- Get access
Summary
Introduction The theory developed in the preceding chapters contains some fundamental results and insights concerning the role of some key forces on the bargaining outcome. It cannot be overemphasized that the focus of this theory is on the fundamentals . Indeed, in the first stage of the development of an understanding of any phenomenon that is precisely the kind of theory that is required — one that cuts across a wide and rich variety of real-life scenarios and focuses upon their common core elements. This objective to uncover the fundamentals of bargaining has meant that my study has centred on some basic, elementary, models. That is how it should be. However, it is important that we now move beyond the fundamentals, in order to develop a richer theory of bargaining. With the theory just developed providing appropriate guidance and a firm foundation, it should be possible to construct tractable and richer models that capture more aspects of real-life bargaining situations. At the same time, future research should continue to develop the fundamentals; not only should we further study the roles of the forces studied in this book — especially the study of models in which many such forces are present — but we should also study the role of other forces that have not been addressed in this book (some of which I mention in Section 11.2). It is worth acknowledging that the role played by the game-theoretic methodology in the development of the theory described in this book has been crucial.
Frontmatter
- Chapter
- Get access
4 - Risk of Breakdown
- Chapter
- Get access
Summary
Introduction While bargaining the players may perceive that the negotiations might break down in a random manner for one reason or another. A potential cause for such a risk of breakdown is that the players may get fed up as negotiations become protracted, and thus walk away from the negotiating table. This type of human behaviour is random, in the sense that the exact time at which a player walks away for such reasons is random. Another possible cause for the existence of a risk of breakdown is that ‘intervention’ by a third party results in the disappearance of the ‘gains from co-operation’ that exists between the two players. For example, while two firms bargain over how to divide the returns from the exploitation of a new technology, an outside firm may discover a superior technology that makes their technology obsolete. Another example is as follows: while a corruptible policeman and a criminal are bargaining over the bribe, an honest policeman turns up and reports the criminal to the authorities. In the next section I analyse a simple modification of the basic alternating-offers model — studied in Section 3.2 — in which the risk of breakdown is a main force that influences the bargaining outcome. It will be shown that the players' payoffs when (and if) negotiations break down and their respective degrees of risk aversion are crucial determinants of the bargaining outcome. Section 4.3 contains an application to the problem of tax collection when the tax inspector is corruptible.
Contents
- Chapter
- Get access
6 - Inside Options
- Chapter
- Get access
Summary
Introduction Consider the basic exchange situation in which a seller and a buyer are bargaining over the price at which the seller sells an indivisible object (such as a house) to the buyer. If agreement is reached on price p , then the seller's payoff is p and the buyer's payoff is π – p . Furthermore, the seller obtains utility at rate gs while the object is in her possession, where gs ≥ 0; thus, for Δ > 0 but small, she obtains a payoff of gs Δ if she owns the house for Δ units of time. Given her discount rate rs > 0, this means that if she keeps possession of the house forever, then her payoff is gs/rs , which is assumed to be less than π — for otherwise gains from trade do not exist. The payoff that the seller obtains while the parties temporarily disagree is her inside option — which equals gs [1 – exp(– rs Δ)]/ rs if they disagree for Δ units of time. In contrast, her outside option is the payoff she obtains if she chooses to permanently stop bargaining, and chooses not to reach agreement with the buyer; for example, this could be the price p * (where p * > gs/rs ) that she obtains by selling the house to some other buyer. A main objective of this chapter is to explore the role of inside options on the bargaining outcome.
3 - The Rubinstein Model
- Chapter
- Get access
Summary
Introduction In this chapter I study Rubinstein's model of bargaining. A key feature of this model is that it specifies a rather attractive procedure of bargaining: the players take turns to make offers to each other until agreement is secured. This model has much intuitive appeal, since making offers and counteroffers lies at the heart of many real-life negotiations. Rubinstein's model provides several insights about bargaining situations. One insight is that frictionless bargaining processes are indeterminate. A bargaining process may be considered ‘frictionless’ if the players do not incur any costs by haggling (i.e., by making offers and counteroffers) — in which case there is nothing to prevent them from haggling for as long as they wish. It seems intuitive that for the players to have some incentive to reach agreement they should find it costly to haggle. Another insight is that a player's bargaining power depends on the relative magnitude of the players' respective costs of haggling, with the absolute magnitudes of these costs being irrelevant to the bargaining outcome. An important reason for the immense influence that Rubinstein's model has had, and continues to have, is that it provides a basic framework, which can be adapted, extended and modified for the purposes of application. This will become evident in several later chapters of this book. In the next section I describe and analyse a simple version of Rubinstein's model in which two players are bargaining over the partition of a cake (or ‘surplus’) of fixed size.
10 - Repeated Bargaining Situations
- Chapter
- Get access
Summary
Introduction In this chapter I study situations in which two players have the opportunity to be involved in a sequence of (possibly different and/or interdependent) bargaining situations. Such a situation will be called a ‘repeated’ bargaining situation (RBS). Examples of repeated bargaining situations abound. For instance: (i) in any marriage the wife and the husband are in a RBS, and (ii) in most bilateral monopoly markets the seller and the buyer are in a RBS. To illustrate the potential for interdependence amongst the bargaining situations in a RBS, consider a bilateral monopoly market for some input in which the seller and the buyer have the opportunity to be involved in a sequence of ‘one-shot’ transactions, and suppose that the buyer's reservation value for the input depends on the level of her capital stock. Since the price at which trade occurs determines the buyer's profit — which, in turn, determines her investment in capital stock — it follows that the buyer's reservation value in any one transaction is determined by the outcomes of past transactions. Hence, any pair of one-shot transactions are interdependent. In Sections 10.2–10.4 I study repeated bargaining models, in which the outcomes of any pair of bargaining situations are negotiated separately, and moreover, the outcome of each bargaining situation is negotiated when (and if) it materializes. Although in the formal structure of these repeated bargaining models there is no reference to contracts, it is possible to provide the following contractual interpretation: the repeated bargaining models embody the notion that the RBS is governed by a sequence of short-term (or, limited-term) contracts.
2 - The Nash Bargaining Solution
- Chapter
- Get access
Summary
Introduction A bargaining solution may be interpreted as a formula that determines a unique outcome for each bargaining situation in some class of bargaining situations. In this chapter I study the bargaining solution created by John Nash. The Nash bargaining solution is defined by a fairly simple formula, and it is applicable to a large class of bargaining situations — these features contribute to its attractiveness in applications. However, the most important of reasons for studying and applying the Nash bargaining solution is that it possesses sound strategic foundations: several plausible (game-theoretic) models of bargaining vindicate its use. These strategic bargaining models will be studied in later chapters where I shall address the issues of why, when and how to use the Nash bargaining solution. A prime objective of the current chapter, on the other hand, is to develop a thorough understanding of the definition of the Nash bargaining solution, which should, in particular, facilitate its characterization and use in any application. In the next section I define and characterize the Nash bargaining solution of a specific bargaining situation in which two players bargain over the partition of a cake (or ‘surplus’) of fixed size. Although this type of bargaining situation is not uncommon, a main purpose of this section is to introduce — in a relatively simple and concrete context — some of the main concepts involved in defining Nash's bargaining solution.
