# On the serial cost sharing rule

@article{Albizuri2003OnTS, title={On the serial cost sharing rule}, author={M. Josune Albizuri and Juan Carlos Santos and Jos{\'e} Manuel Zarzuelo}, journal={International Journal of Game Theory}, year={2003}, volume={31}, pages={437-446} }

Abstract. In this paper we study a solution for discrete cost allocation problems, namely, the serial cost sharing method. We show that this solution can be computed by applying the Shapley value to an appropriate TU game and we present a probabilistic formula. We also define for cost allocation problems a multilinear function in order to obtain the serial cost sharing method as Owen (1972) did for the Shapley value in the cooperative TU context. Moreover we show that the pseudo average cost…

## 16 Citations

### A polynomial rule for the problem of sharing delay costs in PERT networks

- Computer ScienceComput. Oper. Res.
- 2008

### A Nash Equilibrium Solution for the Discrete Two-Person Cost Sharing Problem

- Economics, Mathematics
- 2012

In this paper we study the discrete cost sharing problem. We restrict the problem when there exists only a pair of agents with the same demand of discrete goods (not necessarily the same kind of…

### The Serial Property and Restricted Balanced Contributions in discrete cost sharing problems

- Economics, Mathematics
- 2006

We show that the Serial Poperty and Restricted Balanced Contributions characterize the subsidy-free serial cost sharing method (Moulin (1995)) in discrete cost allocation problems.

### The $$a$$a-serial cost sharing rule

- EconomicsCentral Eur. J. Oper. Res.
- 2016

A new family of cost sharing rules for cost sharing problems is proposed, which generalizes the family of $$\alpha $$α-serial cost sharingrules which contains the serial cost sharing rule among others.

### The pseudo-average rule: bankruptcy, cost allocation and bargaining

- EconomicsMath. Methods Oper. Res.
- 2011

A division rule for claims problems, also known as bankruptcy or rationing problems, based on the pseudo-average solution, is studied and it is shown that it coincides with the rule associated to the equal area bargaining solution (this is not true for n = 3).

### Selected Topics in Cooperative Game Theory

- Economics
- 2010

This chapter shall provide the theoretical basis coming from cooperative game theory. We start with a survey of historical developments in the field of game theory. After this short excursion, we…

### Allocation of Firm-Energy Rights Among Hydro Plants: An Aumann–Shapley Approach

- EconomicsIEEE Transactions on Power Systems
- 2009

The firm energy of generation plants is a critical component in some electricity markets. It is usually calculated by the regulator and sets a cap to the amount a plant can trade in capacity markets…

### Marginalism, Egalitarianism and Efficiency in Multi-Choice Games

- EconomicsSSRN Electronic Journal
- 2021

The search for a compromise between marginalism and egalitarianism has given rise to many discussions. In the context of cooperative games, this compromise can be understood as a trade-off between…

## References

SHOWING 1-10 OF 11 REFERENCES

### Serial Cost Sharing

- Economics
- 1992

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…

### ON ADDITIVE METHODS TO SHARE JOINT COSTS

- Economics
- 1995

The Shapley value theory is extended to cost functions with multiple outputs (or to production functions with multiple inputs) where each output is demanded by a different agent and the level of…

### A shapley value for games with restricted coalitions

- Economics
- 1993

A “restriction” is a monotonic projection assigning to each coalition of a finite player setN a subcoalition. On the class of transferable utility games with player setN, a Shapley value is…

### Potential, value, and consistency

- Economics
- 1989

Let P be a real-valued function defined on the space of cooperative games with transferable utility, satisfying the following condition: In every game, the marginal contributions of all players…

### Characterizations of a multi-choice value

- EconomicsInt. J. Game Theory
- 1999

This paper provides several other characterizations of the extended Shapley value, one of which is the analogue of Shapley's (1953) original characterization, and is inspired by Myerson's (1980) characterization of the Shapleyvalue using balanced contributions.

### Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing

- Business
- 1961

A goal of good management should be to design a reward system for those who take risks in making decisions in such a manner that the rewards to the individual correlate positively with the worth of…

### Monotonicity and dummy free property for multi-choice cooperative games

- Economics
- 1992

Given a coalition of ann-person cooperative game in characteristic function form, we can associate a zero-one vector whose non-zero coordinates identify the players in the given coalition. The…

### The Shapley value: The Aumann-Shapley prices: a survey

- Engineering
- 1988

In a system for analyzing a fluid such as blood or blood plasma contained in capillaries, the capillaries, open at both ends, are filled with the fluid to be analyzed. These capillaries are carefully…