International Journal of Game Theory

, Volume 19, Issue 1, pp 45–57 | Cite as

Monotonicity of the core and value in dynamic cooperative games

  • E. C. Rosenthal


We examine behavior of the core and value of certain classes of cooperative games in which a dynamic aspect is introduced. New players are added to the games while the underlying structure is held constant. This is done by considering games that satisfy properties like convexity, or games that are derived from optimization problems in which a player's addition can be defined naturally. For such games we give conditions regarding monotonicity of the core and value.

Key Words

Cooperative games core Shapley value monotonicity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aumann RJ (1985) An Axiomatization of the Non-Transferable Utility Value, Econometrica 53, 599–612Google Scholar
  2. [2]
    Dubey P, Shapley LS (1984) Totally Balanced Games Arising From Controlled Programming Problems, Math. Programming 29, 245–267Google Scholar
  3. [3]
    Granot D, Huberman G (1981) On Minimum Cost Spanning Tree Games, Math. Programming 21, 1–18Google Scholar
  4. [4]
    Grofman B, Owen G (1982) A Game Theoretic Approach to Measuring Degree of Centrality in Social Networks, Social Networks 4, 213–224Google Scholar
  5. [5]
    Harsanyi JC (1963) A Simplified Bargaining Model for the N-Person Cooperative Game, Inter. Econ. Rev. 4, 194–220Google Scholar
  6. [6]
    Hart S (1985) An Axiomatization of Harsanyi's Non-Transferable Utility Solution, Econometrica 53, 1295–1313Google Scholar
  7. [7]
    Ichiishi T (1981) Super-Modularity: Applications to Convex Games and to the Greedy Algorithm for LP, J. Econ. Theory 25, 283–286Google Scholar
  8. [8]
    Ichiishi T (1988) Comparative Cooperative Game Theory, Working Paper #88-03, Department of Economics, The Ohio State UniversityGoogle Scholar
  9. [9]
    Kalai E, Samet D (1985) Monotonic Solutions to General Cooperative Games, Econometrica 53, 307–327Google Scholar
  10. [10]
    Kalai E, Smorodinsky M (1975) Other Solutions to Nash's Bargaining Problem, Econometrica 43, 513–518Google Scholar
  11. [11]
    Kalai E, Zemel E (1982) Totally Balanced Games and Games of Flow, Math. Oper. Res. 7, 476–478Google Scholar
  12. [12]
    Kalai E, Zemel E (1982) Generalized Network Problems Yielding Totally Balanced Games, Oper. Res. 30, 998–1008Google Scholar
  13. [13]
    Lawler EL (1976) Combinatorial Optimization: Networks and Matroids. Holt, Rinehart and Winston, New YorkGoogle Scholar
  14. [14]
    Maschler M, Owen G (1986) The Expected Marginal Payoff Value for Hyperplane Games, technical reportGoogle Scholar
  15. [15]
    Mo J-P (1988) Entry and Structures of Interest Groups in Assignment Games, J. Econ. Theory 46, 66–96Google Scholar
  16. [16]
    Myerson RB (1977) Graphs and Cooperation in Games, Math. Oper. Res. 2, 225–229Google Scholar
  17. [17]
    Owen G (1975) On the Core of Linear Production Games, Math. Programming 9, 358–370Google Scholar
  18. [18]
    Owen G (1982) Game Theory. Second Edition. Academic Press, New YorkGoogle Scholar
  19. [19]
    Owen G (1986) Values of Graph-Restricted Games, SIAM J. Alg. Disc. Meth. 7, 210–220Google Scholar
  20. [20]
    Rosenthal EC (1985) Cooperative Games Arising From Mathematical Programming Problems, unpublished Ph. D. thesis, Department of Industrial Engineering and Management Sciences, Northwestern UniversityGoogle Scholar
  21. [21]
    Rosenthal EC (1988) Communication Networks and Their Role in Cooperative Games, Social Networks 10, 255–263Google Scholar
  22. [22]
    Rosenthal EC (1988) Communication and its Cost in Graph-Restricted Games, Theory and Decision 25, 275–286Google Scholar
  23. [23]
    Shapley LS (1953) A Value for N-Person Games, in Kuhn HW, Tucker AW, eds., Contributions to the Theory of Games II, Princeton University Press, PrincetonGoogle Scholar
  24. [24]
    Shapley LS (1971) Cores of Convex Games, Int. J. Game Theory 1, 11–26Google Scholar
  25. [25]
    Shapley LS, Shubik M (1972) The Assignment Game I: The Core, Int. J. Game Theory 2, 111–130Google Scholar
  26. [26]
    Sharkey WW (1981) Convex Games Without Side Payments, Int. J. Game Theory 10, 101–106Google Scholar
  27. [27]
    Sharkey WW (1985) Cores and Implications for Pricing in a Model of Production with Fixed Costs and Shared Facilities, technical reportGoogle Scholar
  28. [28]
    Shubik M (1982) Game Theory in the Social Sciences. MIT Press, Cambridge, MAGoogle Scholar
  29. [29]
    Tamir A (1980) On the Core of Cost Allocation Games Defined on Location Problems, technical reportGoogle Scholar
  30. [30]
    Topkis DM (1983) Activity Selection Games and the Minimum-Cut Problem, Networks 13, 93–105Google Scholar
  31. [31]
    von Neumann J, Morgenstern O (1944) Theory of Games and Economic Behavior, Princeton University Press, PrincetonGoogle Scholar
  32. [32]
    Young HP (1985) Monotonic Solutions of Cooperative Games, Int. J. Game Theory 14, 65–72Google Scholar

Copyright information

© Physica-Verlag 1990

Authors and Affiliations

  • E. C. Rosenthal
    • 1
  1. 1.Department of Management Science and Operations Management, School of Business and ManagementTemple UniversityPhiladelphiaUSA

Personalised recommendations