Wait and See. Joint work with Yuk-fai Fong (Northwestern University, Kellogg M&S).
[Pdf]
Abstract:
We study a dynamic cheap talk model with multiple senders where the
receiver can choose when to make her decision and communication can
take place over time. No player has the ability to commit to any action
in the future, in particular, the receiver cannot commit to delay the decision.
In contrast to the results in static versions of the model, we show
that when the senders have common knowledge about the state of the
world, there exists an equilibrium with instantenous, full revelation irrespective
of the size and direction of the senders’ biases. We show that the
equilibrium is robust to various perturbations including the introduction
of noise in the senders’ signals about the state.
JEL Nos.: D82, D83, D72, D74;
Keywords: multi-sender cheap talk, full revelation, noisy signals, delay
Disagreement and Evidence Production in Pure Communication Games.
Joint work with Adam Galambos (Lawrence University, Department of Economics).
[Pdf]
Abstract:
We expand the Crawford-Sobel (1982) model of information transmission
to allow for the costly provision of “hard evidence” in addition
to free “soft signals” (i.e., conventional cheap talk). We prove the existence
of an interval-partition equilibrium, where each cheap-talk
message is sent by an interval of Sender-types, while hard signals are
sent by types belonging to a finite union of intervals. We also show
that the availability of costly hard signals may reverse one of the important
implications of the classical cheap talk model, namely, that
diverging preferences always lead to less communication.
JEL Nos.: D82, D83, D72, D74;
Keywords: cheap talk, hard information, partition-equilibrium
Robust Deviations from Signaling Equilibria. Joint with James Schummer (Northwestern University, Kellogg MEDS)
[Pdf]
Abstract:
We propose a criterion to select among equilibria in Sender-Receiver (signaling) games
based on the following idea. By sending an out-of-equilibrium message, the Sender
should not be able to create a self-fulfilling prophecy—specifically, to generate the
belief that he belongs to a unique set of types who unambiguously gain by sending that
message when the Receiver believes it was sent by one of those types. This mild,
forward-induction type requirement restricts equilibrium outcomes—without further refining
off-equilibrium beliefs—to D1 equilibrium outcomes in the standard class of monotonic
signaling games. Additionally, our refinement makes precise predictions in a less structured
class of signaling games, where other refinements can be ineffective. Therefore it provides
the predictive power needed in much of the literature while avoiding the motivational
ambiguities of other concepts.
JEL Nos.: C70, C72; Keywords: signalling games, refinements
Costly Signaling with Career Concerns. Joint with Kim-Sau Chung (Northwestern University)
Abstract:
We analyze a game where a player who is privately, but imperfectly, informed
about the state of nature (his productivity) can choose among overt
actions that generate public signals about the state. His payoff depends in
the short run on the public perception of his productivity, and in the long
run on the state and his career choice. Since learning the public signals is
helpful for his long-run choice, the player faces a conflict between verifiable
and costly signaling: Choosing a more-informative action can signal confidence
in his productivity, but it also signals self-doubt as a high type can
more easily forego learning about the state. We show that under certain
conditions a tri-partite equilibrium exists where low and high types pool on
a less-informative action while intermediate types send a more-informative
public signal. This equilibrium is non-monotonic and the average productivity
of an agent choosing a less informative action is greater. We show
that both features are present in any separating equilibrium. We discuss
applications such as signaling and countersignaling in talent markets.
JEL Nos.: D82,D86; Keywords: signaling, career concerns
The Price of Advice. Joint with Balazs Szentes (University of Chicago)[Pdf]
Abstract:
We develop a model of consulting (advising) where the role of the consultant
is that she can reveal signals to her client which refine the client’s
original private estimate of the profitability of a project. Importantly, only
the client can observe or evaluate these signals, the consultant cannot. We
characterize the optimal contract between the consultant and her client. It is
a menu consisting of pairs of transfers specifying payments between the two
parties (from the client to the consultant or vice versa) in case the project is
undertaken by the client and in case it is not. The main result of the paper
is that in the optimal mechanism, the consultant obtains the same profit as
if she could evaluate the impact of the signals (whose release she controls) on
the client’s profit estimate.
JEL Nos.: C72, D49, D82, D83; Keywords: Mechanism Design, Information Disclosure, Consulting, Advising.
The One Who Controls the Information Appropriates Its Rents.
Joint with Balazs Szentes (University of Chicago)
[Pdf].
Abstract:
We analyze a Principal-Agent model where the Principal can influence the precision
of the Agent's private information by releasing, without observing, additional signals
that refine the Agent's initial private type-estimate. We derive the Principal's
optimal contract, whose terms incorporate an information disclosure policy, and
characterize its properties. We show that in the optimal contract, the Principal
always releases the information that she controls. Moreover, we show that the Principal
is able to implement the same allocation and obtain the same utility as if she
could observe the realizations of the additional signals.
JEL Nos.: C72, D82, D83;
Keywords: Adverse Selection, Information Disclosure, Mechanism Design
Optimal Information Disclosure in Auctions: The Handicap Auction.
Joint with Balazs Szentes (University of Chicago)
[Pdf].
Abstract:
We analyze a situation where a monopolist is selling an indivisible good to
risk neutral buyers who only have an estimate of their private valuations. The
seller can release, without observing, certain additional signals that affect the
buyers’ valuations. Our main result is that in the expected revenue maximizing
mechanism, the seller makes available all the information that she can, and her
expected revenue is the same as it would be if she could observe the part of the
information that is “new” to the buyers.
We also show that this mechanism can be implemented by what we call a
handicap auction in interesting applications. In the first round of this auction,
each buyer picks a price premium from a menu offered by the seller (a smaller
premium costs more). Then the seller releases the additional signals. In the
second round, the buyers bid in a second-price auction where the winner pays the
sum of his premium and the second highest non-negative bid. In the case of a
single buyer, this mechanism simplifies to a menu of European call options.
JEL Nos.: C72, D44, D82, D83;
Keywords: Optimal Auction, Private Values, Information Disclosure
Bribing and Signaling in the Second Price Auction.
Joint with James Schummer (Kellogg MEDS, Northwestern)
[Pdf].
Abstract:
We examine whether a 2-bidder, second-price auction for a single
good (with private, independent values) is immune to a simple form
of collusion, where a fixed bidder may bribe the other to commit to
stay away from the auction (i.e. submit a bid of zero).
First, we consider a situation in which only a bribe of a fixed size b
may be offered. There are only two equilibria in this extended game:
a "bribing" and a "no-bribing" equilibrium. While the bribing equilibrium
survives any common refinement, we provide a necessary and
sufficient condition for the no-bribing equilibrium to survive iterated
deletion of dominated strategies. We also introduce a refinement similar
to the Intuitive Criterion, and show that the no-bribing equilibrium
fails it.
Second, we consider the case in which bribes of any size may be
offered. We show that there is a unique equilibrium in continuous
bribing strategies. It is mostly-separating, in that
most briber-types reveal their type through their bribe b, which is
accepted by sufficiently low types, while all sufficiently high briber
types commonly offer such a high bribe that it is always accepted (so
those types pool). This equilibrium survives all standard refinements.
Bribing equilibria in both cases lead to inefficiency.
Designing Optimal Benefit Rules for Flexible Retirement.
Joint with Andras Simonovits (Institute of Economics, Budapest)
[Pdf].
Abstract:
This paper applies the techniques of mechanism design to find an optimal nonlinear
pension benefit rule for flexible old-age retirement. We assume that individuals have
private information regarding their expected lifespans. The government's goal is to
design a pension system (a payroll tax and a function relating benefits to employment
length), which maximizes a social welfare function and satisfies a social budget constraint.
Since individuals with different expected lifespans optimize their employment lengths
conditional on the benefit function, the government must also take into account
incentive constraints.
We characterize the solution to this problem for various social welfare functions.
Under utilitarianism, the solution is a completely inflexible system, where all
individuals retire at the same age with the same (yearly) benefits; and,
surprisingly, the first-best (complete information) aggregate welfare is attained.
If the social welfare function is strictly concave, then individuals with shorter
expected lifespans retire earlier with benefits lower than those in the first-best.
In the optimal pension system, individuals with shorter expected lifespans subsidize
those who expect to live longer. We also compute the optimal benefit rule for several
specifications with CRRA utility functions and realistic parameter values, and discuss
the numerical results.
JEL Nos.: D82, D91 and H55; Keywords: flexible retirement,
asymmetric information, actuarial fairness, mechanism design
Multi-Good Efficient Auctions with Multi-Dimensional Information (with
Eric Maskin)
[Pdf],
[Ps].
Abstract: We show that when multiple goods
are sold, an extension of the Groves-Clarke mechansim (allowing the buyers
to make their bids contingent on other buyers' valuations) is incentive-efficient
in a broad and important class of cases when buyers have multi-dimensional
types and there are common values.
JEL Nos.: D44; Key words: auctions, efficiency, multi-unit auctions,
multi-dimensional signals
Efficiency in Multi-Unit English Auctions (1999)
[Pdf],
[Ps].
Abstract: In a general (common values)
multi-object setting we show that Ausubel's generalization of the English
auction is efficient with two bidders, but it is generically inefficient
for more than two bidders. We propose a modification of Ausubel's multi-object
English auction (essentially, parallel pairwise Ausubel auctions with a
modified clinching rule) that is efficient for any number of bidders. This
mechanism can be seen as the English counterpart of the mechanism proposed
by Perry and Reny (1998) which simplifies the generalized Vickrey auction
of Dasgupta and Maskin (1998) for identical substitute objects.
JEL Nos.: D44; Key words: auctions, efficiency, English auction, multi-unit
auctions
Precautionary Bidding in Auctions (with Lucy White)
(1999)
[Pdf].
Abstract:
We analyze bidding behavior in auctions when risk-averse bidders bid for an object
whose value is risky. We show that, as risk increases, decreasingly risk-averse bidders
will reduce their bids by more than the risk premium. Ceteris paribus, bidders will be
better off bidding for a more risky object in first-price, second-price, English, and
all-pay auctions with affiliated private values. We then extend the results to common
value settings. This `precautionary bidding' effect arises because the expected
marginal utility of income increases with risk, so bidders are reluctant to bid so
highly. We show that precautionary bidding also arises in response to common values risk.
This precautionary bidding behavior can make decreasingly risk-averse bidders better
off when they face a `winner's curse' than when they do not.
JEL Nos.: D44, D81; Key words: Risk, Risk-Aversion, Prudence, First-Price Auctions,
Second-Price Auctions, All-Pay Auctions
Correlation and Risk Aversion in Optimal Auctions, (1999)
[Pdf],
[Ps-file],
[Figure].
Abstract: We consider an auction setting
where the buyers are risk averse with private but correlated valuations
(CARA preferences, binary types), and characterize the optimal mechanism
for
a
risk
neutral
seller. We show that in this model, the optimal auction extracts all consumer
surplus whenever the correlation is sufficiently strong (greater than 1/3 in
absolute value).
In contrast, we note that a sufficiently risk averse seller would not use a full-rent-extracting
mechanism for any positive correlation of the valuations even if the buyers were
risk neutral.
JEL Nos.: D43, D81; Key words: optimal auctions, risk aversion, correlated
values
Auction Design with a Risk Averse Seller (with Gábor Futó), (1998)
[Pdf],
[Ps].
Abstract: We consider auctions with a
risk averse seller in independent private values environments with risk
neutral buyers. We show that for every incentive compatible selling mechanism
there exists a mechanism which provides deterministically the same (expected)
revenue.
JEL Nos.: D44, D81; Key words: auctions, risk aversion, insurance.
(c) by Elsevier Science Publishing Co. (Economics
Letters)
MathCamp Notes (1998-1999).
[Pdf],
[Ps]
The notes I used in the MathCamp for G1-s
at Harvard University (during the second half of the first week).
It summarizes some linear algebra (vector spaces, matrices, determinants,
separating hyperplanes), analysis, and optimization.
This knowledge is required in the micro theory sequence (2010ab).
