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Communication and its cost in graph-restricted games

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Abstract

We consider cooperative games which are modified by subordination to communication networks. Two players i and j will be able to cooperate only if they pay for the cost w ij of their communication link (i,j). Coalitions of players are treated similarly and a new characteristic function form game is developed thus. We also examine incentive for players to cooperate in such situations as well as a related index of a player's communicative strength.

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References

  • Bird, C. G.: 1976, ‘On Cost Allocation for a Spanning Tree: A Game Theory Approach’, Networks 6, 335–350.

    Google Scholar 

  • Claus, A., and Kleitman, D. J.: 1973, ‘Cost Allocation for a Spanning Tree’, Networks 3, 289–304.

    Google Scholar 

  • Dubey, P. and Shapley, L. S.: 1984, ‘Totally Balanced Games Arising from Controlled Programming Problems’, Mathematical Programming 29, 245–267.

    Google Scholar 

  • Granot, D. and Granot, F.: 1986, ‘A Fixed-Cost Spanning-Forest Problem’, working paper no. 1235, Faculty of Commerce and Business Administration, University of British Columbia.

  • Granot, D. and Huberman, G.: 1981, ‘Minimum Cost Spanning Tree Games’, Mathematical Programming 21, 1–18.

    Google Scholar 

  • Granot, D. and Huberman, G.: 1982, ‘The Relationship Between Convex Games and Minimum Cost Spanning Tree Games: A Case for Permutationally Convex Games’, SIAM J. Alg. Meth. 3, 288–292.

    Google Scholar 

  • Grofman, B. and Owen, G.: 1982, ‘A Game-Theoretic Approach to Measuring Degree of Centrality in Social Networks’, Social Networks 4, 213–224.

    Google Scholar 

  • Kalai, E. and Zemel, E.: 1982, ‘Totally Balanced Games and Games of Flow’, Math. Oper. Res. 7, 476–478.

    Google Scholar 

  • Kalai, E. and Zemel, E.: 1982, ‘Generalized Network Problems Yielding Totally Balanced Games’, Operations Research 30, 998–1008.

    Google Scholar 

  • Megiddo, N.: 1978, ‘Computational Complexity and the Game Theory Approach to Cost Allocation for a Tree’, Math. Oper. Res. 3, 189–196.

    Google Scholar 

  • Meyerson, R. B.: 1977, ‘Graphs and Cooperation in Games’, Math. Oper. Res. 2, 225–229.

    Google Scholar 

  • Owen, G.: 1975, ‘On the Core of Linear Production Games’, Mathematical Programming 9, 358–370.

    Google Scholar 

  • Owen, G.: 1982, Game Theory. Second Edition. Academic Press, New York.

    Google Scholar 

  • Owen, G.: 1986, ‘Values of Graph-Restricted Games’, SIAM J. Alg. Disc. Meth. 7, 210–220.

    Google Scholar 

  • Papadimitriou, C., and Steiglitz, K.: 1982, Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Rosenthal, E. C.: 1985, ‘Cooperative Games Arising from Mathematical Programming Problems’, unpublished Ph.D. thesis, Department of Industrial Engineering and Management Sciences, Northwestern University.

  • Rosenthal, E. C.: 1987, ‘The Minimum Cost Spanning Forest Game’, Economics Letters 23, 355–357.

    Google Scholar 

  • Rosenthal, E. C.: 1988, ‘Communication Networks and Their Role in Cooperative Games’, to appear in Social Networks.

  • Shapley, L. S.: 1971, ‘Cores of Convex Games’, Int. J. Game Theory 1, 11–26.

    Google Scholar 

  • Shapley, L. S. and Shubik, M.: 1972, ‘The Assignment Game: I. The Core’, 'Int. J. Game Theory 2, 111–130.

    Google Scholar 

  • Topkis, D. M.: 1983, ‘Activity Selection Games and the Minimum Cut Problem’, Networks 13, 93–105.

    Google Scholar 

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Rosenthal, E.C. Communication and its cost in graph-restricted games. Theor Decis 25, 275–286 (1988). https://doi.org/10.1007/BF00133166

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