Partial cooperation in strategic multi-sided decision situations

Subhadip Chakrabarti, Robert P. Gilles, Emiliya Lazarova

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We consider a normal-form game in which there is a single exogenously given coalition of cooperating players that can write a binding agreement on pre-selected actions. The actions representing other dimensions of the strategy space remain under the sovereign, individual control of the players. We consider a standard extension of the Nash equilibrium concept denoted as a partial cooperative equilibrium as well as an equilibrium concept in which the coalition of cooperators has a leadership position. Existence results are stated and we identify conditions under which the various equilibrium concepts are equivalent. We apply this framework to existing models of multi-market oligopolies and international pollution abatement. In a multi-market oligopoly, typically, a merger paradox emerges in the partial cooperative equilibrium. The paradox vanishes if the cartel attains a leadership position. For international pollution abatement treaties, cooperation by a sufficiently large group of countries results in a Pareto improvement over the standard tragedy of the commons outcome described by the Nash equilibrium.
Original languageEnglish
Pages (from-to)455–478
Number of pages24
JournalTheory and Decision
Issue number3-4
Early online date26 Jun 2018
Publication statusPublished - Oct 2018


  • Non-cooperative game
  • partial cooperation
  • Partial Cooperative Equilibrium
  • Leadership Equilibrium
  • multi-market oligopoly
  • international pollution abatement

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