Chapter

Equilibrium Theory for Cournot Oligopolies and Related Games

Part of the series Springer Series in Game Theory pp 245-268

Date:

Two-Group Contests with Communication Within and Between Groups

  • Federico QuartieriAffiliated withDipartimento di scienze economiche e statistiche, Università degli studi di Napoli Federico II Email author 
  • , Ryusuke Shinohara

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Abstract

We consider a two-group contest game with weakest-link social composition functions and convex cost functions and prove the existence of a unique group-proof Nash equilibrium. Such a refinement of the Nash equilibrium prescribes the same communication possibilities as those required by a coalition-proof Nash equilibrium—in the precise sense of Bernheim et al. (J Econ Theory 42:1–12, 1987)—only among the contenders of the same group and between the two groups. We show how a fictitious game with “most inefficient fictitious contenders” can be constructed to prove the existence of a unique group-proof Nash equilibrium of the original two-group contest game. An example evidences that cautious arguments on the (twice) differentiability of cost functions must be used in such a construction.