Computation of Stationary Equilibrium Payoffs in Coalitional Bargaining

Abstract      

In this paper, we provide an algorithm to compute the equilibrium payoffs in the coalitional bargaining model of Eraslan-McLennan (Journal of Economic Theory, 2013) by using recent developments in methods of numerical algebraic geometry. The Eraslan-McLennan model is a legislative bargaining model which studies weighed voting games, with players that are heterogeneous in their discount factors, voting weights and in terms of the probabilities of being selected as the proposer. Eraslan-McLennan characterizes the equilibria as fixed points of a set-valued function. In this paper, we show that the equilibria of the same can be characterized by solutions to a system of polynomial equations and provide an algorithm to compute the equilibrium payoffs. As an alternative approach, we show that all equilibria of such games can be characterized by fixed pointed of a continuous function, and use a variety of fixed point algorithms to execute this observation. These algorithms have implications for computing equilibria of dynamic models and should be useful in other applied work.