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On the convexity of communication games

Abstract

A communication situation consists of a game and a communication graph. By introducing two different types of corresponding communication games, point games and arc games, the Myerson value and the position value of a communication situation were introduced.

This paper investigates relations between convexity of the underlying game and the two communication games. In particular, assuming the underlying game to be convex, necessary and sufficient conditions on the communication graph are provided such that the communication games are convex. Moreover, under the same conditions, it is shown that the Myerson value and the posi tion value are in the core of the point game. Some remarks are made on superadditivity and balancedness.

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References

  1. Borm PEM, Owen G, Tijs S (1990) Values of points and arcs in communication situations. Report 9004, Dept of Mathematics, University of Nijmegen, The Netherlands

  2. Myerson RB (1977) Graphs and cooperation in games. Math Oper Res 2, 225–229

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  4. Shapley LS (1953) A value for n-person games. Annals of Math Studies 28, 307–317

  5. Shapley LS (1971) Cores of convex games. Int J of Game Theory 1, 11–26

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van den Nouweland, A., Borm, P. On the convexity of communication games. Int J Game Theory 19, 421–430 (1991). https://doi.org/10.1007/BF01766431

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Keywords

  • Economic Theory
  • Game Theory
  • Posi Tion
  • Communication Graph
  • Communication Situation