INDUSTRIAL ENGINEERING AND
OPERATIONS RESEARCH
PRESENTS
IEOR MONDAY SEMINAR
TOWARD DISCRETE AND LOCAL TATONNEMENT ALGORITHMS FOR THE MARKET EQUILIBRIUM PROBLEM
Lisa Fleischer
ABSTRACT
In the market equilibrium problem, there is a market consisting of a set of
infinitely divisible goods; and a set of agents with an initial allocation of
the goods and a utility function over combinations of goods. Trade is driven by the prices of the
goods. Each agent can buy at most the
worth of their initial allocation.
Prices provide an equilibrium if, in addition, the demand for each good
is bounded by the supply. It was shown by
a fixed point argument in the 1950's that an equilibrium
always exists.
Since then, focus has been on developing constructive proofs
or computable mechanisms. Prior work
focuses either on global optimization procedures or continuous-time mechanisms (differential
equations).
In contrast, we propose a dynamic, discrete time,
distributed mechanism that may indicate how a market arrives at an equilibrium. We prove
(fast) convergence properties for this mechanism in some types of markets. This is, to the best of our knowledge, the
first convergent, discrete, local algorithm for any version of the market
problem.
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