Pure strategy Nash equilibria for bargaining models of collective choice - Malte Braack; Christian Henning; Johannes Ziesmer (International Journal of Game Theory, 2023)
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: C72; C73; C78; D72; D78; 330; Legislative Bargaining; Local and global Nash equilibria; Non-cooperative Game Theory