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Similarities in axiomatizations: equal surplus division value and first-price auctions

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  • Takumi Kongo

    (Fukuoka University)

Abstract

We compare axiomatizations between a value for cooperative games with transferable utilities (TU games), and a rule for auctions. The equal surplus division value on the set of zero-monotonic TU games is characterized by the following: individual rationality, Pareto efficiency, and equal effect of players’ nullification on others. Meanwhile, first-price auctions, on the general preference domain, are characterized by individual rationality, envy-freeness, and weak equal effect of buyers’ nullification on others. Here, envy-freeness implies Pareto efficiency in the model of auctions. Given the agents’ general preferences in the auction model, the characteristic of a weak equal effect of buyers’ nullification on others weakens the requirement of equal effect of players’ nullification on others. Although the two models are different, the corresponding axioms in both models require conditions corresponding to each other. In particular, individual rationality requires voluntary participation of agents, Pareto efficiency (or its stronger axiom of envy-freeness in the model of auctions) requires outcomes with no waste, and (weak) equal effect of players’ (buyers’) nullification on others requires equal treatment of agents when an agent is nullified. Therefore, in terms of axiomatizations, we can similarly interpret the equal surplus division value and first-price auctions.

Suggested Citation

  • Takumi Kongo, 2020. "Similarities in axiomatizations: equal surplus division value and first-price auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 199-213, December.
    • Handle: RePEc:spr:reecde:v:24:y:2020:i:3:d:10.1007_s10058-020-00233-4
    DOI: 10.1007/s10058-020-00233-4
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    More about this item

    Keywords

    Axiomatization; Equal surplus division value; First-price auction; Nullification;
    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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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