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Complements and Substitutes in Generalized Multisided Assignment Economies

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Abstract

We consider a finitely populated economy in which there are different types of agent, each agent is of exactly one type, and profit is created by coalitions containing at most one agent of each type (or side). The surplus of a so-called generalized multisided assignment economy is defined as the maximum aggregate profit that can be attained by matching agents into pairwise disjoint coalitions of the above kind. We present negative results that establish that when the economy consists of more than two sides (i) agents on different sides may not be complements, i.e., they do not necessarily reinforce each other’s influence on the surplus and (ii) agents on the same side may not be substitutes, i.e., they do not necessarily interfere with each other’s influence on the surplus. These findings are in marked contrast with the results for two-sided assignment economies (Shapley, 1962). We propose novel notions for the complementarity and the substitutability of disjoint subsets of agents and we find conditions that ensure that the former are satisfied.

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  • Oriol Tejada, 2013. "Complements and Substitutes in Generalized Multisided Assignment Economies," CER-ETH Economics working paper series 13/180, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    • Handle: RePEc:eth:wpswif:13-180
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    References listed on IDEAS

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    1. Demange, Gabrielle, 2009. "The strategy structure of some coalition formation games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 83-104, January.
    2. Stuart, Harborne Jr, 1997. "The supplier-firm-buyer game and its m-sided generalization," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 21-27, August.
    3. Quint, Thomas, 1991. "The core of an m-sided assignment game," Games and Economic Behavior, Elsevier, vol. 3(4), pages 487-503, November.
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    5. Guillermo Owen, 1992. "The Assignment Game : The Reduced Game," Annals of Economics and Statistics, GENES, issue 25-26, pages 71-79.
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    7. Oriol Tejada & Carles Rafels, 2010. "Symmetrically multilateral-bargained allocations in multi-sided assignment markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 249-258, March.
    8. repec:adr:anecst:y:1992:i:25-26:p:03 is not listed on IDEAS
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    Cited by:

    1. Ata Atay & Francesc Llerena & Marina Núñez, 2016. "Generalized three-sided assignment markets: core consistency and competitive prices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 572-593, October.

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    More about this item

    Keywords

    multisided assignment economy; complements; substitutes.;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D40 - Microeconomics - - Market Structure, Pricing, and Design - - - General

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