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The Tradewise-Function Form for Transferable Utility Games

Author

Listed:
  • Marilda Sotomayor
  • David Pérez-Castrillo

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.

Suggested Citation

  • Marilda Sotomayor & David Pérez-Castrillo, 2025. "The Tradewise-Function Form for Transferable Utility Games," Working Papers 1481, Barcelona School of Economics.
  • Handle: RePEc:bge:wpaper:1481
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    More about this item

    Keywords

    core; tradewise; Pareto optimality; TU Games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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