The Tradewise-Function Form for Transferable Utility Games

  • Authors: Marilda Sotomayor and David Pérez-Castrillo.
  • BSE Working Paper: 1481 | March 25
  • Keywords: core , tradewise , Pareto optimality , TU Games
  • JEL codes: C71
  • core
  • tradewise
  • Pareto optimality
  • TU Games
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Abstract

We introduce a new cooperative game form called the cooperative game in the tradewise-function form and denote it Γ . In Γ , we consider allocations that encompass the players’ payoff and the coalitional structure they form. The set of feasible allocations is restricted to t-feasible allocations, those we can expect to result, at any step of a coalition formation process, from the optimal cooperative behavior of the players. We show that the core of Γ is non-empty and coincides with the set of Pareto optimal allocations of Γ and with the set of t-feasible allocations that cannot be t-extended by any t-feasible allocation. Moreover, the cores of the characteristic-function and the tradewise-function forms coincide when the first is not empty. Hence, when the core in the characteristic-function form is not empty, whether we consider all the feasible allocations or only the t-feasible allocations is irrelevant to the final outcome. However, our theory also provides a prescription, in the same spirit, for games in which the core of the characteristic-function form is empty.

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