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Preconvex games

Author

Listed:
  • Eric Bahel

    (Department of Economics, Virginia Polytechnic Institute and State University)

  • Christian Trudeau

    (Department of Economics, University of Windsor)

  • Haoyu Wang

    (Department of Economics, Virginia Polytechnic Institute and State University)

Abstract

We introduce the notion of preconvexity, which extends the familiar concept of convexity found in cooperative games with transferable utility. In a convex game, the larger the group joined by an agent, the larger the marginal value brought to the group by that agent. By contrast, in strictly preconvex games, an agent's marginal contribution is initially decreasing (when joining small groups), and it eventually becomes increasing at (and above) some critical group size. As a consequence, the core of a preconvex game may be empty. Defining the property of semicohesiveness (related to marginal contributions at this critical group size), we prove that it is sufficient to guarantee a nonempty core. We also propose a new solution for the set of preconvex games; and we characterize this solution by combining three axioms which are natural in our framework. A stronger cohesiveness property (guaranteeing that our solution falls in the core) is also studied. Some additional results are provided for the special case of anticonvex games, for which marginal contributions are always non-increasing.

Suggested Citation

  • Eric Bahel & Christian Trudeau & Haoyu Wang, 2025. "Preconvex games," Working Papers 2501, University of Windsor, Department of Economics.
    • Handle: RePEc:wis:wpaper:2501
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    References listed on IDEAS

    as
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    Keywords

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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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