Coordination Failure in Market Statistic Games
John Van Huyck and Raymond Battalio
January 1998
Prepared for Handbook of Experimental Economics Results
Editors: Charles R. Plott and Vernon L. Smith
© 1998 by the authors. A central question in economics
is how do markets coordinate the behavior of anonymous decision
makers in a many person decentralized economy. Economic theory
has traditionally addressed the question using the equilibrium
method, which abstracts away from an important aspect of the
general coordination problem, because it assumes an equilibrium. For
abstract games, an equilibrium is defined as an assignment to
each player of a strategy that is best for him when the others
use the strategies assigned to them. The relevance of this
abstract mutual consistency requirement for economic modeling is
an open question, see Kreps (1990). The requirement has two related problems:
disequilibrium and coordination failure. First, the mutual
consistency requirement of an equilibrium assignment is not an
implication of individual rationality, but an additional strong
assumption. Individual rationality means internal consistency and
internally consistent beliefs and actions of different players
may not be mutually consistent. In economies with stable and
unique equilibrium points, the influence of inconsistent beliefs
and actions would disappear over time, see Robert Lucas (1987).
The power of the equilibrium method derives from its ability to
abstract from the complicated dynamic process that induces
equilibrium and to abstract from the historical accident that
initiated the process. Second, there is often more than one
equilibrium assignment. For example, multiple Pareto ranked
equilibria arise in both macroeconomic models with production,
search, or trading externalities and microeconomic models of
monopolistic competition, technology adoption and diffusion, and
manufacturing with non-convexities. These superficially
dissimilar market and non-market models share the common property
that a decision maker's best "level of effort" depends
positively upon other decision makers' "level of
effort." This property is called strategic complementarity
in the coordination failure literature, see Cooper and John
(1988). When these equilibria can be Pareto ranked it is possible
for historical accident and dynamic process to lead to
inefficient equilibria, that is, coordination failure.
Consequently, understanding the origin of mutually consistent
behavior is an essential complement to the theory of equilibrium
points. The experimental method provides a tractable
and constructive approach to the equilibrium selection problem.
This chapter reviews experiments using a class of generic market
statistic games with multiple equilibria, which are strictly
Pareto ranked, and it reports experiments that provide evidence
on how human subjects behave under conditions of strategic
uncertainty. Strategic uncertainty exists when the
players actions are not mutual knowledge. A laboratory environment
capturing the essential aspects of the mutual consistency problem
in a many person decentralized economy must include three
features: First, the environment must not assume away the problem
by allowing an arbiter--or any other individual--to make common
knowledge preplay assignments. Second, the environment must allow
individuals little ability to unilaterally alter market outcomes.
Finally, the environment must allow repeated interaction amongst
the decision makers so that they have a chance to learn to
coordinate. For laboratory research, a
tractable class of market processes with these features are
market statistic games. Let xit denote the
action of player i in period t. An action
combination is the vector of actions xt = (x1t,...,xnt)
for the n players. A homogenous action combination
occurs when all players take the same action. An abstract market process is a mapping from the action
space into a real number, the market outcome y(x). The market outcome could represent market
thickness, industry production, average market price, aggregate
demand, or aggregate supply. In the coordination failure
literature, the mean of the players' actions is a common example
of an abstract market process. As the number of players
increases, the influence of an individual player on the mean goes
to zero and in the limit an individual player can not influence
the market outcome. Order statistics are an effective way to
capture the anonymity of a many person economy without using
enormous group sizes. The jth inclusive order
statistic, mj, is defined by m1
m2 ... mn, where the mj
are the xi of action combination x
arranged in increasing order. When y(x) = mj
and 1 < j < n, an actor contemplating
defection from a homogenous action combination can not influence
the market outcome. Let OS[n,j] denote the stage game of a
finitely repeated order statistic game with n subjects
and jth order statistic. Let the payoff
function be such that an actor's unique best response to the
market statistic y(x) in the stage game is
simply xi* = y(x). This
class of order statistic games has the property that any feasible
homogenous action combination is a strict equilibrium and
depending on the payoff function these equilibria may or may not
be ranked by efficiency. [ Top
| Download | Introduction | John's Web ] Adobe Acrobat (PDF) format: Text: The PDF file size is 245k. Surface mail request (comments, suggestions,
references, etc.): john.vanhuyck@tamu.edu [ Top | Download | Introduction |
John's Web ] John Bryant, "A Simple
Rational Expectations Keynes-Type Model", The Quarterly
Journal of Economics, vol. 98, no.3, August 1983, 525-528. Russell Cooper and Andrew John,
"Coordinating Coordination Failures in Keynesian
Models," The Quarterly Journal of Economics,
103(3), August 1988, 441-464. David M. Kreps, Game Theory
and Economic Modelling, (Oxford,UK: Clarendon Press, 1990). Robert E. Lucas, Jr.,
"Adaptive Behavior and Economic Theory," in Rational
Choice, ed. R. Hogarth and M. Reder, Chicago: University of
Chicago Press, 1987. J.B. Van Huyck, R.C. Battalio,
and R.O. Beil, "Tacit Coordination Games, Strategic
Uncertainty, and Coordination Failure," The American Economic Review
80(1), March 1990, 234-248. J.B. Van Huyck, R.C. Battalio,
and R.O. Beil, "Strategic Uncertainty, Equilibrium
Selection, and Coordination Failure in Average Opinion
Games," The
Quarterly Journal of Economics, 106(3), August 1991,
885-911. J.B. Van Huyck, R.C. Battalio,
and F.W. Rankin, "Evidence on Learning in Coordination
Games,"
laser-script, May 1997. J.B. Van Huyck, J.P. Cook, and
R.C. Battalio, "Adaptive Behavior and Coordination
Failure,"
forthcoming in Journal of Economic Behavior and Organization. [ Top | Download | Introduction |
John's Web ]