cost-sharing, only the latter two possess at least one Nash equilibrium on a reasonable domain of individual preferences. Only the serial cost sharing equilibria pass the equity tests of No Envy and Stand Alone cost.

Serial Cost Sharing

The authors consider the problem of cost sharing in the case of a fixed group of agents sharing a one input, one output technology with decreasing returns. They introduce and analyze the serial cost sharing method. Among agents endowed with convex and monotonic preferences, serial cost sharing is dominance solvable and its unique Nash equilibrium is also robust to coalitional deviations. The authors show that no other smooth cost sharing mechanism yields a unique Nash equilibrium at all preference profiles. Copyright 1992 by The Econometric Society.