THE IMPACT OF ENTITLEMENTS AND EQUITY ON COOPERATIVE BARGAINING: AN EXPERIMENT

Abstract

I. INTRODUCTION We consider a set of bargaining situations in which the disagreement outcome, or backstop, B, is chosen by a third party. For example, a government agency may signal that it will adopt as policy any agreement that stakeholders reach among themselves; but that otherwise, it will impose a policy of its own choosing. (1) Or an arbitrator may announce the award that will be imposed if a union and employer fail to reach agreement on a new contract. Of particular interest are those situations in which the status quo allocation of resources, Q, is Pareto inferior to the imposed backstop. Although axiomatic models of cooperative bargaining (Kalai and Smorodinsky 1975; Nash 1950) presume that negotiators in such cases will condition their agreements on B and ignore Q, literatures on entitlements and focal points (Bazerman 1985; Nozick 1974) suggest that history matters. That is, bargainers may be influenced by the status quo entitlement even when it lies outside the set of outcomes that are Pareto superior to the backstop. In addition, the experimental literature on inequality aversion (e.g., Fehr and Schmidt 1999; Hoffman and Spitzer 1985; Nydegger and Owen 1975) suggests that negotiators may be attracted to outcomes that equalize gains. In this article, we use a laboratory experiment to test the standard cooperative, entitlement, and egalitarian hypotheses in a multidimensional bargaining game. We begin in Section II by describing a two-party, two-attribute bargaining space, based on the classic Edgeworth box. Drawing from the literature on cooperative bargaining, we initially hypothesize that: (1) the parties will reach an agreement, and that this agreement will be (2) Pareto efficient; (3)Pareto superior to the backstop; and (4) at the Nash bargain. As alternatives to (3) and (4), we consider two predictions from the literatures on entitlements/focal points and inequality aversion. These are that the agreements that parties reach will (5)be conditioned on the status quo allocation rather than the backstop, and (6) equalize the parties' payoffs (when the Nash bargain does not). In Section III, we describe the design of a laboratory experiment in free-form cooperative bargaining to test these hypotheses. Our design does not use the one-dimensional mechanisms usually employed to analyze bargaining outcomes--such as dictator, divide the pie, or ultimatum games. These mechanisms offer few opportunities for subjects to choose outcomes that are inefficient or Pareto inferior to the backstop, nor a clear method of differentiating the status quo allocation from the backstop. Instead, we employ an Edgeworth box game involving two subjects with Cobb-Douglas payoff functions over two goods, X and Y. We impose a Pareto inefficient backstop allocation of these goods and allow our subjects to negotiate a reallocation. If they reach an agreement, each party receives the associated value from his or her payoff table; otherwise each receives the payoff associated with the backstop. Each party's payoff table has roughly 200 possible combinations of X and Y over which he or she can bargain. In Section IV, we present our results. We find that agreement rates are high and that those agreements are mostly in, or close to, the Pareto efficient set. The Nash bargain, however, is only supported when it equalizes the value of subjects' payoffs. When the (Pareto efficient) equal payoff outcome differs from the Nash bargain, subjects tend to compromise between the two allocations, some even agreeing to allocations that are Pareto inferior to the backstop. We also find that the tendency of subjects to choose the equal payoff outcome is strengthened when they perceive that the status quo distribution had also been equitable. Section V concludes the article with a discussion of the implications of our findings. II. HYPOTHESES We motivate our design with an environmental example drawn from collaborative bargaining over the use of public lands. …