Social and Behavioral Sciences Commons^™

Let Me, Or Let George? Motives Of Competing Altruists, Ted Bergstrom, Rodney Garratt, Greg Leo

Ted C Bergstrom

Sometimes a costly action taken by a single individual is sufficient to benefit an entire group. This should imply technical economies of scale to groups of larger size. But in a group of selfishly motivated agents, a countervailing force, the free-rider problem, may actually reduce the likelihood of provision as group size increases. Yet there are con- spicuous real-world cases where, in seeming defiance of the free-rider problem, a small minority provides a public good that benefits a large population. Examples include unpaid contributions to Wikipedia, Linux, and the bone-marrow registry. We suggest that these successful outcomes occur because a …

On The Evolution Of Hoarding, Risk-Taking, And Wealth Distribution In Nonhuman And Human Populations, Ted C. Bergstrom

Ted C Bergstrom

This paper applies the theory of the evolution of risk-taking in the presence of idiosyncratic and environmental risks to the example of food hoarding by animals and explores implications of the resulting theory for human attitudes toward risk.

Measures Of Assortativity, Ted Bergstrom

Ted C Bergstrom

This paper discusses alternative measures of assortative matching and relates them to Sewall Wright's F-statistic. We also explore applications of measures of assortativity to evolutionary dynamics. We generalize Wright's statistic to allow the possibility that some types match more assortatively than others, and explore the possibility of identifying parameters of this more general model from the observed distribution of matches by the partners' types.

The Good Samaritan And Traffic On The Road To Jericho, Ted C. Bergstrom

Ted C Bergstrom

Stem Cell Matching For Patients Of Mixed Race, Ted C. Bergstrom

Ted C Bergstrom

Patients with leukemia and other blood diseases stand a good chance of recovery and a return to normal life if they receive a stem cell transplant from a living donor. In the absence of a transplant, their survival prospects are grim. For a transplant to be successful, the human leukocyte antigens (HLA) of the donor and recipient must be a close genetic match. To facilitate non-sibling matches, the developed nations of the world have set up national volunteer registries. The larges such registry is the NMDP (National Marrow Donor Program). We estimate the distribution of HLA types for individuals of …

Simple Economies With Multiple Equilibria, Ted C. Bergstrom, Ken-Ichi Shimomura, Takehiko Yamato

Ted C Bergstrom

This paper studies a general class of pure exchange economies that have multiple equilibria, which extend an example presented by Lloyd Shapley and Martin Shubik. For such economies, we find easily verified conditions that determine whether there are multiple equilibria. We also provide simple methods for constructing economies in which arbitrary pre-specified sets of prices are equilibria. These economies have simple comparative statics, since prices at interior competitive equilibrium depend on the parameters of utility but not on the endowment quantities.

Solving The Beautiful Mind Coordination Problem, Ted C. Bergstrom

Ted C Bergstrom

There are n boys and m girls. The boys are all expected utility maximizers and agree about the desirability of the prospect of dating each girl. Boys assign utility v_i to a date with girl i, where v_1>v_2>\dots v_n>0 and a utility of 0to having no date. Girls don't care which boy they go out with and they prefer having a date to not having a date. We find the Nash equilibrium strategy for boys.

Rationality And Personality In A Restaurant Entry Game: Is There An Entrepreneurial Personality Type?, Ted Bergstrom, Jon Sonstelie

Ted C Bergstrom

Students in a large principles class participated in a market experiment in which they had opportunities to take entrepreneurial action. These students had also taken the Meyers-Briggs personality test. We explore the relation between personality characteristics and participation decisions.

Natural Kantian Or Zoo Economicus? Evolutionary Theories Of Selfishness And Altruism Among Men And Beasts, Ted C. Bergstrom

Ted C Bergstrom

This paper addresses the question of whether our evolutionary history suggests that humans are likely to be individually selected selfish maximizers or group selected altruists. It surveys models from the literature of evolutionary biology in which groups are formed and dissolved and where the reproductive success of individuals is determined by their payoffs in a game played within groups. We show that if groups are formed randomly and reproductive success of group founders is determined by a multi-person prisoners’ dilemma game, then selfish behavior will prevail over maximization of group payoffs. However, interesting models can be found for which “group …

Log-Concave Probability And Its Applications, Ted Bergstrom, Mark Bagnoli

Ted C Bergstrom

In many applications,assumptions about the log-concavity of a probability distribution allow just enough special structure to yield a workable theory.This paper catalogs a series of theorems relating log-concavity and/or log-convexity of probability density functions,distribution functions,reliability functions,and their integrals. We list a large number of commonly-used probability distributions and report the log-concavity or log-convexity of their density functions and their integrals. We also discuss a variety of applications of log-concavity that have appeared in the literature. (The current draft corrects a typo in Table 3.)

Experimental Markets And Chamberlin's Excess Trading Conjecture, Ted Bergstrom

Ted C Bergstrom

Edward Chamberlin conjectured that the number of trades in realistic trading systems is likely to exceed that predicted by competitive equilibrium theory. He supported this conjecture by data from a large number of classroom experiments and with a plausible argument based on a numerical example. This paper states and proves a theorem that supports and illuminates Chamberlin's intuition, supplies examples of trading processes that lead to excess trading, and presents some additional experimental evidence.

When Non-Transitive Relations Take Maxima And Competitive Equilibria Can't Be Beat, Ted Bergstrom

Ted C Bergstrom

The paper generalizes theorems of Ky Fan and Hugo Sonnenschein on the existence of maximal elements for non-transitive relations. I used these results to show that a binary relation could be constructed whose maximal element must be a competitive equilibrium. Thus proving the existence of competitive equilibrium under somewhat more general conditions than had been done previously. In 1975, I thought this was a useful extension of the Gale Mas Collel existence theorem. Journal referees then didn't agree with me, so I let it ripen in my desk for 15 years. I still think it is worth looking at if …

Vernon Smith's Insomnia And The Dawn Of Economics As Experimental Science, Ted Bergstrom

Ted C Bergstrom

A retrospective on Vernon Smith's contributions to experimental economics, written for the Scandinavian Journal of Economics.

Evolution Of Social Behavior: Individual And Group Selection, Ted Bergstrom

Ted C Bergstrom

How selfish does our evolutionary history suggest that humans will be? We explore models in which groups are formed and dissolved and where reproduction of individuals is determined by their payoffs in a game played within groups. If groups are formed ``randomly'' and reproductive success of group founders is determined by a multi-person prisoners' dilemma game, then selfish behavior will prevail over maximization of group payoffs. However, interesting models exist in which ``group selection'' sustains cooperative behavior. Forces that support cooperative behavior include assortative matching in groups, group longevity, and punishment-based group norms.

Storage For Good Times And Bad: Of Rats And Men, Ted Bergstrom

Ted C Bergstrom

How do rats and squirrels decide how much to hoard for the winter when they do not know how long the winter will be? This paper argues that natural selection is likely to result in random differences in the attitudes toward systemic risk by genetically identical individuals.

Nonsubstitution Theorems For A Small Trading Country, Ted Bergstrom

Ted C Bergstrom

In 1951, Paul Samuelson showed that a surprisingly rich class of economies the production possibility frontier is a linear and even with neoclassical substitution possibilities, as outputs adjust, firms continue to use inputs and outputs in the same proportions. This model is often thought to be of limited practical value since it assumes that there is only one non-produced factor, and no joint production. The single factor assumption rules out economies in which agriculture and mining are important and the lack of joint production leaves no good way to handle durable capital goods. In this paper, I extend the Samuelson …

Love And Spaghetti, The Opportunity Cost Of Virtue, Ted Bergstrom

Ted C Bergstrom

This paper was written in the form of two puzzles. One puzzle concerns Romeo and Juliet who love spaghetti and each other. They wear flimsy clothing and have abdominal hedonimeters. The other puzzle asks who benefits from tax deductions to the rich for charitable deductions.

Soldiers Of Fortune, Ted Bergstrom

Ted C Bergstrom

This paper shows that if workers have identical wealths, abilities, and preferences then a draft lottery is Pareto superior to a voluntary army. It also shows that if being a civilian is a "normal good", then the optimal pay schedule will be such that people prefer not being chosen for the army. The paper shows how this idea extends to occupational choice in general and shows that pure gambles taken prior to occupational choice can substitute for lotteries that determine one's occupation. This paper repairs what I think is a major flaw in standard general equilibrium theory, which assumes away …

When Do Market Games Have Transferable Utility?, Ted Bergstrom, Hal Varian

Ted C Bergstrom

A question with a nice clean answer. When do market games have transferable utility? Subject to some regularity conditions, the answer is if and only if indirect utility can be represented in the Gorman polar form.

Independence Of Allocative Efficiency From Distribution In The Theory Of Public Goods, Ted Bergstrom, Richard Cornes

Ted C Bergstrom

When is the Pareto optimal amount of public goods independent of income distribution? Subject to some regularity conditions, the answer is when preferences of every individual i can be represented by a utility function of the form U(X_i,Y)=A(Y)X_i+B_i(Y) where X_i is i's consumption of private goods and Y is the amount of public goods.

Can Courtship Be Cheatproof?, Ted Bergstrom, Richard Manning

Ted C Bergstrom

In 1983, I told Richard Manning about Gale and Shapley's beautiful 1962 paper on matching. He asked whether in the Gale-Shapley it was in the interest of all participants to tell the truth. We rather quickly showed that in general it is not in the interest of the recipients of offers to be truthful. In fact we were able to show that no mechanism can guarantee efficient assignments and be cheatproof. We were very pleased. We sent it to a journal, only to learn that Al Roth had beat us to it in a paper that was to appear in …

Counting Groves-Ledyard Equilibria Via Degree Theory, Ted Bergstrom, Carl Simon, Charles Titus

Ted C Bergstrom

A Nash equilibria of the Groves-Ledyard mechanism is Pareto optimal. But this may not be much use if there are many distinct Nash equilibria, since it is not clear that the mechanism would converge on any one of them. This paper shows that if preferences are quasi-linear, the Groves-Ledyard mechanism has a unique Nash equilibrium, but even in the simplest class of preferences in which demands for public goods are affected by incomes, the number of equilibria increases exponentially with the number of consumers. The paper makes use of some pretty mathematics and even sports a drawing of Whitney's umbrella.

When Is A Man's Life Worth More Than His Human Capital?, Ted Bergstrom

Ted C Bergstrom

This paper develops a "subjectivist" theory of the value that individuals place on risks to their lives. It explains the paradox that although individuals may view their lives as priceless, they still will take small risks for a finite amount of money. Typical public projects that alter risks to life result in small changes in survival probability for a large number of people. Standard tools of benefit cost can therefore be applied, where statistical lives saved are valued at a price equal to the marginal rate of substitution between survival probability and wealth. This "value" is compared to human capital …

Gorman And Musgrave Are Dual: An Antipodean Theorem On Public Goods, Ted Bergstrom, Richard Cornes

Ted C Bergstrom

This paper finds the conditions under which an allocation branch can determine the efficient amount of public goods to produce, independently of the distribution of private goods. The result is similar to that found in our Econometrica paper, but uses a quite different method--solving a differential equation.

Collective Choice And The Lindahl Allocation Method, Ted Bergstrom

Ted C Bergstrom

This paper contains a proof of the existence of Lindahl equilibrium in a very general model of externalities, public goods, and non-selfish preferences. The trick in this paper is to treat all goods as pure public goods, with private goods and their competitive prices treated as special cases induced by special structure within the public goods, Lindahl framework.

How To Discard Free Disposability--At No Cost, Ted Bergstrom

Ted C Bergstrom

This paper shows how to prove the existence of competitive equilibrium without assuming either monotonic preferences or free disposability--and without adding any new assumptions.

The Existence Of Maximal Elements And Equilibria In The Absence Of Transitivity, Ted Bergstrom

Ted C Bergstrom

This paper generalizes results of Ky Fan and Hugo Sonnenschein on the existence of maximal elements for non-transitive binary relations. It proves a generalization of Nash's theorem on the existence of non-cooperative equilibrium. It also shows that existence of competitive equilibrium can be proved as a consequence of the existence of a maximal element for an appropriately chosen binary relation.

The Core When Strategies Are Restricted By Law, Ted Bergstrom

Ted C Bergstrom

The alpha-core is defined to be the set of feasible allocations such that no coalition can do better for its members by selecting alternative strategies given “worst-case” assumptions about the behavior of other players. This paper explores the way that the alpha-core of a game is affected by restrictions on the legally admissible strategies of the players. It also explores the relation between Lindahl equilibrium and alpha-cores with suitable restrictions on strategies.

Competitive Equilibrium Without Transitivity, Monotonicity, Or Free Disposal, Ted Bergstrom

Ted C Bergstrom

This paper shows how to relax several of the standard assumptions used to prove the existence of competitive equilibrium. I thought it was more interesting than the referees did. Some of the ideas in this paper appear in my other papers on general equilibrium.

On Efficient Provision Of Social Overhead Goods, Ted Bergstrom

Ted C Bergstrom

This paper was my attempt to build a theory of "public factors of production" such as scientific knowledge and to see whether there is any way that Arrow-Debreu general equilibrium theory can cope with the nonconvexities that arise. I propose that the economy might be partitioned into provision of "social overhead goods" and ordinary goods in such a way that given the quantities of social overhead goods, the remaining activities satisfy the assumptions needed for the existence of competitive equilibrium. I proposed and examined a notion of "Lindahl-Hotelling equilibrium" in which individuals were assigned Lindahl prices for the social overhead …