Introduction

In this chapter we survey the axiomatic theory of bargaining for a fixed number of agents. Although Nash's paper has enjoyed great popularity since its publication, and the Nash solution has been used in numerous studies of actual conflict situations, the central role played by this solution was very seriously challenged in the mid-1970s by the introduction and the characterization of other solutions, notably the Kalai–Smorodinsky and Egalitarian solutions. Largely spurred by these developments, an explosion of contributions to the theory has occurred since. Here, we will describe the main aspects of the theory, with particular emphasis on results concerning the solutions that will be at the center of our own theory.

The main solutions

Although alternatives to the Nash solution were proposed soon after the publication of Nash's paper, it is fair to say that until the mid-1970s, the Nash solution was often seen by economists and game theorists as the main, if not the only, solution to the bargaining problem. This preeminence is explainable by the fact that Nash developed a natural strategic model yielding exactly the same outcomes at equilibrium, as well as by his elegant characterization. In spite of the lack of unanimous agreement on some of the specific axioms that he used (in fact, one of them, the independence axiom, was subjected to a significant amount of criticism early on), the appeal of the axiomatic methodology is such that the revival of the theory can be dated to the new characterizations developed in the mid-1970s.

Recently survival analysis has made its debut in econometrics as a technique for modeling the observed labor force experience of individuals over time. Although continuous-time theoretical models of optimal dynamic labor force participation are available, little use of them has been made in the empirical literature. Recent papers by Burdett et al. (1982), by Flinn and Heckman (1982) and by Olsen and Farkas (1982) are exceptions. Burdett et al. develop a continuous-time Markov decision model of an individual worker's labor force participation decision problem and use the model to interpret their empirical estimates of what can be regarded as “reduced form” relationships between rates of transition between states – employment, unemployment, and non-participation – and worker characteristics. Flinn and Heckman present a different but related participation model and discuss the problem of empirically identifying its “structure.” Finally, Olsen and Farkas suggest an econometric method of estimating the “structure” of continuous-time Markov chain models. This chapter makes three contributions. First, a general dynamic continuous-time discrete choice model is set down which includes those of all three papers as special cases. Second, the problem of identifying the structure of special cases of the model is studied. Third, the method suggested by Olsen and Farkas is used to estimate the structure of the Burdett et al. model.

In all three papers, “choice” is a dichotomous decision made by the individual from time to time to be in one of a finite number of mutually exclusive states.

The neoclassical model of demand is the economist's basic tool for studying the relationship among prices, incomes, and quantities consumed. The theory is intuitively pleasing and delivers empirically meaningful restrictions which may form the basis for specification checking. There is an extensive literature on the estimation and interpretation of models of demand in this tradition; important treatments include Deaton and Muellbauer (1980), Phlips (1974) and Theil (1975). The neoclassical model predicts the behavior of the consumer who takes prices as parametric, and who adjusts quantities consumed continuously so that the marginal utilities per dollar spent are equal across commodities. An important class of purchases do not fit well into this framework, namely tied sales and negotiated agreements. An important case in point is the employment agreement.

This chapter considers methods of inferring utility (or demand) function parameters from data on negotiated agreements. These parameters are important for understanding consumer behavior, and practically for predicting responses to policy changes or changes in institutions, whether or not the neoclassical model is appropriate. As we shall see, the specification of the stochastic structure of the model is crucial to the problem of inference when agreements are involved. Additive “errors” cannot simply be tacked on to deterministic demand functions as is typically done when the neoclassical model is applied (but see Theil (1975) for a supporting theory).

Introduction

A major part of the theory of social choice is based on the assumption of collective rationality – that social decisions be made consistently with the maximization of some ordering on the space of alternatives, where by an ordering is meant a binary relation that is reflexive, transitive, and complete. For example, collective rationality is a defining property of an Arrow (1951) social welfare function (Arrow SWF), which produces social orderings of a given set of physical alternatives from profiles of individual orderings of those alternatives. Another well-known example is the family of Bergson–Samuelson social welfare functions (Bergson, 1938; Samuelson, 1947).

By a Bergson–Samuelson SWF is usually meant a real-valued function defined on utility space, representing a social ordering of all possible utility allocations for the society under consideration. As pointed out by Sen (1970, pp. 34–5), it is in general the social ordering itself that is of primary interest for social decision making. Therefore, any ordering of utility space will here be referred to as a Bergson–Samuelson SWF regardless of whether it has a real-valued representation.

Observe that the domain of definition of a Bergson–Samuelson SWF differs from that of an Arrow SWF: A Bergson–Samuelson SWF is defined on a space of utility allocations, whereas an Arrow SWF is defined on a space of individual orderings, for example, a space of utility functions.

A condition that is often imposed on the Bergson–Samuelson SWF is Separability, or Independence of Unconcerned Individuals, as it is also sometimes called.

In the 17 years after Stigler's work on search theory, economists have relied increasingly on the notion of search activity to explain diverse economic phenomena. The explanation of one type of unemployment – search, or frictional unemployment – is sometimes considered to be the essential contribution of search theory, but this is a narrow view. The concept of productive investment in search has been used to explain such diverse phenomena as price rigidity (Gordon and Hynes 1970), advertising expenditure (Gould 1970; Butters 1974), duration of unemployment spells (Ehrenberg and Oaxaca 1976; Classen 1977), retention of military personnel (Gotz 1975), the effects of minimum wages (Mincer 1976), quits and layoffs (Mortensen 1977; Parsons 1973), and marriage and divorce rates (Becker, Landes, and Michael 1977). Despite the wide and growing list of empirical phenomena which have been “explained” by search theory, it seems a fair assessment of the subject would have to state that, apart from tightening some theoretical arguments on several topics, the concept has had little effect on the way economists interpret data and almost no effect on matters of public policy.

A major reason for this current situation is the lack of empirical work on search theory. Moreover, what empirical research has been done generally has been only minimally related to the underlying theory. In consequence, it has been difficult to interpret the empirical results, and, more important, it has been impossible to infer whether a given set of results is or is not consistent with a search-theoretic interpretation.

Introduction

In this chapter we offer a characterization of the Egalitarian solution based on the axiom of Population Monotonicity introduced in Chapter 3 as well as on several familiar axioms. Specifically, we show that the Egalitarian solution is the only solution to satisfy Weak Pareto-Optimality, Symmetry, Independence of Irrelevant Alternatives, Continuity, and Population Monotonicity. This list of axioms differs from the list used in Chapter 3 to characterize the Kalai–Smorodinsky solution only in that the independence axiom replaces the invariance axiom. The independence axiom has already been briefly encountered in Chapter 2. The present chapter opens with its detailed evaluation.

First, recall that the independence axiom originally introduced by Nash (his property 7 on p. 159 in 1950, his axiom V on p. 137 in 1953) states that restricting a problem without eliminating the alternative chosen as best for that problem should leave this best alternative unaffected. Since there are fewer alternatives with which the originally chosen alternative is competing, this should strengthen its appeal. The axiom has been the object of a large amount of attention, and it has been adapted to a number of other contexts. In the social choice literature, it is now known under a variety of names, such as Property α, contraction consistency, and the Chernoff condition. [See, for instance, Sen (1979), who discusses it and relates it to similar axioms.] Here we will keep the phrase independence of irrelevant alternatives, which seems to have remained standard in bargaining theory (see Roth, 1979b), with a warning that the axiom should not be confused with the condition of the same name used by Arrow (1951).

A concept of the urban system

We use the term ‘urban’ to convey a simple image: the familiar concentration of bricks and mortar, varying enormously in scale from the village to the metropolis and conurbation, which contrasts with the rural. But the image is over simple. Webber has pointed out a second meaning: the relatively sophisticated urban life-style which can be obtained in the rural area by those having a high, i.e. urban, standard of living (television, radio, cars, private planes, etc.).

There is a further dimension to the term which is significant for us. No urban area, except perhaps the remotest jungle-bound or desert village, is self-contained in that only residents use it. In contrast, the typical town is used in part by residents and in part by others who visit for various activities (work, education, recreation, etc.); and some of the town's residents will travel outside for their activities (work, recreation, etc.). Thus any town can be defined in relation to this functional criss-crossing of ‘urban activities’. This definition in itself must bring in the ‘regional system’ in which the town functions. In this sense, the ‘urban’ embraces the ‘regional’ system within which it functions.

Any town or region thus comprises a diverse array of physical elements (buildings of all kinds and spaces between them, parks, roads, etc.) and of diverse human activities (shopping, production, recreation, etc.). In the diversity there is some order, for otherwise people would not get to work on time, they would not have the milk bottle on the doorstep each morning, and they would not meet in groups for religion, culture, etc. Diagrams 1.1 and 1.2 give one version of this order.

Context

In Chapter 7 we introduced a model for the approach to financial analysis for management of the built environment at any stage in the life cycle, and in Chapter 8 showed how this could be adapted for conservation of the CBH. We now demonstrate the use of the analysis for the central theme of our concern: the decision whether to rehabilitate or redevelop heritage buildings? But while answering this particular question the estimates can also illuminate others of relevance to conservation: what price to pay for a property subject to conservation via rehabilitation? What is the ceiling on capital costs of works which could be incurred with an eye to viability? What would be the limit on operating costs which could be incurred having regard to the rents to be realised?

These and related questions can be answered by the application of a generic method of financial appraisal/valuation. We do not propose to reproduce here the wide array of foundation material on this analysis, but to demonstrate the principles by reference to an imaginary example.

An illustration of financial analysis

Let us return to the 100 year old merchant house of (8.3.3) comprising 15,000 sq. ft. gross on a site of half an acre in the centre of town. It is located in the business area but has been kept in residential use until recently by the last descendant of an old family who has died.

Context

We introduced above (Introductory, 13.3 and 14.2) the term ‘social’ to reflect that financial and economic analysis was concerned in each case with repercussions on sectors other than those who were promoting the project under consideration. But even under this connotation the range of the sectors brought in is only partial. For example in social financial analysis they exclude off-site costs not borne by the promoters; and while social cost benefit analysis is capable of handling the sectors which are indirectly affected, it typically does not set out to do so.

But there are decision situations in which consideration of the impact on the whole community is essential, as in urban and regional planning, where the ‘public interest’ requires that decisions take into account the impact on all relevant sectors of the relevant community. Thus a full analysis is required which will encompass all the off-site linkages and effects which were introduced in Table IV. 1, thus including all relevant externalities and spillovers. Thus a fully social form of analysis is required. This is provided by community impact analysis.

But even if social cost benefit analysis were to attempt to cover the whole range of sectors and externalities involved, it typically has the following limitations. Being founded in economic analysis it tends to have regard primarily to economic impacts and thus ignores others which are relevant, such as social and environmental, which come outside the ‘measuring rod of money’ and are not in the economic content of national income accounts.

The CBH as a resource

Certain buildings are created with the intention of their being monuments (royal palaces, royal burial chambers, mansions intended to be the home of a family for generations, churches or mosques). These apart, when the CBH is initially developed it would not be seen as distinct from the generality of the built environment; it is by definition only later that the social decision is taken to conserve it.

Such a decision certainly constrains the use of the stock in question as a resource. For example, how can you expand the economic base of the community in manufacturing, retailing, commerce, etc. if large parts of the relevant fabric were designed with an eye to the requirements of centuries ago and conserved since? But in other respects the CBH can be seen as a resource of even higher value than if it were not so earmarked, as the following examples show:

1. Stock designed in a previous age can provide an environment which will not or cannot be reproduced today, and therefore offers a relatively scarce opportunity for both stability in the physical environment and enrichment of human experience.

2. Architecture from earlier centuries can give an aesthetic character to a locality which is distinctive from that provided solely by recent and contemporary generations, and can so enrich the human experience.

3. […]

This book is a sequel of joint research in 1982-84 by the writer and Professor Joseph Schweid with a grant from the Jerusalem Institute for Israel Studies. The Research Report, The Role of Economics in the Conservation of the Cultural Built Heritage: Policy Conclusions for Israel, was presented in English in four parts:

1. I Planned Conservation of the Built Environment

2. II Economics in the Conservation of the Built Environment

3. III Two Jerusalem Case Studies

4. IV Application to Israel: Principles, Practice and Procedures

The Jerusalem Institute asked that the Report be published in two versions: in Hebrew for the Israeli audience and in English for Israel and abroad.

Since the Israeli audience would be primarily concerned with Parts III and IV, these were highlighted in the Israeli version with the remainder being presented as summaries. This version, edited by Joseph Schweid, appeared under the title Conservation of the Built Heritage (Jerusalem: The Jerusalem Institute for Israel Studies, 1986).

By the same token the English version required adaptation of the Research Report, in this instance the omission of Parts III and IV, and concentration on Parts I and II. In addition there was a further significant enlargement of scope. This arose from the experience of writing the Research Report, namely, that it was not practicable to discuss the economics of conservation without first presenting as a context the subject matter of conservation; and not practicable to present the conservation of the cultural built heritage without discussing as a context the conservation of the built heritage in general.