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On the Pure Strategy Nash Equilibrium in the Spatial Model with Dual Additive Valence

Author

Listed:
  • Mathieu Martin
  • Linus Thierry Nana Noumi
  • Zéphirin Nganmeni
  • Ashley Piggins

    (CY Cergy Paris Université, THEMA)

Abstract

In spatial voting games, the valence is traditionally modeled as a non-ideological attribute that is uniformly assigned to a candidate by all voters, independent of their policy preferences. In its original for-mulation, additive valence is assumed to be entirely detached from the candidate policy considerations. In this paper, we explore an alterna-tive framework in which additive valence interacts with the candidates' policy platforms. Each candidate possesses an individual valence level,but voters choose to recognize this valence only if the candidate is perceived as competent in defending their proposed policy. This perceived competence is assumed to be common knowledge among voters. The core objective of this study is to determine the conditions under which Nash equilibria arise in the context of electoral competition with policy-dependent additive valence.

Suggested Citation

  • Mathieu Martin & Linus Thierry Nana Noumi & Zéphirin Nganmeni & Ashley Piggins, 2026. "On the Pure Strategy Nash Equilibrium in the Spatial Model with Dual Additive Valence," Thema Working Papers 2026-03, THEMA (Théorie Economique, Modélisation et Applications), CY Cergy-Paris University, ESSEC and CNRS.
    • Handle: RePEc:ema:worpap:2026-03
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    References listed on IDEAS

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    1. Mathieu Martin & Zéphirin Nganmeni & Craig Tovey, 2021. "Dominance in spatial voting with imprecise ideals," Post-Print hal-04257716, HAL.
    2. Owen, G & Shapley, L S, 1989. "Optimal Location of Candidates in Ideological Space," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(3), pages 339-356.
    3. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2016. "On the uniqueness of the yolk," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(3), pages 511-518, October.
    4. Norman Schofield, 1983. "Generic Instability of Majority Rule," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 695-705.
    5. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    6. Mathieu Martin & Zéphirin Nganmeni & Craig A. Tovey, 2021. "Dominance in spatial voting with imprecise ideals," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 181-195, July.
    7. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, vol. 12(3), pages 472-482, June.
    8. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    9. Stokes, Donald E., 1963. "Spatial Models of Party Competition," American Political Science Review, Cambridge University Press, vol. 57(2), pages 368-377, June.
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    Keywords

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    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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