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Null or Zero Players: The Difference between the Shapley Value and the Egalitarian Solution

Author

Listed:
  • René van den Brink

    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

Abstract

This discussion paper led to a publication in the 'Journal of Economic Theory', 2007, 136, 767-775. A situation in which a finite set of players can generate certain payoffs by cooperation can be described by a cooperative game with transferable utility. A solution for TU-games assigns to every TU-game a distribution of the payoffs that can be earned over the individual players. Two well-known solutions for TU-games are the Shapley value and the egalitarian solution. The Shapley value is characterized in various ways. Most characterizations use some axiom related to null players, i.e. players who contribute nothing to any coalition. We show that in these characterizations, replacing null players by zero players characterizes the egalitarian solution, where a player is a zero player if every coalition containing this player earns zero worth. We illustrate this difference between these two solutions by applying them to auction games.

Suggested Citation

  • René van den Brink, 2004. "Null or Zero Players: The Difference between the Shapley Value and the Egalitarian Solution," Tinbergen Institute Discussion Papers 04-127/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20040127
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    File URL: https://papers.tinbergen.nl/04127.pdf
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    More about this item

    Keywords

    Null players; zero players; Shapley value; egalitarian solution; strong monotonicity; coalitional monotonicity; auction games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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