The evolution of private property
Introduction
The endowment effect is the notion that people value a good that they possess more highly than the same good when they do not possess it. Experimental studies (see Section 2) have shown that subjects exhibit a systematic endowment effect. The endowment effect can be modeled by amending the standard rational actor model to include an agent's current holdings as a parameter. The endowment effect gives rise to loss aversion, according to which agents are more sensitive to losses than to gains. The leading analytical model of loss aversion is prospect theory (Kahneman and Tversky, 1979). This paper, for the first time, suggests a plausible argument for the existence and importance of the endowment effect and loss aversion.
Carmichael and MacLeod (1999) and Huck et al. (2005) have attempted to explain the endowment effect by showing that agents subject to the endowment effect do better in bargaining than those who have no special attachment to their current holdings. However, the endowment effect appears even when there is no scope for bargaining. Indeed, the effect may disappear in market-like settings (Zeiler and Plott, 2004). This paper shows that the endowment effect can be modeled as respect for private property in the absence of legal institutions ensuring third-party contract enforcement. In this sense, preinstitutional “natural” private property has been observed in many species, in the form of the recognition of territorial possession. We develop a model loosely based on the Hawk, Dove, Bourgeois game (Maynard Smith and Parker, 1976) and the War of Attrition (Maynard Smith and Price, 1973) to explain the natural evolution of private property.1
We show that if agents in a group exhibit the endowment effect for an indivisible resource, then property rights in that resource can be established on the basis of incumbency, assuming incumbents and those who contest for incumbency are of equal perceived fighting ability.2 The enforcement of these rights will then be carried out by the agents themselves, so no third-party enforcement is needed. This is because the endowment effect leads the incumbent to be willing to expend more resources to protect his incumbency than an intruder will be willing to expend to expropriate the incumbent. For simplicity, we consider only the case where the marginal benefit of more than one unit of the resource is zero (e.g., a homestead, a spider's web, or a bird's nest).
The model assumes the agents know the present value πg of incumbency, as well as the present value πb of non-incumbency, measured in units of biological fitness. We assume utility and fitness coincide, except for one situation, described below: this situation explicitly involves loss aversion, where the disutility of loss exceeds the fitness cost of loss. When an incumbent faces an intruder, the intruder determines the expected value of attempting to seize the resource, and the incumbent determines the expected value of contesting versus ceding incumbency when challenged. These conditions will not be the same, and in plausible cases there is a range of values of πg/πb for which the intruder decides not to fight, and the incumbent decides to fight if challenged. We call this a (natural) private property equilibrium. In a private property equilibrium, since the potential contestants are of equal power, it must be the case that individuals are loss averse, the incumbent being willing to expend more resources to hold the resource than the intruder is to seize it.
Of course, πg and πb will generally be endogenous in a fully specified model. Their values will depend on the supply of the resource relative to the number of agents, the intrinsic value of the resource, the ease in finding an unowned unit of the resource, and the like.
Our model of decentralized private property is like the “Bourgeois” equilibrium in the Hawk, Dove, Bourgeois game, in that agents contest for a unit of an indivisible resource, contests may be very costly, and in equilibrium, incumbency determines who holds the resource without costly contests. Our model, however, fills in critical gaps in the Hawk, Dove, Bourgeois game. The central ambiguity of the Hawk, Dove, Bourgeois game is that it treats the cost of contesting as exogenously given and taking on exactly two values, high for Hawk and low for Dove. Clearly, however, these costs are in large part under the control of the agents themselves and should not be considered exogenous. In our model, the level of resources devoted to a contest is endogenously determined, and the contest itself is modeled explicitly as a modified War of Attrition, the probability of winning being a function of the level of resources committed to combat. One critical feature of the War of Attrition is that the initial commitment of a level of resources to a contest must be behaviorally ensured by the agent, so that the agent will continue to contest even when the costs of doing so exceed the fitness benefits. Without this pre-commitment, the incumbent's threat of “fighting to the death” would not be credible (i.e., the chosen best response of the agent would not be subgame perfect). From a behavioral point of view, this pre-commitment can be summarized as the incumbent have a degree of loss aversion leading his utility to differ from his fitness.
Our fuller specification of the behavioral underpinnings of the Hawk, Dove, Bourgeois game allows us to determine the conditions under which a property equilibrium will exist while its corresponding anti-property equilibrium (in which a new arrival rather than the first entrant always assumes incumbency) does not exist. This aspect of our model is of some importance because the inability of the Hawk, Dove, Bourgeois game to favor private property over anti-private property is a serious and rarely addressed weakness of the model (but see Mesterton-Gibbons, 1992).
Section snippets
The endowment effect and territoriality
The endowment takes the form of a good being more highly prized by an agent who is in possession of the good than one who is (Tversky and Kahneman, 1981, Kahneman et al., 1991, Thaler, 1992). Thaler describes a typical experimental verification of the phenomenon as follows. Seventy-seven students at Simon Fraser University were randomly assigned to one of three conditions, Seller, Buyer, or Chooser. Sellers were given a mug with the University logo (selling for US$ 6.00 at local stores) and
Property rights in young children
Long before they become acquainted with money, markets, bargaining and trade, children exhibit possessive behavior and recognize the property rights of others on the basis of incumbency.3 In one study (Bakeman and Brownlee, 1982), participant observers studied a group of 11 toddlers (12–24 months old) and a group of 13 preschoolers (40–48 months old) at a day care center. The observers found that each group was
Respect for possession in non-human animals
In a famous paper, Maynard Smith and Parker noted that two animals are competing for some resource (e.g., a territory), and if there is some discernible asymmetry (e.g., between an “owner” and a later animal), then it is evolutionarily stable for the asymmetry to settle the contest conventionally, without fighting. Among the many animal behaviorists who put this theory to the test, perhaps none is more elegant and unambiguous than Davies, who studied the speckled wood (Pararge aegeria), a
Conditions for private property equilibrium
Suppose that two agents, prior to fighting over possession, simultaneously pre-commit to expending a certain level of resources to the contest. As in the War of Attrition (Bishop and Cannings, 1975), a higher level of resource commitment entails a higher fitness cost, but increases the probability of winning the contest. We assume throughout this paper that the two contestants, an incumbent and an intruder, are ex ante equally capable contestants in that the costs and benefits of battle are
Property and anti-property equilibria
To determine πg and πb, we must flesh out the above model of incumbents and migrants. Consider a field with many patches, each of which is indivisible, and hence can have only one owner. In each time period, a fertile patch yields a benefit b > 0 to the owner, and dies with probability p > 0, forcing its owner (should it have one) to migrate elsewhere in search of a fertile patch. Dead patches regain their fertility after a period of time, leaving the fraction of patches that are fertile constant
An anti-private property equilibrium
Consider a situation in which agents die unless they have access to a fertile patch at least once every n days. While having access, they reproduce at rate b per period. A agent who comes upon a fertile patch that is already owned may value the patch considerably more than the current owner, since the intruder will have, on average, less time to find another fertile patch than the current owner, who has a full n days. In this situation, the current owner may have no incentive to put up a
Conclusion
Humans share with many other species a predisposition to recognize private property. This takes the form of loss aversion: an incumbent is prepared to commit more vital resources to defending his property, ceteris paribus, than an intruder is willing to commit to taking the property. The major proviso is that if the property is sufficiently valuable, a private property equilibrium will not exist (Theorem 1).
History is written as though private property is a product of modern civilization, a
Acknowledgements
I would like to thank Eldridge Adams, Carl Bergstrom, Chris Boehm, Samuel Bowles, Peter Hammerstein, Marc Hauser, Mike Mesterton-Gibbons, the late John Maynard Smith, and an anonymous referee for helpful comments, and the John D. and Catherine T. MacArthur Foundation for financial support.
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