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Household Nash Equilibrium with Voluntarily Contributed Public Goods

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  • Valerie Lechene
  • Ian Preston

Abstract

We study noncooperative models with two agents and several voluntarily contributed public goods. We focus on interior equilibria in which neither agent is bound by non negativity constraints, establishing the conditions for existence and uniqueness of the equilibrium. While adding-up and homogneity hold, negativity and symmetry properties are generally violated. We derive the counterpart to the Slutsky matrix, and show that it can be decomposed into the sum of a symmetric and negative semidefinite matrix and another the rank of which never exceeds the number of public goods plus one. Under separability of the public goods the deviation from symmetry is at most rank two.

Suggested Citation

  • Valerie Lechene & Ian Preston, 2005. "Household Nash Equilibrium with Voluntarily Contributed Public Goods," Economics Series Working Papers 226, University of Oxford, Department of Economics.
  • Handle: RePEc:oxf:wpaper:226
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    References listed on IDEAS

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    Cited by:

    1. Claude d’Aspremont & Rodolphe Dos Santos Ferreira, 2009. "Household behavior and individual autonomy," Working Papers of BETA 2009-17, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    2. Lechene, Valérie & Preston, Ian, 2011. "Noncooperative household demand," Journal of Economic Theory, Elsevier, vol. 146(2), pages 504-527, March.
    3. Valérie Lechene & Ian Preston, 2007. "Demand properties in household Nash equilibrium," IFS Working Papers W07/01, Institute for Fiscal Studies.
    4. Castilla, Carolina, 2010. "Intra-Household Resource Management Structure and Income-Hiding under Incomplete Information," 2010 Annual Meeting, July 25-27, 2010, Denver, Colorado 61607, Agricultural and Applied Economics Association.
    5. Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2009. "Degrees of cooperation in household consumption models: a revealed preference analysis," Working Papers Department of Economics ces09.20, KU Leuven, Faculty of Economics and Business, Department of Economics.
    6. Valerie Lechene & Martin Browning, 2006. "Quelques resultats sur l`effet des transferts cibles," Economics Series Working Papers 294, University of Oxford, Department of Economics.
    7. Martin Browning & Pierre-André Chiappori & Valérie Lechene, 2010. "Distributional Effects in Household Models: Separate Spheres and Income Pooling," Economic Journal, Royal Economic Society, vol. 120(545), pages 786-799, June.
    8. Claude d’Aspremont & Rodolphe Dos Santos Ferreira, 2014. "Household behavior and individual autonomy: an extended Lindahl mechanism," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 643-664, April.
    9. Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2010. "Noncooperative household consumption with caring," Working Papers Department of Economics ces10.34, KU Leuven, Faculty of Economics and Business, Department of Economics.
    10. Marcel Fafchamps & Agnes R. Quisumbing, 2006. "Household Formation and Marriage Markets," Economics Series Working Papers GPRG-WPS-039, University of Oxford, Department of Economics.
    11. Laurens Cherchye & Sam Cosaert & Thomas Demuynck & Bram De Rock, 2017. "Group Consumption with Caring Individuals," Working Papers ECARES ECARES 2017-45, ULB -- Universite Libre de Bruxelles.
    12. Gutierrez, Federico H., 2018. "A Sharing Model of the Household: Explaining the Deaton-Paxson Paradox and Computing Household Indifference Scales," GLO Discussion Paper Series 166, Global Labor Organization (GLO).

    More about this item

    Keywords

    Nash Equilibrum; Intra-household Allocation; Slutsky Symmetry;

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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