Published and forthcoming papers:
Evolution, Population Growth, and History Dependence
with William
Sandholm
Games and Economic Behavior, vol. 22, January
1998, pp84-120.
pdf (165k) , published
version (IDEAL)
Abstract:
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
pdf (212k)
Simulation of the
stochastic bifurcation model
Abstract:
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
with Ehud
Lehrer
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)
Abstract:
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
(previous
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)
Abstract:
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)
Abstract:
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
with Krzysztof
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)
Abstract:
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.
Expectations and
the Timing of Neighborhood Change
Journal of Urban Economics, vol. 51, 2002, pp.
295-314.
with David
Frankel
pdf (450k) , word7 (1M)
Abstract:
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.
Equilibrium
Selection in Global Games with Strategic Complementarities
Journal of Economic Theory, vol. 108, January
2003, pp. 1-44.
with David Frankel and Stephen Morris
pdf
(610k)
Abstract:
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)
Abstract:
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.
Demand Deposit
Contracts and the Probability of Bank Runs
Journal of Finance, vol. 60, June 2005, pp.
1293-1327.
with Itay Goldstein
pdf
(330k) , word
(1.4M)
Abstract:
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)
Abstract:
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
Partnership
Dissolution with Interdependent Values
RAND Journal of Economics. Volume 37, Issue 1,
2006, pp. 1-22.
with Philippe
Jehiel
pdf
(315k) , tex (98k)
Abstract:
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
pdf (80k)
Abstract:
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.
Optimal
Bilateral Trade of Multiple Objects
Games and Economic Behavior, volume
71, issue 2, 2011, pp 503-512.
with Ran Eilat
pdf (170k) , appendix
(70k)
Abstract:
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.
Working papers:
Government's Credit-Rating
Concerns and the Evaluation of Public Projects
with Nadav
Levy
pdf
Abstract:
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
with Eddie
Dekel
pdf
Abstract:
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.