Uncertainty and Information in Economics
(9 May  3 July 2005)
~ Abstracts ~
Computational mechanism design and
auctions
David C. Parkes, Harvard University
Computational Mechanism Design (CMD) aims to develop
protocols to implement desirable outcomes in a distributed
system of selfinterested agents. An outcome might define a
joint plan of action, or an allocation of resources to
agents. CMD brings together economic concepts of
gametheoretic equilibrium and incentivecompatibility
constraints with the traditional computer science concerns
of computational tractability and communication complexity.
This tutorial is designed for a general audience in
computer science and economics, and it should have interest
to both novices and experts in computational mechanism
design and computational game theory. We will begin with
directrevelation and truthful mechanisms, and study the
VickreyClarkeGroves mechanism and then more general
characterization results. Continuing, we will study
iterative mechanisms, including ascendingprice auctions,
and introduce the general problem of incentivecompatible
preference elicitation. In closing, we will define the
problem of mechanism design for sequential decision problems
and mention some challenges in combining learning with
mechanism design.
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Iterated strict dominance in general
games
Xiao Luo, Institute of Economics, Academia Sinica, Taiwan
Following Milgrom and Roberts [Econometrica
58(1990), 12551278], we offer a definition of iterated
elimination of strictly dominated strategies (IESDS) for
games with (in)…finite players, (non)compact strategy sets,
and (dis)continuous payoff functions. IESDS is always a
welldefined order independent procedure that can be used
to solve out Nash equilibrium in dominancesolvable games.
We characterize IESDS by means of a "stability" criterion.
We show by an example that IESDS might generate spurious
Nash equilibria in the class of Reny's betterreply secure
games. We provide sufficient conditions under which IESDS
preserves the set of Nash equilibria. JEL Classifi…cation:
C70, C72.
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Trade with heterogeneous multiple
priors
Atsushi Kajii, Kyoto University
This paper presents a general framework to understand the
possibility of a purely speculative trade under asymmetric
information, where the decision making rule of each trader
conforms to the multiple priors model (Gibloa and Schmeidler,
1989): the agents are interested in the minimum of the
conditional expected value of trade where the minimum is
taken over the set of posteriors. In this framework, we
derive a necessary and sufficient condition on the sets of
posteriors, thus implicitly on the updating rules adopted by
the agents, for nonexistence of trade such that it is
always common knowledge that every agent expects a positive
gain.
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Applications of rich measure spaces
formed from nonstandard models
Peter A. Loeb, University of Illinois at UrbanaChampaign
We review recent work by several authors that utilize the
rich structure of what are called "Loeb measure spaces" in
the literature. In particular, we show that there are many
results, some used for decades without a rigorous
foundation, that are only true for spaces with this rich
structure.
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A reformulation of the rational
expectations equilibrium (REE): Walrasian Bayesian
equilibrium
Nicholas Yannelis, University of Illinois at
UrbanaChampaign
The REE as introduced by Radner in general doesn’t exist,
it fails to be fully Pareto optimal and incentive compatible
and also it is not implementable as a perfect Bayesian
equilibrium of an extensive form game. The lack of all the
above properties is mainly due to the fact the agents are
supposed to predict the equilibrium market clearing price
(as agent’s expected maximized utility is conditioned on the
information that equilibrium prices reveal) which is
compatible with the idea that agents know all the primitives
in the economy, i.e., random initial endowments, random
utility function and private information sets. To get around
this ad hoc equilibrium notion, we introduce a new concept
called Bayesian Walrasian equilibrium (BWE) which has
Bayesian features. In particular, agents try to predict the
market clearing prices using a Bayesian updating and
evaluate their consumption in terms of Bayesian price
estimates which are different for each individual. In this
framework agents maximize expected utility based on their
own private information, subject to a Bayesian estimated
budget constraint. The market clearing it not state wise, it
is in expected terms. However, once learning is introduced
(i.e. filtration of the information partitions) our BWE
becomes fully revealing and leads to a stare wise market
clearing. This new BWE exists under the standard
assumptions, it is Pareto optimal and it is incentive
compatible contrary to the REE.
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Uncoupled dynamics and Nash
equilibrium
Sergiu Hart, Hebrew University of Jerusalem
We call a dynamical system "uncoupled" if the dynamic for
each player does not depend on the payoff functions of the
other players. This is a natural informational restriction.
We study convergence of uncoupled dynamics to Nash
equilibria, and present a number of possibility and
impossibility results. (joint work with Andreu MasColell)
See
http://www.ma.huji.ac.il/hart/abs/uncouplst.html and
also
http://www.ma.huji.ac.il/hart/abs/uncoupl.html.
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Redoing the foundations of
decision theory: Decision theory with subjective state
spaces
Joseph Y. Halpern, Cornell University
The standard approach in decision theory (going back to
Savage) is to place a preference order on acts, where an act
is a function from states to outcomes. If the preference
order satisfies appropriate postulates, then the decision
maker can be viewed as acting as if he has a probability on
states and a utility function on outcomes, and is maximizing
expected utility. This framework implicitly assumes that the
decision maker knows what the states and outcomes are. That
isn't reasonable in a complex situation. For example, in
trying to decide whether or not to attack Iraq, what are the
states and what are the outcomes? We redo Savage viewing
acts essentially as syntactic programs. We don't need to
assume either states or outcomes. However, among other
things, we can get representation theorems in the spirit of
Savage's theorems; for Savage, the agent's probability and
utility are subjective; for us, in addition to the
probability and utility being subjective, so is the state
space and the outcome space. I discuss the benefits, both
conceptual and pragmatic, of this approach.
This is joint work with Larry Blume and David Easley. No
prior knowledge of Savage's work is assumed.
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Information and market design
Ruqu Wang, National University of Singapore and Queens
University, Canada
The effects of information on market design are explored
in a simple setting where firms have private information
about their correlated fixed costs and the government aims
to maximize its expected revenue conditional on achieving
efficient allocations. Government revenues are higher when
the costs are less correlated (or are more of a private
value). The reduced correlation increases the firms'
information rents, but a change in the information structure
also changes the expected market structures with positive
effects on government revenues. If the government faces the
nodeficit constraint, there are situations where efficient
allocations are achieved under asymmetric information but
not under symmetric information.
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Strategic uncertainty and the
Hirshleifer effect
Murali Agastya, University of Sydney
The Hirshleifer effect refers to a situation where an
increase in the amount of information leads to a reduction
in welfare in the Pareto sense, the intuition being that a
"helicopter drop" of information destroys hedging
opportunities and consequently a decline in exante utility.
In many strategic situations, the amount of information that
is ultimately commonknowledge, and hence the set of hedging
opportunities that are available is *endogenous*  it
depends on the equilibrium the players may coordinate upon.
In the context of a stylized model of insider trading, we
show that an informationally inefficient (pooling)
equilibrium can Paerto dominate to an informationally
efficient separating equilibrium.
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Efficiently regulated competition in insurance economies
with adverse selection
Peter Hammond, Stanford University
In insurance economies with a continuum of agents and
adverse selection, it is shown that incentiveconstrained
Pareto efficient allocations correspond to regulated
competitive (or compensated competitive) equilibria in
markets with nonlinear pricing for options to buy insurance
contracts. These options make the incentive constraints
selfenforcing. Efficiency is achieved through a "universal
service" requirement allowing only new contracts or
blocking coalitions that benefit all potential types of each
agent. This regulation prevents "cream skimming" intended
to exclude highrisk agents. Under suitable assumptions,
regulated equilibria are shown to exist and be characterized
as "regulated core" allocations.
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Cominimum additive operator
Takashi Ui, Yokohama National University
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The communication requirements of
social choice rules and supporting budget sets
Ilya Segal, Stanford University
The paper examines the communication requirements of
social choice rules when the (sincere) agents privately know
their preferences. It shows that for a large class of choice
rules, any minimally informative way to verify that a given
alternative is in the choice rule is by verifying a "budget
equilibrium", i.e., that the alternative is optimal to each
agent within a "budget set" given to him. Therefore, any
communication mechanism realizing the choice rule must …nd a
supporting budget equilibrium. We characterize the class of
choice rules that have this property. Furthermore, for any
rule from the class, we characterize the minimally
informative messages (budget equilibria) verifying it. This
characterization is used to identify the amount of
communication needed to realize a choice rules, measured
with the number of transmitted bits or real variables.
Applications include efficiency in convex economies, exact
or approximate surplus maximization in combinatorial
auctions, the core in indivisiblegood economies, and stable
manytoone matchings.
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Uncertainty and hyperbolic
discounting
Eric Maskin, Institute for Advanced Study, Princeton
We propose an evolutionary explanation for the pattern of
intertemporal preference reversals often ascribed to
“hyperbolic discounting.” We take the view that preferences—
manifested, for example, in urges, cravings, and
inclinations— are the outcome of evolutionary forces, and so
will induce animals or humans to make survivalmaximizing
choices in “typical” decision problems. We show that if the
typical problem involves payoffs whose realization times are
uncertain, then optimal preferences give rise to relatively
patient behavior when the time horizon is long but induce a
switch to impatience when the horizon grows short.
Such reversals do not entail dynamic inconsistency in
typical decision problems; behavior there is optimal.
However, if a decisionmaker is confronted with a choice for
which the realizationtime uncertainty falls outside the
evolutionary norm, her preferences may well prompt her to
behave inconsistently. We argue that, if such a choice
problem recurs, her evolutionarily endowed ability to learn
will lead her to make selfcommitments against these urges.
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The comparative statics of
constrained optimization problems
John Quah, University of Oxford
The objective of this paper is to develop and apply some
new results in the theory of monotone comparative statics.
Let f be a realvalued function defined on R^{l},
and consider the problem of maximizing f(x) when x
is constrained to lie in some subset C of R^{l}.
We develop a natural way of ordering constraint sets and
identify the conditions on f which guarantee that the
solution to the maximization problem increases as the
constraint set changes. We apply this to a variety of
problems in economic theory.
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Game theory
Sudhir Shah, University of Delhi
1) Games in extensive form
2) Information structures in games
3) Application I: Auction design
4) Application II: Repeated games
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Safe votes, sincere votes, and
strategizing
Rohit Parikh, City University of New York
We examine the basic notion of strategizing in the
statement of the GibbardSatterthwaite theorem and note that
to talk about strategizing presumes that we already know
what it means to vote sincerely. For a strategic vote is one
which differs from a sincere vote, taking into account how
others are voting. Now the notion of a sincere vote is clear
enough in most commonly used voting systems (which we
identify with the aggregation function Ag) but
there is no general notion of sincerity. It follows that
there cannot be a general notion of strategizing either. In
this paper we define a notion of safe vote and study its
properties. Safe votes exist with plurality, approval voting
and the Borda count, where they concide with sincere votes.
Safe votes do not exist with STV.
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The nature of equilibria under
noncollusive product design and collusive pricing
Kali Rath, University of Notre Dame
It is well known that in a two stage duopoly model of
product choice with quadratic transportation cost, the firms
locate at the extreme endpoints of the market. This paper
examines this model in an infinite horizon setting where in
the initial period the firms choose locations and in
subsequent periods choose prices. The firms collude in
prices and share the profits on the profit possibility
frontier. It is shown that under very general conditions,
both the firms locating at the center is an equilibrium. It
is not necessarily unique and multiple symmetric equilibria
can exist. So, the products are not minimally differentiated
and the degree of differentiation can vary. Sufficient
conditions for three types of equilibria are given: a unique
equilibrium at the center of the market, multiple symmetric
equilibria and multiple asymmetric agglomerated equilibria.
The first two cases obtain if the firms share profits
equally when they are located at the same point and the last
case otherwise.
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Ex ante efficiency and incentive
compatibility
Yeneng Sun, National University of Singapore
We show that when agents become informationally
negligible in a large economy with asymmetric information,
every ex ante efficient allocation must be incentive
compatible. Thus, any ex ante core allocation or ex ante
Walrasian equilibrium is incentive compatible. Furthermore,
asymptotic analogs for such results can be obtained for
large but finite asymmetric information economies. These
results are false in fixed finiteagent economies with
asymmetric information. This is joint work with Nicholas
Yannelis of the University of Illinois at UrbanaChampaign.
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The gcore
and coalition formation
Parkash Chander, National University of Singapore
This paper reinterprets the gcore
(Chander and Tulkens (1995, 1997)) and justifies it as well
as its prediction that the efficient coalition structure is
stable in terms of the coalition formation theory. We assume
that coalitions can freely merge or break apart and are
farsighted (that is, it is the final and not the immediate
payoffs that matter to the coalitions). We then show that
subsequent to a deviation by a coalition, it is ex post
optimal for the nonmembers to break apart into singletons,
as is assumed in the definition of the gcharacteristic
function, and the grand coalition is a stable coalition
structure. Our analysis not only justifies the
gcore in terms of the coalition
formation theory but also shows that in order to rule out
the stability of the efficient coalition structures one must
either place some exogenous restrictions on the process of
coalition formation or assume that the coalitions are not
farsighted.
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Factor taxation and growth under
asymmetric information
Yong Wang City, University of Hong Kong
The literature on growth effects of factor taxation has
revealed that the desirability of capital income taxation,
relative to that of labor income taxation, tends to vary
with the modeling assumption made about lifecycle
considerations. In particular, by considering overlapping
generations models in which government taxes both capital
and labor income, Uhlig and Yanagawa (1996) and Caballé
(1998) show that increasing the tax rate on capital income
leads to higher economic growth. The objective of this paper
is to reexamine the growth effects of factor taxation in an
overlapping generations economy with asymmetric information.
The key feature of our model is that capital accumulation
takes place through investment projects mediated by a credit
market in which asymmetric information between borrowers and
lenders is present. In such an environment, we show that the
presence of asymmetric information introduces an additional
adverse effect of capital income taxation on growth. In so
doing, we present a new argument in favor of using a lower
(higher) capital (labor) income taxation to fund public
spending. As a corollary, we also show that there is a
negative relationship between the optimal tax rate on
capital income and the severity of asymmetric information in
the credit market.
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Stock return autocorrelation is
not spurious
Robert Anderson, University of California at Berkeley
We find compelling evidence that stock return
autocorrelation is not spurious; partial price adjustment is
an important source, and in some cases the main source, of
the autocorrelation. Our tests of partial price adjustment
are direct, using disjoint time intervals, separated by a
trade, to eliminate the nonsynchronous trading effect and
minimize bidask bounce. We find evidence for partial price
adjustment in individual stock returns, portfolio returns,
and in an unlikely setting: the incorporation of ETF price
information into individual stock prices. We find that
partial price adjustment generates a very substantial
fraction of the autocorrelation. (joint with Kyong Shik Eom,
Sang) Buhm Hahn and JongHo Park.
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Implementation with interdependent
valuation
Richard McLean, Rutgers University
There is a large literature aimed at characterizing the
social choice functions that can be implemented in Bayes
Nash equilibria. This literature typically takes agents'
information as exogenously given and fixed throughout the
analysis. While for some problems this may be appropriate,
the assumption is problematic for others. A typical
analysis, relying on the revelation principle, maximizes
some objective function subject to truthful revelation being
a Bayes equilibrium. It is often the case that truthful
revelation is not "ex post incentive compatible", that is,
for a given agent, there are some vectors of the other
agents' types for which the agent may be better off by
misreporting his type than truthfully revealing it. Truthful
revelation, of course, may still be a Bayes equilibrium,
because agents announce their types without knowing other
agents types: choices must be made on the basis of their
beliefs about other agents' types. The difficulty with
assuming that agents' information is exogenous is that when
truthful revelation is not ex post incentive compatible,
agents have incentives to learn other agents' types. To the
extent that an agent can, at some cost, learn something
about other agents' types, agents' beliefs when a mechanism
is applied must be treated as endogenous. A planner who
designs a mechanism for which truthful revelation is ex post
incentive compatible can legitimately ignore agents'
incentives to engage in espionage to discover other agents'
types, and consequently, ex post incentive compatibility is
desirable. The ClarkeGrovesVickrey mechanism (hereafter
CGV) for private values environments is a classic example of
a mechanism for which truthful revelation is ex post
incentive compatible.
There has recently been renewed interest in mechanisms
for which truthful revelation is ex post incentive
compatible. While ex post incentive compatibility is
desirable, nontrivial mechanisms for which truthful
revelation is ex post incentive compatible fail to exist for
a large set of important problems with interdependent
valuations. We introduce in this paper a notion of
eex post
incentive compatibility: a mechanism is
eex post
incentive compatibile if truthful revelation is ex post
incentive compatible with probability at least 1e.
If truthful revelation is eex
post incentive compatible for a mechanism, agents' incentive
to collect information about other agents' is bounded by
e times the
maximal gain from espionage. If espionage is costly, a
mechanism designer can be relatively comfortable in taking
agents' beliefs as exogenous when
e is sufficiently
small. We show that the existence of mechanisms for which
there are eincentive
compatible equilibria is related to the concept of
informational size introduced in McLean and Postlewaite
(2001, 2002). When agents have private information, the
posterior probability distribution on the set of states of
the world Q will vary
depending on a given agent's type. Roughly, an agent's
informational size corresponds to the maximal expected
change in the posterior on Q
as his type varies, fixing other agents' types. We show that
for any e, there
exists d such that if
each agent's informational size is less than
d, there exists an
efficient mechanism for which truthful revelation is an
eincentive
compatible equilibrium.
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Bankruptcy and firm finance
Anne Villamil, University of Illinois at UrbanaChampaign
This paper analyzes how an enforcement mechanism that
resembles a court affects firm finance. The court is
described by two parameters that correspond to enforcement
costs and the amount of creditor/debtor protection. We
provide a theoretical and quantitative characterization of
the effect of these enforcement parameters on the contract
loan rate, the default probability and welfare. We show that
when constraints bind, which give agents an incentive to
default and pursue bankruptcy, the enforcement parameters
have a sharply nonlinear effect on finance and welfare. The
results provide guidance on when models which abstract from
enforcement provide good approximations and when they do
not. The bankruptcy rule corresponds to firm liquidation.
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Uncertainty in mechanism design
Chris Shannon, University of California at Berkeley
We consider mechanism design problems with interdependent
values in which agents perceive Knightian uncertainty.
Uncertainty is formalized using incomplete preferences, as
in Bewley (1986). We show that the seller can extract all
gains from trade with a direct mechanism in which
truthtelling is a Nash equilibrium, in the sense that no
buyer has a unilateral incentive to misrepresent his type.
In these mechanisms, however, truthtelling and
misrepresenting may be incomparable alternatives. We also
consider an equilibrium refinement in which truthtelling is
optimal, i.e. at least as good as any alternative. In this
case the full extraction of all gains from trade is feasible
only if there is sufficient disagreement in beliefs across
types. If all buyers types have sufficiently similar beliefs,
an expost incentive compatible mechanism is optimal for the
seller.
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The theory of coalition
formation
Parkash Chander, National University of Singapore
This tutorial will attempt to provide a comprehensive
theory of coalition formation using both partition function
and noncooperative game theory approaches. Alternative
equilibrium concepts will be discussed and their
implications on the coalition structure will be derived.
Applications of the theory to global environmental problems
and industrial organization will be presented.
Main Reading list:
 Barrett, S. (1994), “Selfenforcing international
environmental agreements”, Oxford Economic Papers,
46, pp. 878894.
 Bloch, F. (1996), “Sequential formation of
coalitions in games with externalities and fixed payoff
division”, Games and Economic Behavior, 14, pp.
90123.
 Chander, P. (2005), “The gammacore and coalition
formation”, CORE Discussion Paper No. 2003/46.
(electronic version available on request by email to
the author).
 Chander, P. and H. Tulkens (1997), “The core of an
economy with multilateral environmental externalities”,
International Journal of Game Theory, 26, pp.
379406.
 Chander, P. and H. Tulkens (1995), “A coretheoretic
solution for the design of cooperative agreements on
transfrontier pollution”, International Tax and
Public Finance, 2, pp. 279293.
 Chwe, M.S.Y. (1994), “Farsighted coalition
stability”, Journal of Economic Theory, 54, pp.
299325.
 Ray, D. and R. Vohra (1997), “Equilibrium binding
agreements”, Journal of Economic Theory, 73, pp.
3078.
 Yi, S. (1997), “Stable coalition structures with
externalities”, Games and Economic Behavior, 20,
pp. 201223.
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A noncooperative theory of
quantityrationing global pollution
Sudhir Shah, University of Delhi
We study an incomplete information, noncooperative game
model of the determination of emissions in a Kyototype
quantityrationing setting with heterogeneous nations. We
model the emission capping negotiations using the best
response dynamic process and provide conditions under which
the process has a unique and globally asymptotically stable
stationary point. We then analyze the link between the type
profile and the stationary point to derive the
typecontingent ordering of emission allocations. Finally,
we study the investment strategies that nations can use
prior to the negotiations in order to manipulate the
equilibrium emission caps.
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Auctions for dynamic
environments: WiFi, lastminute tickets and grid computing
David Parkes, Harvard University
I consider the problem of auction design for dynamic
environments, in which agents arrive and depart dynamically
and in which goods are inherently temporal. Motivating
examples are drawn from the problem of WiFi allocation in
coffee houses, lastminute tickets, and scientific grid
computing. We provide a chracterization for the design of
truthful online auctions, such that it is a domnant strategy
equilibrium for bidders to reveal their true value for
resources immediately upon arrival into a system. The
auctions are online, in the sense that they make allocation
decisions without knowledge of the future. In a setting
without priors, we provide an ecompetitive (for efficiency)
truthful auction for a limitedsupply unitdemand problem,
drawing an analogy with the classic secretary problem. We
also present a 2competitive auction (wrt efficiency) for a
setting with a reusable resource, and and describe a
randomized online auction that achieves a competitive ratio
for revenue of O(log h), where h is the ratio of maximum
value to minimum value among the agents. In closing, we
discuss approaches that utilize priors as an interesting
direction for future work.
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Approximate generalizations and
applied equilibrium analysis
Felix Kubler, Universitaet Mannheim
In this paper I derive conditions on the fundamentals of
general equilibrium models that allow for a generalization
of finitely many examples to statements about (infinite)
classes of economies and I show how these approximate
generalizations can be applied in computational experiments.
If there exist upper bounds on the number of connected
components of onedimensional linear subsets of the set of
parameters for which a conjecture is true, one can conclude
that it is correct for all parameter values in the class
considered, except for a small residual set, once one has
verified it for a predetermined finite set of points. I
spell out assumptions on economic fundamentals which ensure
that these bounds on the number of connected components
exist, and that the residual set can be bounded from above.
I argue that utility and production functions used in
applied equilibrium analysis satisfy these conditions. Using
the theoretical results, I show how computational
experiments can be used to explore qualitative and
quantitative implications of economic models. I give
examples for actual upper bounds in realistically calibrated
economies and discuss both deterministic and random
algorithms for generalizing examples in these economies.
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Manipulation of endowments and
sunspot equilibria
Aditya Goenka, National University of Singapore
We consider the connection between occurrence of
manipulation via reallocating endowments by coalitions and
sunspot equilibria. The un certainty about which coalition
will form introduces extrinsic uncertainty into the economy.
Under certain conditions, manipulation of endowments by
coalitions can occur if and only if sunspots matter.
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Minimal rationality
Isaac Levi, Columbia University
Principles of minimal rationality ought to prescribe the
minimum necessary to insure coherent inquiry into
controversial issues. I argue here for principles of minimum
rationality that retain the core features of Bayesian
rationality (Independence) while abandoning the dogmatic
insistence on the requirement that rational agents should
evaluate their options according to a weak ordering that can
define optimal options. Conflict in values and indeterminacy
in probability argue against this. I shall summarize
elements of an account of rational choice that allows for
indeterminacy in probability and value (or utility) judgment
and breaks with the view that binary comparison is
fundamental to the evaluation of options.
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Asset price volatility with
heterogeneous and rational beliefs
HoMou Wu, National Taiwan University
This paper develops a theoretical model with a continuum
of speculators trading on differences of opinion to analyzes
the effects of margin requirements on asset price
volatility. In our model optimistic speculators conduct
speculation by expanding their credit with margin trading.
We show the existence of a unique general equilibrium with
heterogeneous and rational beliefs. We demonstrate that a
decrease in margin requirement may increase the current
price since it raises the demand of optimistic speculators,
and result in pyramiding/depyramiding phenomenon for the
future prices. Our results also suggest that a decrease in
margin requirement is anticipated, under certain conditions,
to increase asset price volatility.
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Independent random matching
Yeneng Sun, National University of Singapore
We provide microfoundations for independent random
matching of a large population, as widely used in the
economics and genetics literatures. We consider both static
and dynamic systems with random mutation, partial matching
arising from search, and type changes induced by matching.
Under independence assumptions at each randomization step,
we show that there is an almostsure constant
crosssectional distribution of types in a large population,
and moreover that the time evolution of the crosssectional
type process is completely determined from a Markov chain
with known transition matrices. We also construct a joint
agentprobability space, and randomized mutation, partial
matching, and matchinduced typechanging functions that
satisfy the required independence conditions. This is joint
work with Darrell Duffie of Stanford University.
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Repetitive risk aversion
Parkash Chander, National University of Singapore
This paper introduces and investigates the concept of
repetitive risk aversion. The risk aversion of an increasing
and concave utility function is repetitive if the fear of
ruin, which measures agent’s aversion to risking his entire
income, is also increasing and concave. This is shown to be
equivalent to the behaviorally meaningful condition that the
risk premium is increasing at a nonincreasing rate with the
size of the bet. We find an additional justification for
mixed risk aversion, which is known to be stronger than
standard (and thus proper) risk aversion, in terms of this
concept. We discuss several economic applications of
repetitive risk aversion.
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Statespace partitioning methods
for pricing highdimensional Americanstyle options
Xing Jin, National University of Singapore
The pricing of American options by simulationbased
methods is an important and difficult task primarily due to
the feature of early exercise, particularly for
highdimensional derivatives. In this paper, a bundling
method based on quasiMonte Carlo sequences is proposed to
price highdimensional Americanstyle options. The proposed
method extends Tilley's bundling algorithm to
higherdimensional situations. By using lowdiscrepancy
points, this approach partitions the state space and forms
bundles. A dynamic programming algorithm is then applied to
the bundles to estimate the continuation value of an
American option. A convergence proof of the algorithm is
provided. A variety of examples with up to 15 dimensions are
investigated numerically and accurate results are obtained.
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Hart effect and equilibrium in
incomplete markets
Roberto Raimondo, University of Melbourne
It is well known that the GEI Model can fail to have
equilibrium since there are bad spot prices. Using a system
of polynomials and matrix algebra I show that the set of
"bad" spot prices is typically empty if the information
tree, the set of tradable securities satisfies a certain
inequality and randomness condition. I also show that this
condition is always satisfied if the GEI model is the
discretization of a GEI model with continuous distributions.
Finally I prove that under this condition the equilibrium
always exists and I address the computational aspects of my
result.
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When and how to dismantle nuclear
weapons: more on optimal auction with externalities
Jingfeng Lu, National University of Singapore
This paper derives the optimal auction with externalities
between seller and bidders in addition to those among
bidders. An auction with the following features is
established as the optimal auction for the symmetric
setting. (i) Every participant pays a nonnegative entry fee,
which equals to the absolute value of the least externality
he might suffer or enjoy. (ii) If only bidder i does not
show up, the item is assigned to the one (including the
seller) generating him the least externality given this
least externality is nonpositive, otherwise the item is
destroyed by the seller. (iii) If all bidders participate,
the highest bidder wins if his bid is higher than the
reserve price, and he pays the second highest bid or the
reserve price whichever is higher. Each losing bidder pays
an additional payment (positive or negative) equal to the
externality to him/her incurred by the one keeping the item
(including the seller). The optimal reserve price is set
differently depending on whether the summation of the
seller's valuation, the destroying cost of the seller and
the total externalities to the bidders when seller keeps the
item is positive or negative. (iv) If no bidder bids higher
than the reserve price, the seller may keep the item by
himself/herself or destroy the item. The necessary and
sufficient condition for the seller to destroy the auctioned
item (dismantling nuclear weapon) on the equilibrium path is
that the above specified summation is negative. (v) All
bidders participate at the equilibrium.
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On equilibrium in pure strategies
in games with many players
Myrna Wooders, Vanderbilt Universities and University of
Warwick
Treating games of incomplete information with countable
sets of actions and types and finite but large player sets
we demonstrate that for every mixed strategy profile there
is a pure strategy profile that is ‘ε equivalent’.
Our framework introduces and exploits a distinction between
crowding attributes of players (their external effects on
others) and their taste attributes (their payoff functions
and any other attributes that are not directly relevant to
other players). The main assumption is a ‘large game’
property,’ dictating that the actions of relatively small
subsets of players cannot have large effects on the payoffs
of others Since it is well known that, even allowing mixed
strategies, with a countable set of actions a Nash
equilibrium may not exist, we provide an existence of
equilibrium theorem. The proof of existence relies on a
relationship between the ‘better reply security’ property of
Reny (1999) and a stronger version of the large game
property. Our purification theorem are based on a new
mathematical result, of independent interest, applicable to
countable strategy spaces.
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Purestrategy equilibrium in large
games with infinite types
Ali Khan, Johns Hopkins University
In this expository overview of ongoing work with K. Rath
and Y. Sun, I discuss "large" games with a "large" type
spaces. Earlier work (see KhanSun (PNAS 1996 and JME 1999)
for discussion, results and references) done under the
rubric of games with private information and with a finite
number of agents can then be seen as a consideration of
"large" games with finite number of type spaces. Thus, this
talk represents a stocktaking in which the analytical
difficulties are identified and the signal position of Loeb
probability spaces, and the law of large numbers based on
such spaces, is highlighted. In particular, I distinguish
the question of the existence of a purestrategy equilibrium
in such games from that of the purification of their
mixedstrategy equilibria, and examine in this regard the
implications of the theory of vector integration of
corresondences. I also take this opportunity to consider
earlier work of DvoretskyWaldWolfowitz as well as some
ongoing recent work of other authors.
« Back...
Market games, inequality and an
equal treatment property of the core
Myrna Wooders, Vanderbilt Universities and University of
Warwick
It is shown that games with many players whose attributes
are drawn from a compact set, are approximately market games
in the sense that they are representable by economies where
all players have concave utility functions. The games
include those derived from economies with local public
goods, with clubs, and with indivisibilities and
nonconvexities. The conditions required on the games are
only small group effectiveness and that there be no
externalities between groups of players. Small groups are
effective if almost all gains to collective activities can
be achieved by groups bounded in absolute size. Examples
demonstrate that the assumption of per capita boundedness
(finiteness of the supremum of average payoff) introduced in
prior research of this author is not adequate for our
current results. To obtain our results we also provide
another Theorem demonstrating that small group effectiveness
is equivalent to small group negligibility, the condition
dictating that vanishingly small sets of players can have at
most negligible effects on aggregate payoffs of large sets
of players. Finally, for the case of a finite number of
player types, for small ε, an εcore payoff has the property
that most players who have many close substitutes are
treated nearly equally — some, but only limited
discrimination can occur. An example demonstrates that,
simultaneously, players with ‘scarce’ attributes may be
treated vastly unequally.
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