Published and forthcoming papers:
Evolution, Population Growth, and History Dependence
Games and Economic Behavior, vol. 22, January 1998, pp84-120.
pdf (165k) , published
We consider an evolutionary model with mutations which incorporates stochastic population growth. We provide a complete characterization of the effects of population growth on the evolution of play. In particular, we show that if the rate of population growth is at least logarithmic, the stochastic process describing play converges: only one equilibrium will be played from a certain point forward. If in addition the rate of mutation is taken to zero, the prob
On the Time and
Direction of Stochastic Bifurcation
with Krzysztof Burdzy and David Frankel
In Elsevier: Asymptotic Methods in Prob
Simulation of the stochastic bifurcation model
This paper is a mathematical companion to "Fast Equilibrium Selection by Rational Players Living in a Changing World", by Burdzy, Frankel and Pauzner (1997). We use excursion theory to investigate a differential equation that involves a Brownian motion. We show the existence and uniqueness of a solution. Most importantly, we est
Repeated Games with Differential Time Preferences
Econometrica, vol. 67, March 1999, pp. 393-412.
pdf (176k) , word6 (3M) , word6 zipped (265k)
Appendix - pdf (95k) , Appendix - word6 (1.2M) , Appendix - word6 zipped (166k)
When players have identical time preferences, the set of feasible repeated game payoffs coincides with the convex hull of the underlying stage-game payoffs. Moreover, all feasible and individually rational payoffs can be sustained by equilibria if the players are sufficiently patient. Both facts do not generalize to the case of different time preferences. First, players can mutually benefit from trading payoffs across time. Hence, the set of feasible repeated game payoffs is typically larger than the convex hull of the underlying stage-game payoffs. Second, it is not the case that every trade plan that guarantees individually rational payoffs can be sustained by an equilibrium, no matter how patient the players are. This paper provides a simple characterization of the sets of Nash and of subgame perfect equilibrium payoffs in two-player repeated games.
Resolving Indeterminacy in Dynamic Settings: The Role of Shocks
version was called "History, not Expectations")
with David Frankel
Quarterly Journal of
Economics, vol. 115, February 2000, pp. 283-304.
pdf (220k) , word7 (873k) , word7 - zipped (192k)
We introduce exogenous shocks in a standard dynamic model that otherwise would have multiple equilibria. The shocks take the form of a Brownian motion that affects the desir
Independent Mistakes in Large Games
(previous version was called
"Large Economies: When Do Independent Mistakes Matter?")
International Journal of Game Theory, vol. 29, July 2000, pp. 189-209.
pdf (185k) , word6 (1.1M) , word6 -zipped (200k)
Economic models usually assume that agents play precise best responses to others' actions. It is sometimes argued that this is a good approximation when there are many agents in the game, because if their mistakes are independent, aggregate uncertainty is small. We study a class of games in which players’ payoffs depend solely on their individual actions, and on the aggregate of all players’ actions. We investigate whether their equilibria are affected by mistakes when the number of players becomes large. Indeed, in generic games with continuous payoff functions, independent mistakes wash out in the limit. This may not be the case if payoffs are discontinuous. As a counter-example we present the n players Nash bargaining game, as well as a large class of free-rider games.
Fast Equilibrium Selection by Rational Players Living in a Changing World
Burdzy and David Frankel
Econometrica, vol. 68, January 2001, pp. 163-190.
pdf (474k) , tex (97k)
Previous version (with Brownian motion): pdf (463k) , tex (91k)
We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk dominant equilibrium. More precisely, a continuum of fully rational players are randomly matched to play a symmetric 2*2 game. The payoff matrix changes according to a random walk. Players observe these payoffs and the population distribution of actions as they evolve. The game has frictions: opportunities to change strategies arrive from independent random processes, so that the players are locked into their actions for some time. As the frictions disappear, each player ignores what the others are doing and switches at her first opportunity to the risk dominant equilibrium. History dependence emerges in some cases when frictions remain positive.
the Timing of Neighborhood Change
Journal of Urban Economics, vol. 51, 2002, pp. 295-314.
with David Frankel
pdf (450k) , word7 (1M)
We study the role of expectations in neighborhood change when ethnic groups have a preference for segregation and frictions prevent households from moving simultaneously. In a fixed environment, rational expectations can give rise to multiple equilibria, since expectations of an ethnic transition can be self-fulfilling. In contrast, there is a unique equilibrium in an initially segregated neighborhood that is subject to a deterministic, exogenous trend that progressively reduces the utility of current residents from living in the neighborhood. An ethnic transition must begin at the first possible moment: when current residents would sell under the beliefs that most make them want to do so. The same prediction is obtained if, instead of a deterministic trend, there are small shocks to agents’ utility from living in the neighborhood.
Selection in Global Games with Strategic Complementarities
Journal of Economic Theory, vol. 108, January 2003, pp. 1-44.
with David Frankel and Stephen Morris
We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove limit uniqueness: as the signal noise vanishes, the game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and van Damme (1993) for two player, two action games. The surviving profile, however, may depend on fine details of the structure of the noise. We provide sufficient conditions on payoffs for there to be noise-independent selection.
Contagion of Self-Fulfilling Financial Crises Due to Diversification of Investment Portfolios
Journal of Economic Theory, vol 119, November 2004, pp. 151-183.
with Itay Goldstein
pdf (320k) , word xp (1M) , simulation files (ziped) (110k)
We explore a model with two countries. Each might be subject to a self-fulfilling crisis, induced by agents withdrawing their investments in the fear that others will do so. While the fundamentals of the two countries are independent, the fact that they share the same group of investors may generate a contagion of crises. The realization of a crisis in one country reduces agents’ wealth and thus makes them more risk averse (we assume decreasing absolute risk aversion). This reduces their incentive to maintain their investments in the second country since doing so exposes them to the strategic risk associated with the unknown behavior of other agents. Consequently, the probability of a crisis in the second country increases. This yields a positive correlation between the returns on investments in the two countries even though they are completely independent in terms of fundamentals. We discuss the effect of diversification on the probabilities of crises and on welfare. Finally, we discuss the applicability of the model to real world episodes of contagion.
Diamond and Dybvig (1983) show that while demand-deposit contracts let banks provide liquidity, they expose them to panic-based bank runs. However, their model does not provide tools to derive the probability of the bank-run equilibrium, and thus cannot determine whether banks increase welfare overall. We study a modified model in which the fundamentals determine which equilibrium occurs. This lets us compute the ex-ante probability of panic-based bank runs, and relate it to the contract. We find conditions, under which banks increase welfare overall, and construct a demand-deposit contract that trades off the benefits from liquidity against the costs of runs.
Backwards Induction with Players who Doubt Others' Faultlessness
Mathematical Social Sciences,
Vol. 50, November 2005, pp. 252-267.
with Aviad Heifetz
pdf (300k) , rap (SW5) (100k)
We investigate the robustness of the backward-induction outcome, in binary-action extensive-form games, to the introduction of small mistakes in reasoning. Specifically, when a player contemplates the best action at a future decision node, she assigns some small prob
Dissolution with Interdependent Values
RAND Journal of Economics. Volume 37, Issue 1, 2006, pp. 1-22.
with Philippe Jehiel
pdf (315k) , tex (98k)
We study partnership dissolution when the valuations are interdependent and only one party is informed about the valuations. In contrast with the case of private values (Cramton, Gibbons, and Klemperer 1987), in which efficient trade is feasible whenever initial shares are about equal, there exists a wide class of situations in which full efficiency cannot be reached. In these cases: (1) The subsidy required to restore the first-best is minimal when the entire ownership is allocated initially to one of the parties. (2) Ruling out external subsidies, the second-best welfare is maximized when one of the parties initially has full ownership.
Behaviorally Optimal Auction Design: Examples and Observations
Journal of the European Economic Association. Volume
7, Issue 2-3, 2009 pp. 377-387.
with Vincent P. Crawford, Tamar Kugler and Zvika Neeman
This paper begins to explore behavioral mechanism design, replacing equilibrium by a model based on “level-k” thinking, which has strong support in experiments. In representative examples, we consider optimal sealed-bid auctions with two symmetric bidders who have independent private values, assuming that the designer knows the distribution of level-k bidders. We show that in a first-price auction, level-k bidding changes the optimal reserve price and often yields expected revenue that exceeds Myerson’s (1981) bound; and that an exotic auction that exploits bidders’ non-equilibrium beliefs can far exceed the revenue bound. We close with some general observations about level-k auction design.
We study a private-values buyer-seller problem with multiple
objects. Valuations are binary and i.i.d. We
construct mechanisms that span the set of all Pareto-efficient outcomes. The
induced trading rules for objects are linked in a simple way.
Government's Credit-Rating Concerns and the Evaluation of Public Projects
Public projects typically generate both monetary revenue and social benefits that cannot be monetized. Anticipated revenues from government-owned projects increase the liklihood that the government will be able to repay its debt and thus improve its credit rating and lower the financing costs of the debt. This should give monetary revenue an added value relative to social benefits. However, informational problems -- dynamic inconsistency and adverse selection -- push the government to an excessive emphasis on social benefits, ignoring the external effect of monetary revenue on debtholders. Since the credit market anticipates this, the government's credit rating is adversely affected and it is thus unable to extract the full potential of the projects. Finally, we show that while privatization can sometimes alleviate these problems, there are cases in which the government would be better off if its hands were tied and it were not allowed to privatize.
Job satisfaction and the wage gap
For many people there is tradeoff between choosing a job that they will enjoy and one at which they are good and will earn a high income. We embed this observation in a matching model. Consider then men and women who are a priori identical in the sense that both are equally likely to be good at one of two jobs and their satisfaction from each job is drawn from the same distribution. They are randomly matched into households after making a career choice, and have decreasing marginal utility of money. Thus, a career is chosen before knowing one's future spouse's income. If the distribution of enjoyment is log concave and single peaked, with the modal individual enjoying the job at which they are good, then there is either a unique symmetric equilibrium that is stable or an unstable symmetric equilibrium and two (mirror image) asymmetric equilibria that are stable. The latter display a wage gap and an opposite satisfaction gap, with one gender, wlog men, earning more even controlling for occupation. These equilibria display novel comparative statics. For example a tax on high wage couples results in women shifting into their more satisfying jobs and forgoing income (as one would expect), while interestingly men shift into higher income jobs, forgoing job satisfaction.