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
forthcoming, Journal of Finance, June 2005
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.
Partnership
Dissolution with Interdependent Values
forthcoming, RAND Journal of Economics
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.
Backwards
Induction with Players who Doubt Others' Faultlessness
forthcoming, Mathematical
Social Science
with Aviad Heifetz
revised version 1/2005: 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