by Chris Webster
This paper presents a simulation of urban neighbourhood formation and growth based on the economic theory of property rights. The simulation shows that stable and efficient neighbourhoods can evolve from a random distribution of "good" neighbours who offer voluntary reductions in the activities that reduce the welfare of neighbours. However, such neighbourhoods may not evolve and the city may fragment into inefficient neighbourhoods in which the normal prisoner's dilemma dynamic holds; or into unstable neighbourhoods. Which type of city emerges is purely a matter of chance and depends on the initial spatial distribution of good neighbours.
I am grateful to discussants at various conferences for their comments on earlier versions of this paper; and to two anonymous referees.
II. Institutional Evolution, Property Rights And Neighborhood Efficiency
III. Voluntary Agreements And Neighbourhood Equilibrium
IV. A Cellular Model Of Emergent Neighbourhoods Under Voluntary Governance
V. Simulation Results
Neighbourhoods are more than artefacts of urban scholarship. They can be detected from the train window, delineated on maps, priced by real estate agents and discriminated against by homebuyers. The fact that governments make policy for neighbourhoods and that buyers and sellers in property markets are not indifferent to their attributes means that neighbourhoods are economic entities. And yet the neighbourhood in economic geography, urban economics and planning remains inadequately conceptualised. This paper presents the idea of a neighbourhood as a constantly evolving institution the purpose of which is to govern joint consumption in cities. In this, I follow Olson (1971) who posited a self-interested explanation of group formation, arguing that associations form to provide individual members with shared consumption benefits - including comrade and other member's attributes. Viewed in this way, neighbourhoods are joint consumption spheres and spheres of joint agreement (or contract) over the allocation rules that govern the consumption and production of neighbourhood attributes. To consider neighbourhoods as joint consumption spheres is uncontroversial. Economic models of sub-municipal divisions that broadly rest on the consumption-sharing premise may be found in geographical theories of market areas (Christaller 1966, Losch 1954); urban bid rent theory (Alonso 1964); hedonic price theory (Rosen 1974); local public goods theory (Tiebout 1956); club theory (Buchanan 1965); and theories that synthesise these models (Hochman et al 1995). The notion of neighbourhoods as spheres of joint agreement is more novel and it is one of the paper's objectives to illustrate this concept in some depth. By way of introduction, consider the idea that contracts emerge to create and protect rights to consume private and public goods and services (referred to as property rights from hereon). Property rights may be de jure (legal) or de facto (economic) and the former, which may be created by government or market, evolve to protect the latter. Economic property rights are allocated by initial endowment, markets, governments, voluntary agreement and anarchic actions. Individuals with greater economic, political or physical power might be expected to secure for themselves greater economic rights over scarce shared resources. They do this in various ways including colonising land near to facilities that yield positive externalities. It is argued later in the paper that shared goods and services exist where it is inefficient to allocate them between individuals. In efficient neighbourhoods, voluntary or formal contractual agreements ensure a balance in the demand and supply of neighbourhood externalities and the shared goods are left in the public domain because congestion costs are absent, or at least lower than the transaction costs of assigning property rights to individuals. In a less obvious sense, inefficient neighbourhoods are also spheres of joint agreement about property rights. A decision by an individual to over-consume or over-produce at the expense of neighbours because that is the ambient culture of the neighbourhood is, in effect, an agreement to a common rule of conduct. Greater quantities of negative externalities are left in the public domain because from the individual's or household's point of view, the transaction cost of reassigning rights over bad neighbour risks exceeds the benefits to be gained.
Using these and related ideas, the paper presents a cellular automata (CA) simulation that demonstrates how voluntary neighbourhood management institutions can emerge naturally through bi-lateral neighbour agreements. It illustrates the chaotic nature of neighbourhood evolution however, showing that neighbourhood growth, (spread of contracts), can equilibrate in several states: a city-wide stable neighbourhood; fragmented stable neighbourhoods; fragmented unstable neighbourhoods; fragmented anarchy. Section II elaborates on the ideas of institutional emergence and property rights. Section III presents a behavioural model of voluntary neighbourhood contracts, which underlies the simulation and is based on the propositions in section II. Section IV presents the simulation. Section V discusses the results; and Section VI concludes.
Society chooses between a variety of mechanisms to allocate scarce resources and these include governments, markets, voluntary agreements and anarchy. All are active to some degree in effecting the allocation of the shared territorial goods that make up neighbourhoods and the institutions that implement them constantly evolve in shape, size and function. Two important questions underlie many academic and practical discussions about urban management and planning: what are the more efficient institutional forms and what is the efficient size of a particular institutional form? The class of simulation presented in this paper and elsewhere by the author (Webster and Wu 1999a, 1999b, 2001, Wu and Webster 1998, 2000) allows for simultaneous analysis of both efficiency questions. The interdependence between spatial institutions and spatial attributes (neighbourhood public goods) can be made explicit in the language of property rights theory following Alchian 1965, Cheung 1969, Barzel 1997. On the one hand access to neighborhood goods is determined by the nature of the rights governing their consumption; and these property rights (de jure and de facto) therefore shape urban morphology. On the other hand, property rights are determined by urban morphology and it is this circularity that leads to institutional evolution. Consider the following proposition:
Propostition 3 is even stronger, suggesting that there are real costs of leaving neighbourhood attributes in the public domain. These are the costs that arise when neighbours compete to consume congested shared-resources - costs that could be avoided by appropriate assignments of rights over those resources.
The remainder of the paper examines an interesting class of voluntary institution: one that is crucial to the composition and evolution of cities. The institution is the collective agreement that renders many residential neighbourhoods distinct and stable - or the lack of it that renders them indistinct or unstable. Formally constituted homeowners' associations are rare outside of the U.S. and yet cities the world over contain well-functioning neighbourhoods governed by informal cultures of consumption and undocumented rules of behaviour. This is so with and without effective government regulation of land use and environmental nuisances. Where collective action is not the cause of these informal neighbourhood norms, then individual action must be and it is worth asking how this works. As an institutional phenomenon a neighbourhood may be thought of as a joint producer-consumer club in which every household stands to gain if it and all others consume and/or produce (home investment 'products' etc) at socially optimal levels. In this sense, the neighbourhood is co-produced. However, one must ask what the individual incentive is to voluntarily adjust consumption and home-based production when free-riding will maximise individual payoff. One answer is that the economists have got it wrong and that the prisoner's dilemma is a fiction. Or perhaps the difference between successful and unsuccessful neighbourhoods is accounted for by differences in preferences -- a preponderance of public spirited residents overcome the collective consumption dilemma faced by the more selfish residents of less cohesive neighbourhoods. The idea is worth pursuing and it has obvious similarities with Tieboutian notions of spatial sorting into homogenous preference groups. However an alternative explanation of neighbourhood variation is possible that is consistent with the conventional view of residents as individual maximisers. It is an atomistic theory of neighbourhood formation and rests only on the assumption that individuals will exploit mutual benefits in bi-lateral negotiations. The following section elaborates this idea.
Before doing this, however, it will be useful to comment further on why an atomistic neighbourhood might be viewed as a club. Consider the way in which a sport clubs functions. An entrepreneur provides a set of facilities and organises a constitutional framework within which members can participate. They participate not for the good of the club but for their own individual enjoyment. A club may have less or more rules. A swimming pool with no rules apart from the requirement that members should pay a joining fee will develop its own consumption culture over time -- and possibly evolve a constitution to avoid dissipation of benefits. Many residential neighbourhoods are rather like the swimming club. Residents buy-in to a locality which offers them certain facilities including any benefits derived from the personal characteristics of other residents and the benefits of other residents' home investment expenditure. The property market created the club facilities: developers, with subsidy from the municipality perhaps, created the basic infrastructure and subsequent waves of residents created social and environmental capital. The individual maximising behaviour of resident members determines the efficiency of the neighbourhood's consumption culture just as it does in the swimming club. The atomistic neighbourhood is organised at one level, therefore, by market institutions, which governs the allocation of property rights. Without the organising disciplines of the property, land, and insurance markets and the laws that sustain them, neighbourhoods would be truly anarchic. At another level, it is the capricious behaviour of individuals within a neighbourhood that govern the evolution (or not) or additional layers of informal and more formal governance institution. Although these may be seen as having more of a purpose than the market (and more clearly conforming to the popular notion of a club); the property market too, has a purpose -- to balance demand and supply, to price properties in relation to benefits received -- and home-owners buying into a neighbourhood are making a statement about the benefits they expect to receive. In this sense, that part of the locational premium derived from the local neighbourhood, might be thought of as a payment (to the outgoing owner) for securing a scare place in the neighbourhood club. The remaining sections elaborate on the capriciousness of neighbourhood institutions that evolve (or fail to evolve) to assign property rights over neighbourhood attributes that are not typically priced by markets.
Figure 1 represents three neighbours located along a street. Each derives certain benefits from certain consumption-production activities such as using their property for a business, playing music, repairing cars or extending the property. Due to diminishing returns, the marginal benefits decline as the level of activity increases and these are represented by the demand curves . Unrestrained, households would produce/consume q2 of the activity -- the point at which marginal benefit is zero. However, each household generates nuisance (externality) costs for its neighbours, represented by e and these are assumed to rise with the level of activity. The question arises, what will happen if neighbours negotiate with full information? The classic analysis is presented in Coase (1960) but in his account, negotiation involves real compensatory payments (in cash or kind). The case depicted in Figure 1 is a special and interesting case of the general problem since compensation is possible in terms of restraint. Neighbour 1 has the incentive to cut back on an activity that lowers neighbour 2's welfare if the latter offers compensation in the form of restraint on an activity that lowers neighbour 1's welfare. To simplify exposition, neighbours are assumed to be identical in preferences. The bargaining problem is Pareto relevant in that there are mutual gains from trade. Between q2 and q1, the welfare loss of a neighbour due to externalities is greater than the welfare gain due to consumption/production (E+F>F). A household will be willing to lose F by voluntary restraint in order to gain E+F from his neighbour's restraint. Since this is true of both parties, both gain from voluntary restraint and an informal contract can be assumed to emerge, which sets the acceptable level of consumption-production at the social optimum q1. By striking a good-neighbour agreement each party gains E and the neighbourhood of two gains 2E.
FIGURE 1: Consumption/production decisions by three neighbouring households
The simulation described in the next section models this behaviour by making the assumption that voluntary restraining contracts will emerge if at least three adjacent households make simultaneous bids to negotiate for mutual gain. In the one-dimensional case of houses on a street, this assumes that a household requires both neighbours to opt-in to the contract as a condition for opting-in itself. If one neighbour is not offering to restrain (because it's other neighbour is not offering) then the contract fails to emerge -- or dissolves if it had already emerged. Contracts only emerge, therefore where households stand to gain. If a neighbour on one side does not comply, the gains from the compliant neighbour are assumed to be wiped out (it only takes one bad neighbour to reduce welfare and once reduced, an additional source of nuisance adds only a small marginal cost). In a two-dimensional neighbourhood in which contracts can be made with households across a street or adjoining to the rear, the simulation models a situation in which a threshold of two others in the immediate joint-consumption sphere is required in order for a household to offer voluntary restraint.
Cellular automata (CA) is a class of simulation model in which discrete dynamic systems are simulated using cells and the cell transition behaviour is completely specified in terms of local relations (Toffoli and Margolus 1987). In CA, time advances in discrete steps. At each step a cell derives its next state from that of its close neighbours according to a set of local and uniform transition rules. The idea of cellular automata is closely associated with that of microscopic simulation in which the behaviour at a local scale gives rise to an emerging global organisation. Processes of positive feedback gradually confine the state transition of a system and the system is said to self-organise -- into stability, oscillation or chaos. In the application to urban economic systems, CA represents a modelling approach quite different from top-down and macroscopic approaches. The simulation reflects a new way of looking at the manner in which global organisational form emerges from an uncoordinated local decision-making process (Batty, 1995). The CA tradition had its origin in computational ecological experiments, the most famous of which is the Game of Life (Gardner 1970). Driven by a simple set of rules for turning a cell "alive" and "dead", the Game of Life was able to display complex behaviour. Since then, Artificial Life has grown into "a field of study devoted to understanding life by attempting to abstract the fundamental dynamics in other physical media -- such as computers -- making them accessible to experimental manipulation and testing (Langton et al. 1992, xiv). Urban systems are only one of many diverse domains in which the methods have been applied. CA's emphasis on atomistic behaviour; local information; spatial configuration; global-local interactions; and path dependency; makes it a powerful medium for exploring land market processes. (Examples of CA in urban economic, urban geography and planning include: Page 1999; Portugali and Benenson 1995; Webster and Wu 1999a, 1999b, 2001; Wu and Webster 1998, 2000; and White and Engelen 1993.)
The simulation presented below is a very simple conventional CA model in which there are 2 states (values 1 and 3 represent the same state an are necessary for the algorithm):
1(1,1,.,)->3; 2(1,1,.,)->3; 1(.,.,.,)->2; 2(.,.,.,)->2; 3(.,.,.,)->1
Reading across: if a cell (household) that is voluntarily restraining at the social optimum has at least two neighbours doing likewise, then maintain social optimum. If a cell producing at private optimum has at least two neighbours that are voluntarily restraining, then convert to social optimum. If a cell producing at social optimum does not possess at least two neighbours doing likewise, then convert it back to private optimum. Cells producing at private optimum and not having at least two voluntarily restraining neighbours continue to produce at private optimum. The fifth rule is purely algorithmic. The simulation starts with a random seeding of households switched to state 1 -- modelling some random start point in a neighbourhood's evolution at which a minority of households offer to make mutually beneficial agreements with neighbours. The CA proceeds with a 3x3 cellular neighbourhood.
It should be clear that the simulation is a discrete representation of the Coasian model in Figure 1 in which q1 and q2 are represented by discrete states (0,1). Elsewhere I have published continuous versions, which solve for optimal quantities of output and externalities by embedding simultaneous equations in the cell transition rules (Webster and Wu 2001). As well as making the algorithm more complex, such an approach also raises the number of parameters in the model, increasing problems of interpretation. The discrete CA model's relationship to the property rights propositions 1-3 discussed in Section II above should be briefly explained. Proposition 1 says that changes in the value of shared, or public domain goods, lead to demands for property rights reassignment. A neighbourhood of three households (Figure 1) each consuming/producing at q2 has less value than a neighbourhood of three similar households consuming/producing at q1. The difference in value is 3E. Proposition 1 says that the households in the lower value neighbourhood will seek to reassign property rights. This, any of them might do, by offering to restrain individual consumption/production. Such an offer is an attempt to create an informal contract or agreement (or institution, loosely defined) that effectively secures an individual's property right over his/her nuisance risk by imposing an obligation (backed up by threat) on neighbours. The success in bi-lateral institution-building depends, in the model, on the presence of neighbours willing to follow suit.
Figure 2 shows a city of 122,500 households in three stages of neighbourhood evolution. The bright areas are stable neighbourhoods comprising households who have agreed to voluntarily curtail production/consumption activity to a mutually agreed social optimum. Areas with intermediate brightness are unstable neighbourhoods in which households fluctuate between private and social optimum levels of activities as they make and break agreements. Dark areas are inefficient neighbourhoods in the sense that all households maximise individual welfare but in so doing are individually and collectively worse off (each forgoes a welfare gain equal to the area E in Figure 1).
The neighbourhoods in Figure 2 have emerged purely as a result of households making bilateral agreements with neighbours. This means of course that the resultant morphology is dependent on the initial spatial distribution of households offering to make good neighbour contracts (the top image in Figure 2). Had the starting distribution been different, a very different city might have emerged. This point is illustrated in Table 1, which shows the frequency distribution of neighbourhood types emerging in 100 simulations. The simulated city in Table 1 has 2,500 households (50x50) and each simulation is randomly seeded with 375 (15%) households that make an opening bid to make a good neighbour contract.
Reading the bottom row of Table 1: from a starting point of 15 percent socially efficient households, the city has a 0.33 chance of equilibrating to a state in which 91-100 percent of households are in stable efficient neighbourhoods (bottom right cell). The greater probability, however is that only 0-10 percent of households will form such neighbourhoods (0.46). Reading the top row, which is also bi-modal, there is a 0.33 chance of the city stabilising with 0-10 percent of households in neighbourhoods where consumption/production is individually optimal but jointly sub-optimal (inefficient neighbourhoods). The most likely percentage of households in inefficient neighbourhoods at equilibrium, however, is 61-80 percent (0.43). Reading the middle row, there is a roughly equal chance of 0-10 percent and 21-30 percent of households forming unstable alliances as they pursue mutually beneficial contracts.
FIGURE 2: Emergence of neighourhoods in a city of 122,500 households
TABLE 1: Probability of Inefficient, Unstable and Efficient neighbourhood formation
FIGURE 3: Random allocation of neighbourly contact offers and two contrasting equilibrium states (bright neighbourhoods are efficient, dark are inefficient and chequered are unstable)
These results shed an interesting light on debates about more planning vs. less planning; urban ecological evolution; neighbourhood formation and stability; private communities; and many other contemporary urban issues. It's main substantial point is that neighbourhoods can develop from bi-lateral action between households that are motivated by individual welfare maximisation. Areas of common consumption and production behaviour governed by informal rules and norms that might appear to be a spatial expression of collective action can emerge through bi-lateral action. The simulation also shows that neighbourhoods can be understood to be areas in which individuals agree on behavioural norms and voluntary regulation regimes for mutual self-interest. There is no community spirit (altruistic behaviour) built into the model. This means that neighbourhood stability is fragile and susceptible to individuals breaking faith. There is no incentive for this in the model once a stable area has evolved but exogenous factors might break the equilibrium and cause knock-on effects in neighbourhood boundaries throughout the city. Wu and Webster (1998) demonstrate something like this and show how random changes of land use at the boundaries of same-use zones cause a constant shifting of natural (market) land-use zones across the city over time in pursuit of economic efficiency. The fragility of neighbourhoods formed by informal contracts might be supposed to lead to a demand for more formal neighbourhood contracts as the city evolves. Returning to the propositions introduced in section II, this is the more likely the higher value of the nuisance problems (the higher the e curves in Figure 1 and the larger the triangle E) and the higher the risk of reneging neighbours. Two outcomes can be predicted: demand for government legislation that grants more powers of control (property rights) over shared neighbourhood facilities to residents; and a rising demand for private neighbourhoods. From one point of view, all forms of micro-neighbourhood governance including devolved municipal powers and proprietary communities (gated suburbs, condominiums, shopping malls, leisure complexes and industrial parks) might be thought of as a response to the capricious nature of voluntary agreements. Even where there are strong planning and environmental nuisance laws, successful residential, commercial and industrial neighbourhoods rely on a good deal of voluntary compliance in the use of public domain attributes. Where this cannot be relied upon there will be a natural evolution towards clearer property rights assignment and greater control whether this is via legal contracts and the market or via government regulation and policing.
There is a rich vein of ideas at the boundaries between the economic theory of property rights; the social science paradigms of emergence; the natural science paradigm of self-organising systems; and the economic analysis of land and property markets including the analysis of alternative levels, styles and tools of intervention. Fruitful lines for further research in the tradition of the work reported in this paper include the following. First, the simulation presented above does not model mobility. This is a limitation in the light of the importance of mobility in neighbourhood formation and evolution. An interesting extension would to allow relocation of households offering unsuccessful good-neighbour bids. Second, the model focuses only on the benefits from mutual restraint and does not allow neighbours to consume-produce beyond their own efficiency margin in retaliation to bad-neighbour gestures. It would be of interest to allow downward or degenerative evolution in this respect. In the extreme, some neighbourhoods may become dominated by asymmetric exchanges in which positive gestures yield equal reciprocal positive responses but negative gestures yield greater negative responses. Such neighbourhoods might turn into welfare black holes as the rent dissipated by producing and avoiding anti-social behaviour approaches the welfare gained by locating in the neighbourhood. The sum might even be allowed to become negative, simulating neighbourhoods in terminal decline -- something analogous, perhaps, to the tragedy of the commons in which the consumer surplus of everyone in the neighbourhood has been used up and there is no choice but to seek to exit. Third, and less bleakly, the simulation described in this paper only allows bilateral contracts. It would be of interest to simulate institutional growth under multi-lateral contracts. This might include an exploration of thresholds in the number of good-neighbour bidders; the introduction of history into the simulation such that institutions evolve as a function of past institutional configurations not just present; and an analysis of transaction costs and prisoner dilemma dynamics. There is also scope for more sensitivity analysis. In the simulations reported, a critical threshold of approximately 14 percent to 15 percent initially seeded good neighbour bids seems to hold. Above this range, the city eventually turns bright red (efficient). The higher the percentage of initial bids, the speedier the convergence to global social efficiency. Below the threshold, cities fragment into a mixture of efficient, inefficient and unstable neighbourhoods. The lower the percentage, the lower the proportion of efficient neighbourhoods at equilibrium. Fourteen to fifteen percent is the tipping threshold. The particular size of the threshold is at one level, a function of the model's cell geometry. Whether there is any relationship between the threshold-geometry association in modelling space and the equivalent association in real city space is an intriguing empirical question that addresses many familiar issues in environmental psychology, urban design and urban sociology.
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