Skip to main content
SpringerLink
Log in

Operations research games: A survey

  • Published:
Top Aims and scope Submit manuscript

Abstract

This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved. Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players. This interplay between optimisation and allocation is the main subject of the area of operations research games. It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aadland D. and Kolpin V. (1998). Shared irrigation cost: an empirical and axiomatic analysis.Mathematical Social Sciences 35, 203–218.

    Article  Google Scholar 

  • Aarts H (1994). Minimum cost spanning tree games and set games. PhD thesis, University of Twente, Enschede, The Netherlands.

    Google Scholar 

  • Aarts H. and Driessen T. (1993). The irreducible core of a minimum cost spanning tree game.Zeitschrift für Operations Research (Now:Mathematical Methods of Operations Research) 38, 163–174.

    Google Scholar 

  • Assad A. (1978). Multicommodity network flows — a survey.Networks 8, 37–91.

    Google Scholar 

  • Aumann R. and Maschler M. (1985). Game theoretic analysis of a bankruptcy problem from the Talmud.Journal of Economic Theory 36, 195–213.

    Article  Google Scholar 

  • Balinsky M. and Gale D. (1990). On the core of assignment games. In: Leifman L. (ed.),Functional analysis, optimization and mathematical economics: a collection of papers dedicated to the memory of Leonid Vatalévich Kontorovich. Oxford University Press, 274–289.

  • Bilbao M. (2000).Cooperative games on combinatorial structures. Kluwer Academic Publishers.

  • Bird C. (1976). On cost allocation for a spanning tree: a game theoretic approach.Networks 6, 335–350.

    Google Scholar 

  • Bird G. (1981). Cores of monotonic linear production games.Mathematics of Operations Research 6, 420–423.

    Google Scholar 

  • Bjørndal E., Koster M. and Tijs S. (1999). Weighted allocation rules for standard fixed tree games. CentER Discussion Paper 9979, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Borm P., De Waegenaere A., Rafels C., Suijs J., Tijs S., Timmer J. (2001). Cooperation in capital deposits.OR Spektrum 23, 265–281.

    Article  Google Scholar 

  • Borm P., Fiestras-Janeiro G., Hamers H., Sánchez E. and Voorneveld M. (1999). On the convexity of games corresponding to sequencing situations with due dates. CentER Discussion Paper 1999-49, Tilburg University, Tilburg, The Netherlands. (To appear inEuropean Journal of Operational Research).

    Google Scholar 

  • Branzei R., Iñarra E., Tijs S. and Zarzuelo J. (2001). Cooperation by asymmetric agents in a joint project. Technical Report, Bilbao University, Bilbao, Spain.

    Google Scholar 

  • Calleja P., Borm P., Hamers H. and Klijn F. (2001a). On a new class of parallel sequencing situations and related games. CentER Discussion Paper 2001-03, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Calleja P., Borm P. and Hendrickx R. (2001b). Multi-issue allocation games. CentER Discussion Paper 2001-30, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Claus A. and Kleitman D. (1973). Cost allocation for a spanning tree.Networks 3, 289–304.

    Google Scholar 

  • Curiel I. (1997).Cooperative game theory and applications. Kluwer Academic Publishers.

  • Curiel I., Derks J. and Tijs S. (1989). On balanced games and flow games with committee control.OR Spektrum 11, 83–88.

    Article  Google Scholar 

  • Curiel I., Hamers H., Potters J. and Tijs S. (1997). Restricted component additive games.Mathematical Methods of Operations Research 45, 213–220.

    Article  Google Scholar 

  • Curiel I., Maschler M. and Tijs S. (1987). Bankruptcy games.Zeitschrift für Operations Research 31, 143–159.

    Article  Google Scholar 

  • Curiel I., Pederzoli G. and Tijs S. (1988). Reward allocations in production systems. In: Eiselt H. and G. Pederzoli G. (eds.),Advances in Optimization and Control. Springer Verlag, 186–199.

  • Curiel I., Pederzoli G. and Tijs S. (1989). Sequencing games.European Journal of Operational Research 40, 344–35.

    Article  Google Scholar 

  • Curiel I., Potters J., Rajendra Prasad V., Tijs S. and Veltman B. (1994). Cooperation in one machine scheduling.Zeitschrift für Operations Research 38, 113–129.

    Google Scholar 

  • Curiel I., Potters J., Rajendra Prasad V., Tijs S. and Veltman B. (1995). Sequencing and cooperation.Operations Research 42, 566–568.

    Google Scholar 

  • Curiel I. and Tijs S. (1986). Assignment games and permutation games.Methods of Operations Research 54, 323–334.

    Google Scholar 

  • Debreu G. and Scarf H. (1963). A limit theorem on the core of an economy.Econometrica 53, 873–888.

    Google Scholar 

  • Derks J. and Kuipers J. (1997). On the core of routing games.International Journal of Game Theory 26, 193–205.

    Google Scholar 

  • Derks J. and Tijs S. (1985). Stable outcomes for multi-commodity flow games.Methods of Operations Research 50, 493–504.

    Google Scholar 

  • Derks J. and Tijs S. (1986). Totally balanced multi-commodity games and flow games.Methods of Operations Research 54, 335–347.

    Google Scholar 

  • Driessen T. (1988).Cooperative games, solutions and applications. Kluwer Academic Publishers.

  • Dubey P. (1982). The Shapley value as aircraft landing fees revisited.Management Science 28, 869–874.

    Google Scholar 

  • Dubey P. and Shapley L. (1984). Totally balanced games arising from controlled programming problems.Mathematical Programming 29, 245–267.

    Google Scholar 

  • Edmonds J. and Johnson E. (1973). Matching, Euler tours and the Chinese postman.Mathematical Programming 5, 88–124.

    Article  Google Scholar 

  • Feltkamp V. (1995). Cooperation in Controlled Network Structures. PhD thesis, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Feltkamp V., Nouweland A. van den, Borm P., Tijs S. and Koster A. (1993). Linear production with transport of products, resources and technology.Zeitschrift für Operations Research 38, 153–162.

    Google Scholar 

  • Feltkamp V., Tijs S. and Muto S. (1994). Minimum cost spanning extension problems: the proportional rule and the decentralized rule. CentER Discussion Paper 9496, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Fishburn P. and Pollack H. (1983). Fixed route cost allocation.American Mathematical Monthly 90, 366–378.

    Article  Google Scholar 

  • Ford L. and Fulkerson D. (1962).Flows in networks. Princeton University Press.

  • Fragnelli V., Garcia-Jurado I. and Mendez-Naya L. (2000). On shortest path games.Mathematical Methods of Operations Research 52, 251–264.

    Article  Google Scholar 

  • Fragnelli V., Patrone F., Sideri E. and Tijs S. (1999). Balanced games arising from infinite linear models.Mathematical Methods of Operations Research 50, 385–397.

    Article  Google Scholar 

  • Gale D. (1984). Equilibrium in a discrete exchange economy with money.International Journal of Game Theory 13, 61–64.

    Article  Google Scholar 

  • Gale D. and Shapley L. (1962). College admission and the stability of marriage.American Mathematical Monthly 69, 9–15.

    Article  Google Scholar 

  • Galil Z. (1980). Applications of efficient mergeable heaps for optimization problems on trees.Acta Informatica 13, 53–58.

    Article  Google Scholar 

  • Gellekom A. van and Potters J. (1999). Consistent rules for standard tree enterprises. Technical Report 9919, Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands.

    Google Scholar 

  • Gellekom J. van, Potters J., Reijnierse J., Tijs S. and Engel M. (2000). Characterization of the Owen set of linear production processes.Games and Economic Behavior 32, 139–156.

    Article  Google Scholar 

  • Graham R. and Hell P. (1985). On the history of the minimum spanning tree problem.Annals of the History of Computing 7, 43–57.

    Google Scholar 

  • Grahn S. (2001). Core and bargaining set of shortest path games. Discussion Paper 2001:3. Department of Economics, Upssala University, Uppsala, Sweden.

    Google Scholar 

  • Granot D. (1986). A generalized linear production model: a unifying model.Mathematical Programming 34, 212–222.

    Article  Google Scholar 

  • Granot D. and Granot F. (1992a). On some nerwork flow games.Mathematics of Operations Research 17, 792–841.

    Google Scholar 

  • Granot D. and Granot F. (1992b). On the computational complexity of a cost allocation approach to a fixed cost spanning forest problem.Mathematics of Operations Research 17, 765–780.

    Google Scholar 

  • Granot D., Granot F. and Zhu W. (2000). Naturally submodular digraphs and forbidden digraph configurations.Discrete applied mathematics 100, 67–84.

    Article  Google Scholar 

  • Granot D. and Hamers H. (2000). On the equivalence between some local and global Chinese postman and traveling salesman graphs. CentER Discussion Paper 2000-48, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Granot D., Hamers H. and Tijs S. (1999). On some balanced, totally balanced and submodular delivery games.Mathematical Programming 86, 355–366.

    Article  Google Scholar 

  • Granot D. and Huberman G. (1981). On minimum cost spanning tree games.Mathematical Programming 21, 1–18.

    Article  Google Scholar 

  • Granot D. and Huberman G. (1982). The relationship between convex games and minimal cost spanning tree games: A case for permutationally convex games.SIAM Journal of Algorithms and Discrete Methods 3, 288–292.

    Article  Google Scholar 

  • Granot D. and Huberman G. (1984). On the core and nucleolus of minimum cost spanning tree games.Mathematical Programming 29, 323–347.

    Google Scholar 

  • Granot D. and Maschler M. (1998). Spanning network games.International Journal of Game Theory 27, 467–500.

    Article  Google Scholar 

  • Granot D., Maschler M., Owen G. and Zhu W. (1996). The kernel/nucleolus of a standard fixed tree game.International Journal of Game Theory 25, 219–244.

    Article  Google Scholar 

  • Hamers H. (1995). Sequencing and delivery situations: a game theoretic approach. PhD thesis, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Hamers H. (1997). On the concavity of delivery games.European Journal of Operational Research 99, 445–458.

    Article  Google Scholar 

  • Hamers H., Borm P., Leensel R. van de and Tijs S. (1999a). Cost allocation in the Chinese postman problem.European Journal of Operational Research 118, 153–163.

    Article  Google Scholar 

  • Hamers H., Borm P., Suijs J. and Tijs S. (1996). The split core for sequencing games.Games and Economic Behavior 15, 165–176.

    Article  Google Scholar 

  • Hamers H., Borm P. and Tijs S. (1995). On games corresponding to sequencing situations with ready times.Mathematical Programming 70, 1–13.

    Google Scholar 

  • Hamers H., Klijn F., Solymosi T., Tijs S. and Vermeulen D. (1999b). On the nucleolus of neighbour games. CentER Discussion Paper 99111, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Hamers H., Klijn F., Solymosi T., Tijs S. and Villar J. (1999c). On the extreme points of the core of neighbour games and assignment games. CentER Discussion Paper 9943, Tilburg University, Tilburg, The Netherlands. (To appear inGames and Economic Behavior).

    Google Scholar 

  • Hamers H., Klijn F. and Suijs J. (1999d). On the balancedness of multimachine sequencing games.European Journal of Operational Research 119, 678–691.

    Article  Google Scholar 

  • Hartman B., Dror M. and Shaked M. (2000). Cores of inventory centralization games.Games and Economic Behavior 31, 26–49.

    Article  Google Scholar 

  • Hax A. and Candea D. (1984).Production and inventory management. Prentice-Hall.

  • Herer Y. and Penn M. (1995). Characterization of naturally submodular graphs: a polynomial solvable class of the TSP.Proceedings of the AMS 123, 613–619.

    Article  Google Scholar 

  • Izquierdo J. and Rafels C. (1996). A generalization of the bankruptcy game: financial cooperative games. Working Paper E96/09, University of Barcelona, Barcelona, Spain.

    Google Scholar 

  • Kalai E. and Zemel E. (1982a). Generalized network problems yielding totally balanced games.Operations Research 30, 998–1008.

    Google Scholar 

  • Kalai E. and Zemel E. (1982b). Totally balanced games and games of flow.Mathematics of Operations Research 7, 476–478.

    Google Scholar 

  • Kaminski M. (2000). “Hydraulic” Rationing.Mathematical Social Sciences 40, 131–155.

    Article  Google Scholar 

  • Kaneko M. (1982). The central assignment game and the assignment markets.Journal of Mathematical Economics 10, 205–232.

    Article  Google Scholar 

  • Klijn F., Tijs S. and Hamers H. (2000). Balancedness of permutation games and envy-free allocations in indivisible good economies.Economic Letters 69, 323–326.

    Article  Google Scholar 

  • Koster M. (1999). Cost sharing in production situations and network exploitation. PhD thesis, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Koster M., Molina E., Sprumont Y. and Tijs S. (1998). Sharing the cost of a network: core and core allocations. CentER Discussion Paper 9821, Tilburg University, Tilburg.

    Google Scholar 

  • Koster M., Reijnierse J. and M. Voorneveld (1999). Voluntary contribution to multiple facilities: a class of ordinal potential games. CentER Discussion Paper 9988, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Kruskal J. (1956). On the shortest spanning subtree of a graph and the traveling salesman problem.Proceedings of the American Mathematical Society 7, 48–50.

    Article  Google Scholar 

  • Kuipers J. (1993). A note on the 5-person traveling salesman game.Zeitschrift für Operations Research 38, 131–140.

    Google Scholar 

  • Kuipers J., Solymosi T. and Aarts H. (2000). Computing the nucleolus of some combinatorially-structured games.Mathematical Programming 88, 541–563.

    Article  Google Scholar 

  • Lawler E., Lenstra J., Rinnooy Kan A. and Shmoys D. (1993). Sequencing and scheduling: algorithms and complexity. In: Graves S., Rinnooy Kan A. and Zipkin P. (eds.),Logistics of production and inventory. North Holland, 445–522.

  • Lawler E., Lenstra J.K., Rinnooy Kan A. and Shmoys D. (1985).The traveling salesman problem. John Wiley and Sons.

  • Littlechild S. (1974). A simple expression for the nucleolus in a special case.International Journal of Game Theory 3, 21–29.

    Article  Google Scholar 

  • Littlechild S. and Owen G. (1973). A simple expression for the Shapley value in a special case.Management Science 20, 370–372.

    Google Scholar 

  • Littlechild S. and Owen G. (1977). A further note on the nucleolus of the airport game.International Journal of Game Theory 5, 91–95.

    Article  Google Scholar 

  • Littlechild S. and Thompson G. (1977). Aircraft landing fees: a game theory approach.The Bell Journal of Economics 8, 186–204.

    Article  Google Scholar 

  • Llorca N., Tijs S. and Timmer J. (1999). Semi-infinite assignment problems and related games. CentER Discussion Paper 9974, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Maschler M. and Potters J. and Reijnierse J. (1995). Monotonicity properties of the nucleolus of standard tree games. Technical Report 9556, Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands.

    Google Scholar 

  • Meca A., Garcia-Jurado I. and Borm P. (2001). Cooperation and competition in inventory games. CIO Discussion Paper, Universidad Miguel Hernández, Elche, Spain.

    Google Scholar 

  • Meca A., Timmer J., Garcia-Jurado I. and Borm P. (1999). Inventory Games. CentER Discussion Paper 9953, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Megiddo N. (1978). Computational complexity of the game theory approach to cost allocation for a tree.Mathematics of Operations Research 3, 189–196.

    Google Scholar 

  • Mei-Ko Kwan (1962). Graphic programming using odd and even points.Chinese Mathematics 1, 273–277.

    Google Scholar 

  • Moretti S., Norde H., Pham Do K. and Tijs S. (2001). Connection problems in mountains and monotonic cost allocation schemes. CentER Discussion Paper 2001-12, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Moulin H. and Shenker S. (1992a). Average cost pricing versus social cost sharing: an axiomatic comparison.Journal of Economic Theory 64, 178–201.

    Article  Google Scholar 

  • Moulin H. and Shenker S. (1992b). Serial cost sharing.Econometrica 60, 1009–1037.

    Article  Google Scholar 

  • Müller A., Scarsini M. and Shaked M. (2000). The newsvendor game has a non-empty core. Technical report WIOR-594, University of Karlruhe, Karlsruhe, Germany.

    Google Scholar 

  • Nishizaki I. and Sakawa M. (2001). On computational methods for solutions of multiobjective linear production programming games.European Journal of Operational Research 129, 386–413.

    Article  Google Scholar 

  • Norde H., Moretti S. and Tijs S. (2001). Minimum cost spanning tree games and population monotonic allocation schemes. CentER Discussion Paper 2001-18, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Nouweland A. van den, Krabbenborg M. and Potters J. (1992). Flowshops with a dominant machine.European Journal of Operational Research 62, 38–46.

    Article  Google Scholar 

  • Nouweland A. van den, Maschler M. and Tijs S. (1993). Monotonic games are spanning network games.International Journal of Game Theory 21, 419–427.

    Article  Google Scholar 

  • Nuñez M. and Rafels C. (2000). The extreme core allocations of the assignment games. Technical report, University of Barcelona, Barcelona, Spain.

    Google Scholar 

  • O’Neill B. (1982). A problem of rights arbitration from the Talmud.Mathematical Social Sciences 2, 345–371.

    Article  Google Scholar 

  • Owen G. (1975). On the core of linear production games.Mathematical Programming 9, 358–370.

    Article  Google Scholar 

  • Owen G. (1992). The assignment game: the reduced game.Annals of Economics and Statistics 25, 71–79.

    Google Scholar 

  • Potters J. (1987). Linear optimization games. In: Peters H. and Vrieze O. (eds.),Surveys in games theory and related topics. CWI Tract, 251–276.

  • Potters J., Curiel I. and Tijs S. (1992). Traveling salesman games.Mathematical Programming 53, 199–211.

    Article  Google Scholar 

  • Potters J. and Sudhölter P. (1999). Airport problems and consistent allocation rules.Mathematical Social Sciences 38, 83–102.

    Article  Google Scholar 

  • Prim R. (1957). Shortest connection networks and some generalizations.Bell Systems Technical Journal 36, 1389–1401.

    Google Scholar 

  • Quint T. (1991a). Characterization of cores of assignment games.International Journal of Game Theory 19, 413–420.

    Article  Google Scholar 

  • Quint T. (1991b). The core of anm-sided marching game.Games and Economic Behavior 3, 487–503.

    Article  Google Scholar 

  • Quint T. (1996). On one-sided versus two-sided matching markets.Games and Economic Behavior 16, 124–134.

    Article  Google Scholar 

  • Reijnierse J., Maschler M., Potters J. and Tijs S. (1996). Simple flow games.Games and Economic Behavior 16, 238–260.

    Article  Google Scholar 

  • Roth A. and Sotomayor M. (1989).Two sided matching: a study in game theoretic modeling and analyses. Econometric Society Monograph Series, Cambridge University Press.

  • Samet D. and Zemel E. (1984). On the core and the dual set of linear programming games.Mathematics of Operations Research 9, 309–316.

    Google Scholar 

  • Sánchez-Soriano J., Llorca N., Tijs S. and Timmer J. (2000). On the core of semi-infinite transportation games with divisible goods. CentER Discussion Paper 2000-89, Tilburg University, Tilburg, The Netherlands. (To appear inEuropean Journal of Operations Research).

    Google Scholar 

  • Sánchez-Soriano J., López M. and Garcia-Jurado I. (2001). On the core of transportation games.Mathematical Social Sciences 41, 215–225.

    Article  Google Scholar 

  • Sandsmark M. (1999). Production games under uncertainty.Computational Economics 14, 237–253.

    Article  Google Scholar 

  • Sasaki H. (1995). Consistency and monotonicity in assignment problems.International Journal of Game Theory 24, 373–397.

    Article  Google Scholar 

  • Schmeidler D. (1969). The nucleolus of a characteristic function game.SIAM Journal of Applied Mathematics 17, 1163–1170.

    Article  Google Scholar 

  • Shapley L. (1953). A value forn-person games. In: Kuhn H. and Tucker A. (eds.)Contributions to the theory of games II. Annals of Mathematics Studies, 28. Princeton University Press.

  • Shapley L. and Shubik M. (1967). Ownership and the production function.Journal of Economics 8, 88–111.

    Google Scholar 

  • Shapley L. and Shubik M. (1971). The assignment game I: the core.International Journal of Game Theory 1, 111–130.

    Article  Google Scholar 

  • Slikker M., Fransoo J. and Wouters M. (2001). Joint ordering in multiple news-vendor problems: a game-theoretical approach. Mimeo, Technische Universteit Eindhoven, Eindhoven, The Netherlands.

    Google Scholar 

  • Slikker M. and Nouweland A. van den (2001).Social and economic networks in cooperative game theory. Kluwer Academic Publishers.

  • Smith W. (1956). Various optimizers for single-stage production.Naval Research Logistics Quarterly 3, 59–66.

    Google Scholar 

  • Solymosi T., Aarts H. and Driessen T. (1998). On computing the nucleolus of a balanced connection game.Mathematics of Operations Research 23, 983–1009.

    Article  Google Scholar 

  • Solymosi T. and Raghavan T. (1994). An algorithm for finding the nucleolus of assignment games.International Journal of Game Theory 23, 119–143.

    Article  Google Scholar 

  • Solymosi T. and Raghavan T. (2000), Stability of the core of assignment games. University of Economic Sciences and Public Administration Budapest, Budapest, Hungary.

    Google Scholar 

  • Sprumont Y. (1990). Population monotonic allocation schemes for cooperative games with transferable utility.Games and Economic Behavior 2, 378–394.

    Article  Google Scholar 

  • Sprumont Y. (1998). Ordinal cost sharing.Journal of Economic Theory 81, 126–162.

    Article  Google Scholar 

  • Suijs J. (2000).Cooperative decision-making under risk. Kluwer Academic Publishers.

  • Suijs J. (2001). Cost allocation in spanning network enterprises with stochastic connection costs. Technical Report, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Suijs J., Borm P., Hamers H., Koster M. and Quant M. (2001). Communication and cooperation in public network situations. CentER Discussion Paper 2001-44. Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Suijs J., Hamers H. and Tijs S. (1997). On consistency of reward allocation rules in sequencing situations. In: Klein Haneveld W., Vrieze O. and Kallenberg L. (eds.),Ten years LNMB. CWI Tract, 223–232.

  • Tamir, A. (1989). On the core of traveling salesman cost allocation game.Operations Research Letters 8, 31–34.

    Article  Google Scholar 

  • Tersine R. (1994).Principles of inventory and materials management. Elsevier North Holland.

  • Tijs S., Meca A. and López M. (2000). Benefit sharing in holding situations. CIO Discussion Paper I-2000-01, Universidad Miguel Hernández, Elche, Spain.

    Google Scholar 

  • Tijs S., Parthasarathy T., Potters J. and Rajendra Prasad V. (1984). Permutation games: another class of totally balanced games.OR Spektrum 6, 119–123.

    Article  Google Scholar 

  • Tijs S., Timmer J., Llorca N. and Sánchez-Soriano J. (2001). The Owen set and the core of semi-infinite linear production situations. In: Goberna M. and López M. (eds.),Semi-infinite programming: recent advances. Kluwer, 365–386.

  • Timmer J. (2001). Cooperative behaviour, uncertainty and operations research. PhD thesis, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Timmer J., Borm P. and Suijs J. (2000a). Linear transformation of products: games and economies.Journal of Optimization Theory and Applications 105, 677–706.

    Article  Google Scholar 

  • Timmer J., Llorca N., Tijs S. (2000b). Games arising from infinite production situations.International Game Theory Review 2, 97–106.

    Google Scholar 

  • Velzen B. van and Hamers H. (2001). On the balancedness of one player relaxed sequencing games. Technical Report, Tilburg University, Tilburg, The Netherlands.

    Google Scholar 

  • Voorneveld M. and Grahn S. (2000). Cost allocation in shortest path games. Preprint 1142, Department of Mathematics, Utrecht University, Utrecht, The Netherlands.

    Google Scholar 

  • Young H. (1998). Distributive Justice in Taxation.Journal of Economic Theory 48, 321–335.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CentER and Department of Econometrics and Operations Research, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands

    Peter Borm, Herbert Hamers & Ruud Hendrickx

Authors
  1. Peter Borm
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Herbert Hamers
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ruud Hendrickx
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borm, P., Hamers, H. & Hendrickx, R. Operations research games: A survey. Top 9, 139–199 (2001). https://doi.org/10.1007/BF02579075

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02579075

Key Words

AMS subject classification

Search

Navigation