تعهد و سازش در چانه زنی

This paper studies observable and irrevocable commitment in bargaining. We investigate when commitment tactics can cause an impasse and when compromise is feasible. In the static model in which a player’s commitment decision is made simultaneously with his choice of bargaining stance, compromise becomes unattainable (Ellingsen and Miettinen, 2008). We first analyze a static bargaining model, in which the players decide whether to attempt commitment after announcing their demands. In contrast to the aforementioned strong result, our model accommodates both incompatible commitments and compromises as equilibrium outcomes. We then extend our analysis to a dynamic setting. It is shown that compromise is possible if the players can alter their demands quickly and the chances of successful commitment are low.

Impasses periodically arise in real-life bargaining situations, causing significant efficiency losses. As mutually beneficial agreements often exist, it is puzzling to see negotiating parties agree to disagree. In his seminal works, Schelling, 1956, Schelling, 1960 and Schelling, 1966 argues vividly that impasses may occur because rational bargainers are often willing to commit themselves to aggressive bargaining stances to increase their share of the available surplus. Based on Schelling’s view, Crawford (1982) investigates the role of commitment tactics in bargaining using a static game theoretic model. In his model, commitment is observable and retractable with a cost. Crawford shows that when the costs of backing down are likely to be high, compromise at the demand stage is feasible; when these costs are likely to be low, commitments to incompatible demands occur, inducing a positive probability of impasse.1 This analysis confirms Schelling’s intuitive arguments. More recently, Ellingsen and Miettinen (2008) (EM2008 henceforth) also study a static model in which costly commitment is observable and irrevocable, showing that compromise is impossible even when successful commitment is highly likely. This result is rather strong and puzzling: when the probability of success for a commitment attempt is close to 1, impasse occurs almost with certainty. As Ellingsen and Miettinen remarked, “If anything, the model produces incompatible commitments all too readily.” Whereas conflicts arising from incompatible commitments are often observed in reality, compromise among negotiating parties is not a rare occurrence either. Thus, the first goal of this paper is to identify the critical conditions for the strong result reported in EM2008. We modify their model in a realistic way and demonstrate that both incompatible commitments and compromises are possible as equilibrium outcomes. More specifically, in contrast to the two aforementioned models in which the players’ decisions about commitment are made simultaneously with those about demands, we consider a two-stage game with sequential decision making. The players announce their demands in the first stage, and, following incompatible demands, they then decide in the second stage whether to attempt commitment. When the probability of successful commitment is low, the prediction in EM2008 prevails, as both players try to commit themselves to the demand of the entire surplus. When the success probability is high, in contrast, their prediction does not apply: a player may refrain from committing to his demand for the fear of causing an impasse. The simultaneous timing of demand and commitment is thus crucial to the no-compromise result. The basic premise underlying the formulation of the two-step decision making is that immediate commitment is difficult to obtain. Even when a player can always make the two decisions at the same time, whereas his demand is announced instantly, it often takes time for him to achieve commitment. Hence, a player may be willing to withdraw his commitment attempt after learning his rival’s demand. If withdrawal is indeed feasible, then this is equivalent to making the decisions in two steps. A crucial assumption of the static model is that bargaining concludes automatically with a predetermined settlement when the players’ demands are incompatible and neither achieves commitment. As this assumption seems somewhat ad hoc, the second goal of this paper is to extend the analysis to a dynamic setting in which the predetermined settlement is replaced by the continuation of bargaining. In our dynamic model, each player can alter his demand frequently and can attempt commitment repeatedly. A commitment attempt will succeed with positive probability within a certain period of time. Bargaining concludes either with an agreement of compatible demands or with an impasse due to successful incompatible commitments. Equilibrium continues with both players persistently attempting commitment to incompatible demands until one or both succeed. Such an equilibrium is obviously inefficient, given the positive probability of impasse and lengthy delay. Nevertheless, when the players can alter their demands sufficiently quickly and the likelihood of a successful commitment is low, there are also efficient equilibria with immediate agreements provided that at least one player is either impatient or strictly risk averse. The intuition behind this result is straightforward. Put simply, the dynamic bargaining game is analogous to the repeated Prisoner’s Dilemma game, in which cooperation can be sustained by the grim trigger strategy. An important message of our dynamic analysis is that uncertain and irrevocable commitment need not lead to an impasse if bargaining can continue indefinitely and the parties involved can adjust their stances frequently. Hence, the insights built upon analysis of a static model do not extend to a dynamic setting in a certain sense.2 The rest of the paper is organized as follows. Section 2 analyzes a static bargaining model that is a modified version of the two-stage game in EM2008. Section 3 extends the analysis to a dynamic setting in which the players can alter their demands frequently and can attempt commitment repeatedly. Section 4 concludes the paper. All proofs are relegated to the Appendix A.