Skip to main content
SpringerLink
Log in

Cost Sharing

  • Reference work entry
Encyclopedia of Complexity and Systems Science

Definition of the Subject

Throughout we will use a fixed set of agents \(N=\{1,2,\dots,n\} \), where n is a given naturalnumber. For subsets \( { S,T } \)of N, we write \( { S\subset T }\) if each element of S is contained in T; \( { T\backslash S }\) denotes the set of agents in T except those in S. The power set of N is the set of all subsetsof N; each coalition \( { S\subset N }\) will be identified with the element \( {\boldsymbol{1}_S\in \left\{0,1\right\}^N } \), the vector with ith coordinateequal to 1 precisely when \( { i\in S }\). Fix a vector \( { x\in\mathbb{R}^N }\) and \( { S\subset N }\). The projection of x on \( { \mathbb{R}^S } \) is denoted by x S , and \( { x_{N\backslash S} }\) is sometimes more conveniently denoted by \({ x_{-S} } \). For any \( { y\in \mathbb{R}^S }\), \( { (x_{-S},y) }\) stands for the vector \( { z\in\mathbb{R}^N }\) such that \( { z_i=x_i }\) if \( { i\in N\backslash S }\) and \( { z_i=y_i }\) if \( { i\in S }\). We denote \( { x(S)=\sum_{i\in...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 3,499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 549.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

Core :

The core of a cooperative cost game \( { \left\langle N,c\right\rangle } \) is the set of all coalitionally stable vectors of cost shares.

Cost function :

A cost function relates to each level of output of a given production technology the minimal necessary units of input to generate it. It is non‐decreasing function \( { c\colon X\rightarrow \mathbb{R}_+ } \), where X is the (ordered) space of outputs.

Cost sharing problem :

A cost sharing problem is an ordered pair \( { (q,c) } \), where \( { q\in\mathbb{R}^N_+ } \) is a profile of individual demands of a fixed and finite group of agents \( { N=\left\{1,2,\dots,n\right\} } \) and c is a cost function.

Game theory :

The branch of applied mathematics and economics that studies situations where players make decisions in an attempt to maximize their returns. The essential feature is that it provides a formal modeling approach to social situations in which decision makers interact.

Cost sharing rule :

A cost sharing rule is a mapping that assigns to each cost sharing problem under consideration a vector of non‐negative cost shares.

Demand game :

Strategic game where agents place demands for output strategically.

Demand revelation game :

Strategic game where agents announce their maximal contribution strategically.

Strategic game :

An ordered triple \( { G=\langle N, (A_i)_{i\in N},} {(\precsim_i)_{i\in N}\rangle } \), where

  • \( { N=\left\{1,2,\dots,n\right\} } \) is the set of players ,

  • A i is the set of available actions for player i,

  • \( { \precsim_i } \) is a  preference relation over the set of possible consequences C of action.

Bibliography

  1. Aadland D, Kolpin V (1998) Shared irrigation cost: an empirical and axiomatical analysis. Math Soc Sci 35:203–218

    MathSciNet  Google Scholar 

  2. Aadland D, Kolpin V (2004) Environmental determinants of cost sharing. J Econ Behav Organ 53:495–511

    Google Scholar 

  3. Albizuri MJ, Zarzuelo JM (2007) The dual serial cost‐sharing rule. Math Soc Sci 53:150–163

    MathSciNet  Google Scholar 

  4. Albizuri MJ, Santos JC, Zarzuelo JM (2003) On the serial cost sharing rule. Int J Game Theory 31:437–446

    MathSciNet  Google Scholar 

  5. An M (1998) Logconcavity versus logconvexity, a complete characterization. J Econ Theory 80:350–369

    Google Scholar 

  6. Archer A, Feigenbaum J, Krishnamurthy A, Sami R, Shenker S (2004) Approximation and collusion in multicast costsharing. Games Econ Behav 47:36–71

    MathSciNet  Google Scholar 

  7. Arin J, Iñarra E (2001) Egalitarian solutions in the core. Int J Game Theory 30:187–193

    Google Scholar 

  8. Atkinson AB (1970) On the measurement of inequality. J Econ Theory 2:244–263

    Google Scholar 

  9. Aumann RJ (1959) Acceptable points in general cooperative n‑person games. In: Kuhn HW, Tucker AW (eds) Contributions to the Theory of Games, vol IV. Princeton University Press, Princeton

    Google Scholar 

  10. Aumann RJ, Maschler M (1985) Game theoretic analysis of a bankruptcy problem from the Talmud. J Econ Theory 36:195–213

    MathSciNet  Google Scholar 

  11. Aumann RJ, Shapley LS (1974) Values of Non‐atomic Games. Princeton University Press, Princeton

    Google Scholar 

  12. Baumol W, Bradford D (1970) Optimal departure from marginal cost pricing. Am Econ Rev 60:265–283

    Google Scholar 

  13. Baumol W, Panzar J, Willig R (1988) Contestable Markets & the Theory of Industry Structure. 2nd edn Hartcourt Brace Jovanovich. San Diego

    Google Scholar 

  14. Bergantino A, Coppejans L (1997) A game theoretic approach to the allocation of joint costs in a maritime environment: A case study. Occasional Papers, vol 44. Department of Maritime Studies and International Transport, University of Wales, Cardi

    Google Scholar 

  15. Billera LJ, Heath DC (1982) Allocation of shared costs: A set of axioms yielding a unique procedure. Math Oper Res 7:32–39

    MathSciNet  Google Scholar 

  16. Billera LJ, Heath DC, Raanan J (1978) Internal telephone billing rates: A novel application of non‐atomic game theory. Oper Res 26:956–965

    Google Scholar 

  17. Bird CG (1976) On cost allocation for a spanning tree: A game theoretic approach. Networks 6:335–350

    MathSciNet  Google Scholar 

  18. Binmore K (2007) Playing for real: A text on game theory. Oxford University Press, Oxford

    Google Scholar 

  19. Bjorndal E, Hamers H, Koster M (2004) Cost allocation in a bank ATM network. Math Methods Oper Res 59:405–418

    MathSciNet  Google Scholar 

  20. Bondareva ON (1963) Some applications of linear programming to the theory of cooperative games. Problemy Kybernetiki 10:119–139 (in Russian)

    MathSciNet  Google Scholar 

  21. Brânzei R, Ferrari G, Fragnelli V, Tijs S (2002) Two approaches to the problem of sharing delay costs in joint projects. Ann Oper Res 109:359–374

    Google Scholar 

  22. Chen Y (2003) An experimental study of serial and average cost pricing mechanisms. J Publ Econ 87:2305–2335

    Google Scholar 

  23. Clarke EH (1971) Multipart pricing of public goods. Publ Choice 11:17–33

    Google Scholar 

  24. Dasgupta PS, Hammond PJ, Maskin ES (1979) The implementation of social choice rules: Some general results on incentive compatibility. Rev Econ Stud 46:185–216

    MathSciNet  Google Scholar 

  25. Davis M, Maschler M (1965) The kernel of a cooperative game. Nav Res Logist Q 12:223–259

    MathSciNet  Google Scholar 

  26. de Frutos MA (1998) Decreasing serial cost sharing under economies of scale. J Econ Theory 79:245–275

    Google Scholar 

  27. Demers A, Keshav S, Shenker S (1990) Analysis and simulation of a fair queueing algorithm. J Internetworking 1:3–26

    Google Scholar 

  28. Denault M (2001) Coherent allocation of risk capital. J Risk 4_7–21

    Google Scholar 

  29. Dewan S, Mendelson H (1990) User delay costs and internal pricing for a service facility. Manag Sci 36:1502–1517

    Google Scholar 

  30. Dutta B, Ray D (1989) A concept of egalitarianism under participation constraints. Econometrica 57:615–635

    MathSciNet  Google Scholar 

  31. Dutta B, Ray D (1991) Constrained egalitarian allocations. Games Econ Behav 3:403–422

    MathSciNet  Google Scholar 

  32. Flam SD, Jourani A (2003) Strategic behavior and partial cost sharing. Games Econ Behav 43:44–56

    MathSciNet  Google Scholar 

  33. Fleurbaey M, Sprumont Y (2006) Sharing the cost of a public good without subsidies. Université de Montréal, Cahier

    Google Scholar 

  34. Friedman E (2002) Strategic properties of heterogeneous serial cost sharing. Math Soc Sci 44:145–154

    Google Scholar 

  35. Friedman E (2004) Paths and consistency in additive cost sharing. Int J Game Theory 32:501–518

    Google Scholar 

  36. Friedman E, Moulin H (1999) Three methods to share joint costs or surplus. J Econ Theory 87:275–312

    MathSciNet  Google Scholar 

  37. Friedman E, Shenker S (1998) Learning and implementation on the Internet. Working paper 199821, Rutgers University, Piscataway

    Google Scholar 

  38. González-Rodríguez P, Herrero C (2004) Optimal sharing of surgical costs in the presence of queues. Math Methods Oper Res 59:435–446

    Google Scholar 

  39. Granot D, Huberman G (1984) On the core and nucleolus of minimum cost spanning tree games. Math Program 29:323–347

    MathSciNet  Google Scholar 

  40. Green J, Laffont JJ (1977) Characterization of satisfactory mechanisms for the revelation of preferences for public goods. Econometrica 45:427–438

    MathSciNet  Google Scholar 

  41. Groves T (1973) Incentives in teams. Econometrica 41:617–663

    MathSciNet  Google Scholar 

  42. Haimanko O (2000) Partially symmetric values. Math Oper Res 25:573–590

    MathSciNet  Google Scholar 

  43. Harsanyi J (1967) Games with incomplete information played by Bayesian players. Manag Sci 14:159–182

    MathSciNet  Google Scholar 

  44. Hart S, Mas-Colell A (1989) Potential, value, and consistency. Econometrica 57:589–614

    MathSciNet  Google Scholar 

  45. Haviv M (2001) The Aumann–Shapley price mechanism for allocating congestion costs. Oper Res Lett 29:211–215

    MathSciNet  Google Scholar 

  46. Hougaard JL, Thorlund-Petersen L (2000) The stand-alone test and decreasing serial cost sharing. Econ Theory 16:355–362

    Google Scholar 

  47. Hougaard JL, Thorlund-Petersen L (2001) Mixed serial cost sharing. Math Soc Sci 41:51–68

    MathSciNet  Google Scholar 

  48. Hougaard JL, Tind J (2007) Cost allocation and convex data envelopment. mimeo University of Copenhagen, Copenhagen

    Google Scholar 

  49. Henriet D, Moulin H (1996) Traffic‐based cost allocation in a network. J RAND Econ 27:332–345

    Google Scholar 

  50. Iñarra E, Isategui JM (1993) The Shapley value and average convex games. Int J Game Theory 22:13–29

    Google Scholar 

  51. Israelsen D (1980) Collectives, communes, and incentives. J Comp Econ 4:99–124

    Google Scholar 

  52. Jackson MO (2001) A crash course in implementation theory. Soc Choice Welf 18:655–708

    MathSciNet  Google Scholar 

  53. Joskow PL (1976) Contributions of the theory of marginal cost pricing. Bell J Econ 7:197–206

    Google Scholar 

  54. Kalai E (1977) Proportional solutions to bargaining situations: Interpersonal utility comparisons. Econometrica 45:1623–1630

    MathSciNet  Google Scholar 

  55. Kaminski M (2000) ‘Hydrolic’ rationing. Math Soc Sci 40:131–155

    MathSciNet  Google Scholar 

  56. Kolpin V, Wilbur D (2005) Bayesian serial cost sharing. Math Soc Sci 49:201–220

    MathSciNet  Google Scholar 

  57. Koster M (2002) Concave and convex serial cost sharing. In: Borm P, Peters H (eds) Chapters in game theory. Kluwer, Dordrecht

    Google Scholar 

  58. Koster M (2005) Sharing variable returns of cooperation. CeNDEF Working Paper 05–06, University of Amsterdam, Amsterdam

    Google Scholar 

  59. Koster M (2006) Heterogeneous cost sharing, the directional serial rule. Math Methods Oper Res 64:429–444

    MathSciNet  Google Scholar 

  60. Koster M (2007) The Moulin–Shenker rule. Soc Choice Welf 29:271–293

    MathSciNet  Google Scholar 

  61. Koster M (2007) Consistent cost sharing. mimeo, University of Amsterdam

    Google Scholar 

  62. Koster M, Tijs S, Borm P (1998) Serial cost sharing methods for multi‐commodity situations. Math Soc Sci 36:229–242

    Google Scholar 

  63. Koster M, Molina E, Sprumont Y, Tijs ST (2002) Sharing the cost of a network: core and core allocations. Int J Game Theory 30:567–599

    MathSciNet  Google Scholar 

  64. Koster M, Reijnierse H, Voorneveld M (2003) Voluntary contributions to multiple public projects. J Publ Econ Theory 5:25–50

    Google Scholar 

  65. Koutsoupias E, Papadimitriou C (1999) Worst-case equilibria. In: 16th Annual Symposium on Theoretical Aspects of Computer Science, Trier. Springer, Berlin, pp 404–413

    Google Scholar 

  66. Legros P (1986) Allocating joint costs by means of the Nucleolus. Int J Game Theory 15:109–119

    MathSciNet  Google Scholar 

  67. Leroux J (2004) Strategy‐proofness and efficiency are incompatible in production economies. Econ Lett 85:335–340

    MathSciNet  Google Scholar 

  68. Leroux J (2006) Profit sharing in unique Nash equilibrium: characterization in the two-agent case, Games and Economic Behavior 62:558–572

    MathSciNet  Google Scholar 

  69. Littlechild SC, Owen G (1973) A simple expression for the Shapley value in a simple case. Manag Sci 20:370–372

    Google Scholar 

  70. Littlechild SC, Thompson GF (1977) Aircraft landing fees: A game theory approach. Bell J Econ 8:186–204

    Google Scholar 

  71. Maniquet F, Sprumont Y (1999) Efficient strategy‐proof allocation functions in linear production economies. Econ Theory 14:583–595

    MathSciNet  Google Scholar 

  72. Maniquet F, Sprumont Y (2004) Fair production and allocation of an excludable nonrival good. Econometrica 72:627–640

    MathSciNet  Google Scholar 

  73. Maschler M (1990) Consistency. In: Ichiishi T, Neyman A, Tauman Y (eds) Game theory and applications. Academic Press, New York, pp 183–186

    Google Scholar 

  74. Maschler M (1992) The bargaining set, kernel and nucleolus. In: Aumann RJ, Hart S (eds) Handbook of Game Theory with Economic Applications, vol I. North–Holland, Amsterdam

    Google Scholar 

  75. Maschler M, Reijnierse H, Potters J (1996) Monotonicity properties of the nucleolus of standard tree games. Report 9556, Department of Mathematics, University of Nijmegen, Nijmegen

    Google Scholar 

  76. Maskin E, Sjöström T (2002) Implementation theory. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of Social Choice and Welfare, vol I. North–Holland, Amsterdam

    Google Scholar 

  77. Matsubayashi N, Umezawa M, Masuda Y, Nishino H (2005) Cost allocation problem arising in hub-spoke network systems. Europ J Oper Res 160:821–838

    MathSciNet  Google Scholar 

  78. McLean RP, Pazgal A, Sharkey WW (2004) Potential, consistency, and cost allocation prices. Math Oper Res 29:602–623

    MathSciNet  Google Scholar 

  79. Mirman L, Tauman Y (1982) Demand compatible equitable cost sharing prices. Math Oper Res 7:40–56

    MathSciNet  Google Scholar 

  80. Monderer D, Shapley LS (1996) Potential games. Games Econ Behav 14:124–143

    MathSciNet  Google Scholar 

  81. Moulin H (1987) Equal or proportional division of a surplus, and other methods. Int J Game Theory 16:161–186

    MathSciNet  Google Scholar 

  82. Moulin H (1994) Serial cost‐sharing of an excludable public good. Rev Econ Stud 61:305–325

    Google Scholar 

  83. Moulin H (1995) Cooperative microeconomics: A game–theoretic introduction. Prentice Hall, London

    Google Scholar 

  84. Moulin H (1995) On additive methods to share joint costs. Japan Econ Rev 46:303–332

    Google Scholar 

  85. Moulin H (1996) Cost sharing under increasing returns: A comparison of simple mechanisms. Games Econ Behav 13:225–251

    MathSciNet  Google Scholar 

  86. Moulin H (1999) Incremental cost sharing: Characterization by coalition strategy‐proofness. Soc Choice Welf 16:279–320

    MathSciNet  Google Scholar 

  87. Moulin H (2000) Priority rules and other asymmetric rationing methods. Econometrica 68:643–684

    Google Scholar 

  88. Moulin H (2002) Axiomatic cost and surplus‐sharing. In: Arrow KJ, Sen AK, Suzumura K (eds) Handbook of Social Choice and Welfare. Handbooks in Economics, vol 19. North–Holland, Amsterdam, pp 289–357

    Google Scholar 

  89. Moulin H (2006) Efficient cost sharing with cheap residual claimant. mimeo Rice University, Housten

    Google Scholar 

  90. Moulin H (2007) The price of anarchy of serial, average and incremental cost sharing. mimeo Rice University, Housten

    Google Scholar 

  91. Moulin H, Shenker S (1992) Serial cost sharing. Econometrica 60:1009–1037

    MathSciNet  Google Scholar 

  92. Moulin H, Shenker S (1994) Average cost pricing versus serial cost sharing; an axiomatic comparison. J Econ Theory 64:178–201

    Google Scholar 

  93. Moulin H, Shenker S (2001) Strategy‐proof sharing of submodular cost: budget balance versus efficiency. Econ Theory 18:511–533

    MathSciNet  Google Scholar 

  94. Moulin H, Sprumont Y (2005) On demand responsiveness in additive cost sharing. J Econ Theory 125:1–35

    MathSciNet  Google Scholar 

  95. Moulin H, Sprumont Y (2006) Responsibility and cross‐subsidization in cost sharing. Games Econ Behav 55:152–188

    MathSciNet  Google Scholar 

  96. Moulin H, Vohra R (2003) Characterization of additive cost sharing methods. Econ Lett 80:399–407

    MathSciNet  Google Scholar 

  97. Moulin H, Watts A (1997) Two versions of the tragedy of the commons. Econ Des 2:399–421

    Google Scholar 

  98. Mutuswami S (2004) Strategy proof cost sharing of a binary good and the egalitarian solution. Math Soc Sci 48:271–280

    MathSciNet  Google Scholar 

  99. Myerson RR (1980) Conference structures and fair allocation rules. Int J Game Theory 9:169–182

    MathSciNet  Google Scholar 

  100. Myerson RR (1991) Game theory: Analysis of conflict. Harvard University Press, Cambridge

    Google Scholar 

  101. Nash JF (1950) Equilibrium points in n‑person games. Proc Natl Acad Sci 36:48–49

    MathSciNet  ADS  Google Scholar 

  102. O’Neill B (1982) A problem of rights arbitration from the Talmud. Math Soc Sci 2:345–371

    Google Scholar 

  103. Osborne MJ (2004) An introduction to game theory. Oxford University Press, New York

    Google Scholar 

  104. Osborne MJ, Rubinstein A (1994) A Course in Game Theory. MIT Press, Cambridge

    Google Scholar 

  105. Peleg B, Sudhölter P (2004) Introduction to the theory of cooperative games, Series C: Theory and Decision Library Series. Kluwer, Amsterdam

    Google Scholar 

  106. Pérez-Castrillo D, Wettstein D (2006) An ordinal Shapley value for economic environments. J Econ Theory 127:296–308

    Google Scholar 

  107. Potters J, Sudhölter P (1999) Airport problems and consistent allocation rules. Math Soc Sci 38:83–102

    Google Scholar 

  108. Razzolini L, Reksulak M, Dorsey R (2004) An experimental evaluation of the serial cost sharing rule. Working paper 0402, VCU School of Business, Dept. of Economics, Richmond

    Google Scholar 

  109. Ritzberger K (2002) Foundations of non‐cooperative game theory. Oxford University Press, Oxford

    Google Scholar 

  110. Rosenthal RW (1973) A class of games possessing pure‐strategy Nash equilibria. J Econ Theory 2:65–67

    Google Scholar 

  111. Roth AE (ed) (1988) The Shapley value, essays in honor of Lloyd S Shapley. Cambridge University Press, Cambridge, pp 307–319

    Google Scholar 

  112. Samet D, Tauman Y, Zang I (1984) An application of the Aumann–Shapley prices for cost allocation in transportation problems. Math Oper Res 9:25–42

    MathSciNet  Google Scholar 

  113. Sánchez SF (1997) Balanced contributions axiom in the solution of cooperative games. Games Econ Behav 20:161–168

    Google Scholar 

  114. Sandsmark M (1999) Production games under uncertainty. Comput Econ 14:237–253

    Google Scholar 

  115. Schmeidler D (1969) The Nucleolus of a characteristic function game. SIAM J Appl Math 17:1163–1170

    MathSciNet  Google Scholar 

  116. Shapley LS (1953) A value for n‑person games. Ann Math Study, vol 28. Princeton University Press, Princeton, pp 307–317

    Google Scholar 

  117. Shapley LS (1967) On balanced sets and cores. Nav Res Logist Q 14:453–460

    Google Scholar 

  118. Shapley LS (1969) Utility comparison and the theory of games. In: Guilbaud GT (ed) La decision: Aggregation et dynamique des ordres de preference. Editions du Centre National de la Recherche Scientifique. Paris pp 251–263

    Google Scholar 

  119. Shapley LS (1971) Cores of convex games. Int J Game Theory 1:1–26

    MathSciNet  Google Scholar 

  120. Sharkey W (1982) Suggestions for a game–theoretic approach to public utility pricing and cost allocation. Bell J Econ 13:57–68

    Google Scholar 

  121. Sharkey W (1995) Network models in economics. In: Ball MO et al (eds) Network routing. Handbook in Operations Research and Management Science, vol 8. North–Holland, Amsterdam

    Google Scholar 

  122. Shubik M (1962) Incentives, decentralized control, the assignment of joint cost, and internal pricing. Manag Sci 8:325–343

    MathSciNet  Google Scholar 

  123. Skorin-Kapov D (2001) On cost allocation in hub-like networks. Ann Oper Res 106:63–78

    MathSciNet  Google Scholar 

  124. Skorin-Kapov D, Skorin–Kapov J (2005) Threshold based discounting network: The cost allocation provided by the nucleolus. Eur J Oper Res 166:154–159

    Google Scholar 

  125. Sprumont Y (1998) Ordinal cost sharing. J Econ Theory 81:126–162

    MathSciNet  Google Scholar 

  126. Sprumont Y (2000) Coherent cost sharing. Games Econ Behav 33:126–144

    MathSciNet  Google Scholar 

  127. Sprumont Y (2005) On the discrete version of the Aumann–Shapley cost‐sharing method. Econometrica 73:1693–1712

    MathSciNet  Google Scholar 

  128. Sprumont Y, Ambec S (2002) Sharing a river. J Econ Theory 107:453–462

    MathSciNet  Google Scholar 

  129. Sprumont Y, Moulin H (2005) Fair allocation of production externalities: Recent results. CIREQ working paper 28-2005, Montreal

    Google Scholar 

  130. Sudhölter P (1998) Axiomatizations of game theoretical solutions for one‐output cost sharing problems. Games Econ Behav 24:42–71

    Google Scholar 

  131. Suijs J, Borm P, Hamers H, Koster M, Quant M (2005) Communication and cooperation in public network situations. Ann Oper Res 137:117–140

    MathSciNet  Google Scholar 

  132. Tauman Y (1988) The Aumann–Shapley prices: A survey. In: Roth A (ed) The shapley value. Cambridge University Press, Cambridge, pp 279–304

    Google Scholar 

  133. Thomas LC (1992) Dividing credit‐card costs fairly. IMA J Math Appl Bus & Ind 4:19–33

    Google Scholar 

  134. Thomson W (1996) Consistent allocation rules. Mimeo, Economics Department, University of Rochester, Rochester

    Google Scholar 

  135. Thomson W (2001) On the axiomatic method and its recent applications to game theory and resource allocation. Soc Choice Welf 18:327–386

    MathSciNet  Google Scholar 

  136. Tijs SH, Driessen TSH (1986) Game theory and cost allocation problems. Manag Sci 32:1015–1028

    MathSciNet  Google Scholar 

  137. Tijs SH, Koster M (1998) General aggregation of demand and cost sharing methods. Ann Oper Res 84:137–164

    MathSciNet  Google Scholar 

  138. Timmer J, Borm P, Tijs S (2003) On three Shapley‐like solutions for cooperative games with random payoffs. Int J Game Theory 32:595–613

    MathSciNet  Google Scholar 

  139. van de Nouweland A, Tijs SH (1995) Cores and related solution concepts for multi‐choice games. Math Methods Oper Res 41:289–311

    Google Scholar 

  140. von Neumann J, Morgenstern O (1944) Theory of games and economic behavior. Princeton University Press, Princeton

    Google Scholar 

  141. Watts A (2002) Uniqueness of equilibrium in cost sharing games. J Math Econ 37:47–70

    MathSciNet  Google Scholar 

  142. Weber RJ (1988) Probabilistic values for games. In: Roth AE (ed) The Shapley value. Cambridge University Press, Cambridge

    Google Scholar 

  143. Young HP (1985) Producer incentives in cost allocation. Econometrica 53:757–765

    Google Scholar 

  144. Young HP (1985) Monotonic solutions of cooperative games. Int J Game Theory 14:65–72

    Google Scholar 

  145. Young HP (1985) Cost allocation: Methods, principles, applications. North-Holland, Amsterdam

    Google Scholar 

  146. Young HP (1988) Distributive justice in taxation. J Econ Theory 44:321–335

    Google Scholar 

  147. Young HP (1994) Cost allocation. In: Aumann RJ, Hart S (eds) Handbook of Game Theory, vol II. Elsevier, Amsterdam, pp 1193–1235

    Google Scholar 

  148. Young HP (1998) Cost allocation, demand revelation, and core implementation. Math Soc Sci 36:213–229

    Google Scholar 

Download references

I thank Hervé Moulin as a referee of this article, and his useful suggestions.

Author information

Authors and Affiliations

  1. University of Amsterdam, Amsterdam, Netherlands

    Maurice Koster

Authors
  1. Maurice Koster
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag

About this entry

Cite this entry

Koster, M. (2009). Cost Sharing. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_108

Download citation

Publish with us

Policies and ethics

Search

Navigation