Group selection and social norms
In recent years evolutionary game theory has become a popular tool of economic theory. It is often thought that the evolutionary approach shows that equilibrium in economic and social interaction depends much less on individual rationality than has traditionally been believed. The standard evolutionary game theory model, however, has a built-in group selection assumption. By group selection is meant that behaviours that always do worse relative to other behaviours in the same group nevertheless survive in the long run because they make the group do better relative to other groups. If this group selection effect is removed from the evolutionary game theory model, central results, such that, for example, strictly dominated strategies are weeded out in the long run, cease to hold. One part of the project aims at developing models of evolution in games without group selection, and hence to deepen our understanding of the role of group selection for central results in the literature. Another part of the project deals with utilizing group selection effects to explain the emergence of social norms that, for example, prescribe that the individual contribute to the provision of public goods even in the absence of direct incentives.
Karl Wärneryd, Stockholm School of Economics
The project has (so far) resulted in two publications, "Sexual Reproduction and Time-Inconsistent Preferences" (Economics Letters 95, pp 14-16, 2007) and "Long-Run Selection and the Work Ethic" (joint with Jens Josephson, forthcoming in Games and Economic Behavior). The contents of these papers are discussed below.
Sexual Reproduction and Time-Inconsistent Preferences
This paper provides an evolutionary explanation for non-exponential, time-inconsistent discounting---a phenomenon well-known from, e.g., laboratory experiments. The idea here is that because humans used to live in small groups, the probability that the offspring of a gene's carrier would itself have the gene may have been greater than one-half. This suggests that fitness-maximizing time preference would have been biased toward the present.
Suppose there is a gene that causes its carrier to defer to the future some consumption that could have been engaged in today. From the point of view of the gene, it does not matter which individual carrier does the consumption, as long as the fitness of the gene itself is increased. During the evolutionary period when most of our current genetic makeup would have been selected for, some or most of such saved resources would, since average life expectancy was low, ultimately have been consumed by the offspring of an individual.
Since in diploid species a child on average gets half of its genes from each parent, this perspective can be used to construct an evolutionary explanation of subjective discounting. In fact, since grandchildren, on this account, have one-fourth of the genes of the original individual, it specifically suggests the evolutionary origins of exponential discounting, along with a specific discount factor.
There appears to be ample evidence, from introspection, anecdote, and experiments, that humans as well as animals do in fact discount the future. But the same evidence typically also suggests that
this discounting is done at a rate that declines with time, so that plans that are optimal from the point of view of today may no longer be optimal tomorrow.
An individual with a stationary utility function u discounts the future if the utility of a stream of consumption levels c_0, c_1, c_2, . . . is
U:=u(c_0)+d_1 u(c_1)+d_2 u(c_2) . . .,
where 0<=d_i<1 and d_{i+1}
Now consider a gene that controls intertemporal consumption allocation. A gene that takes into account that its carrier's offspring have a positive probability of carrying the same gene may maximize its inclusive fitness by leaving some consumption that could have been indulged in today to future generations of carriers. What, from this perspective, is the optimal valuation of a unit of consumption performed by offspring?
Let p_1 be the probability that a first-generation child carries the gene. Earlier literature takes this probability to be equal to the expected coefficient of relatedness under sexual reproduction in diploid species. Since in this setting an offspring gets in expectation half of its genes from each parent, the coefficient is equal to .5. Hence the fitness-optimizing intertemporal consumption allocation gene should be indifferent between one unit of consumption by the present carrier and two units of consumption by the present carrier's first-generation offspring, and between one unit now and four units consumed by the carrier's grandchildren. This corresponds to an exponential discounting scheme with d_i=p_1^i. Note that since typically individuals from several generations will be alive at the same time, the relevant time periods may be much shorter than a generation.
The account given above implicitly assumes that when an individual mates, the mate is drawn from a population where in effect the probability of encountering a copy of the same gene is
zero. But in the evolutionary setting we need to consider humans lived in small groups usually numbering no more than 150 individuals. In such a group the degree of inter-relatedness would have been fairly high, and the probability of mating with somebody who was also carrying the time-preference gene would have been positive.
Suppose a mate selected at random has the time-preference gene with probability a>0. Then on average a child of the first generation will have the gene with probability p_1:=.5+.5a, and a grandchild will have the gene with probability
p_2:=.5p_1+.5a=.25+.75.
Since we have
p_2=.25+.75a<.5+.5a=p_1
for any a<1, this is indeed a discounting scheme in the standard sense. Since we also have
p_2=.25+.75a>.25+.5a+.25a^2=p_1^2,
it is time-inconsistent with a bias toward the present.
Here we have assumed that the environmental probability a of a mate already having the gene remains constant over time. As indeed it would, if there were no additional relative fitness advantage associated with carrying the gene.
Long-Run Selection and the Work Ethic
well-established observation in the experimental literature. Since a contributor is always strictly worse off than a non-contributor the question is raised if an intrinsic motivation to contribute can survive in an evolutionary setting. In this paper we apply stochastic evolutionary dynamics and give conditions for equilibria with a positive number of contributors to be selected in the long run.
In a social dilemma the provision of a public good requires some costly effort from one or more individuals, but explicit contracting is not possible. Each participant in a dilemma therefore has an incentive to free-ride on the contributions of the others. How social institutions mitigate social dilemmas is the subject of a large literature both in economics and the social sciences more generally. In this paper, we instead study the evolutionary survival properties of an intrinsic motivation
to contribute in dilemma situations.
Consider the case of cooperation within the firm. When individual contributions to output are not verifiably measurable, complete contracting within the firm is impossible, and a free-rider
problem is present. This observation has been used as the basis for explanations of the organizational structure of the firm, such as the monitoring and budget-balance-breaking roles of an
outside owner.
But free-rider problems in team production may also be overcome if individual agents have an internalized work ethic. Experimental evidence of long standing suggests that
1. people do in fact contribute in dilemma situations even though contribution is not enforceable, and
2. the rate of contribution is declining in group size and the individual cost of contributing.
In a broad sense, laboratory behavior therefore more or less conforms to some of the possible predictions of a noncooperative public goods provision model introduced by Palfrey and
Rosenthal, which we take as our basic model in this paper.
The general Palfrey-Rosenthal model typically has multiple equilibria, some of which involve positive contributions, others which do not. In this paper we embed the game in a dynamic evolutionary setting with random mutations, which allows us to predict the equilibria we would be likely to observe in the long run. By evolution we mean cultural evolution by means of imitation of successful behavior, but our model is also open to other interpretations. We show that for group sizes small enough, and a cost of contributing low enough, in the long run we are most likely to observe a positive amount of contributions even when also non-contribution is a stable state of the deterministic model.
Consider a simple example: A firm consists of two individuals. An individual is programmed to be either a worker or a shirker. If there is at least one worker in the firm, the firm is successful, and each individual gets a gross payoff, or fitness, of 1. Otherwise each individual gets a payoff of zero. A worker also always sustains the cost k, with 0
Publications
1. Wärneryd, K, “Sexual Reproduction and Time-Inconsistent Preferences”, Economics Letters 95:14—16, 2007.
2. Josephson, J; Wärneryd, K, “Long-Run Selection and the Work Ethic”, under utgivning i Games and Economic Behavior.