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Uncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying

Author

Listed:
  • Raouf Boucekkine

    (Rennes SB - Rennes School of Business)

  • Fabien Prieur

    (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier)

  • W. Ruan

    (Purdue University [West Lafayette])

  • B Zou,

    (uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg)

Abstract

We study a 2-player stochastic differential game of lobbying. Players invest in lobbying activities to alter the legislation in her own benefit. The payoffs are quadratic and uncertainty is driven by a Wiener process. We consider the Nash symmetric game where players face the same cost and extract symmetric payoffs, and we solve for Markov Perfect Equilibria (MPE) in the class of affine functions. First, we prove a general sufficient (catching up) optimality condition for two-player stochastic games with uncertainty driven by Wiener processes. Second, we prove that the number and nature of MPE depend on the extent of uncertainty (i.e. the variance of the Wiener processes). In particular, we prove that while a symmetric MPE always exists, two asymmetric MPE emerge if and only if uncertainty is large enough. Third, we study the stochastic stability of all the equilibria. We notably find, that the state converges to a stationary invariant distribution under asymmetric MPE. Fourth, we study the implications for rent dissipation asymptotically and compare the outcomes of symmetric vs asymmetric MPE in this respect, ultimately enhancing again the role of uncertainty.

Suggested Citation

  • Raouf Boucekkine & Fabien Prieur & W. Ruan & B Zou,, 2024. "Uncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying," Post-Print hal-03641961, HAL.
    • Handle: RePEc:hal:journl:hal-03641961
    DOI: 10.1007/s00199-021-01403-3
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    Cited by:

    1. Chen, Yiwen & Paulus, Nora & Wan, Xi & Zou, Benteng, 2024. "Optimal timing of carbon capture and storage policies — A social planner’s view," Energy Economics, Elsevier, vol. 136(C).
    2. Matthias Birkner & Niklas Scheuer & Klaus Wälde, 2023. "The dynamics of Pareto distributed wealth in a small open economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 607-644, August.
    3. Markus Eigruber & Franz Wirl, 2025. "On the non-uniqueness of linear Markov perfect equilibria in linear-quadratic differential games: a geometric approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(3), pages 911-943, May.

    More about this item

    Keywords

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    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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