Pure strategy Nash equilibria for bargaining models of collective choice

Malte Braack (), Christian Henning () and Johannes Ziesmer ()
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Malte Braack: University of Kiel
Christian Henning: University of Kiel
Johannes Ziesmer: Leibniz Institute for Educational Trajectories

International Journal of Game Theory, 2024, vol. 53, issue 2, No 5, 373-421

Abstract: Abstract This paper considers pure strategy Nash equilibria of non-cooperative legislative bargaining models. In contrast to existing legislative bargaining models, we derive legislators behavior from stochastic utility maximization. This approach allows us to prove the existence of a stationary Pure Local and Global Nash Equilibrium under rather general settings. The mathematical proof is based on a fixed point argument, which can also be used as a numerical method to determine an equilibrium. We characterize the equilibrium outcome as a lottery of legislators’ proposals and prove a Mean Voter Theorem, i.e., proposals result dimension-by-dimension as a weighted mean of legislators’ ideal points and are Pareto-optimal. Based on a simple example, we illustrate different logic of our model compared to mixed strategy equilibrium of the legislative bargaining model suggested by Banks and Duggan (Am Polit Sci Rev 94(1):73–88. https://doi.org/10.2307/2586381 , 2000).

Keywords: Legislative Bargaining; Local and global Nash equilibria; Non-cooperative Game Theory (search for similar items in EconPapers)
JEL-codes: C72 C73 C78 D72 D78 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00182-023-00882-z

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