Hidden
Markov Models of Strategic Information Control
by
Bart
Taub
University of Illinois at Urbana-Champaign
Abstract
A stochastic process impinges
on an agent and a principal in distinct ways.
From the agent’s perspective the process is noise that interferes with
his perception of productivity states, leading him to sometimes take actions
that are in retrospect mistaken. From
the principal’s perspective the noise is in fact the productivity of the
agent’s action, and he would like to coordinate the agent’s actions with the
process.
The principal is not able to provide direct material payoffs to the agent in
order to induce this coordination. He
is however allowed to communicate with the agent.
If he fully communicates the state of the noise process, the agent will
eliminate all response to it, thus vitiating the principal’s interests.
If he communicates nothing, the agent’s reactions to the noise are
random, and will be in synchrony with the principal’s interests only by
accident. The principal can send a
Pareto-improving signal however. Such
a signal requires that the agent from his perspective make mistakes, and fails
to fully coordinate actions with states from the principal’s perspective.
The strategic use of information is modeled using a hidden Markov model
framework. In this framework, the state of a Markov process is
unobservable, but it drives a signal that is correlated with it. This framework allows the agent’s optimization problem to
be simplified using a measure change (which may be familiar to some readers as a
Girsanov transformation). The
simplified representation of the agent’s problem then becomes a set of
constraints for the principal. The
key methodological innovation here is that the informativeness of the signal is
directly controllable by the principal. The
informativeness is represented by elements of a matrix, reducing the information
strategy to choosing elements of the matrix.
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Last
updated March 27, 2002 by Linda Huff
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