Bargaining in Markets

Abstract

In the first chapter I describe a method to construct fair—or symmetry-preserving—stable sets of compound simple games from fair stable sets of their quotient and components, and I discuss how it contributes to the characterization of the set of simple games that admit a fair stable set. In the second chapter I study an infinite-horizon model of coalitional bargaining in stationary markets with strategic choice of bargaining partners: In each period, a player is selected to be the proposer and selects a coalition as well as how to share its surplus among its members. Players respond in sequence; if all players accept, they leave the market and—to maintain stationarity—are replaced by replicas. I describe an algorithm that characterizes the essentially-unique stationary subgame-perfect equilibrium. This algorithm reveals that the coalitions that form in equilibrium have a tier structure, with equilibrium payoffs determined from the top tier down. In the third chapter I present an application of the model of the second chapter to networked markets. In the unique subgame-perfect equilibrium, each player has a preferred neighbor to whom she always extends offers in equilibrium. Each component (or submarket) of the preferred-neighbor network has exactly one pair of mutually preferred neighbors, whose terms of trade determine the price at which all trades occur in their submarket. I describe a simple method to compute the highest and the lowest equilibrium price in the limit as bargaining frictions vanish, and I use it to formalize the idea that the law of one price holds if and only if the market is thick enough.