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Computer Science, Computer Science and Game Theory, cs.GT,Computer Science, Data Structures and Algorithms, cs.DS
Abstract:
We present the first analysis of Fisher markets with buyers that have
budget-additive utility functions. Budget-additive utilities are elementary
concave functions with numerous applications in online adword markets and
revenue optimization problems. They extend the standard case of linear
utilities and have been studied in a variety of other market models. In
contrast to the frequently studied CES utilities, they have a global satiation
point which can imply multiple market equilibria with quite different
characteristics. Our main result is an efficient combinatorial algorithm to
compute a market equilibrium with a Pareto-optimal allocation of goods. It
relies on a new descending-price approach and, as a special case, also implies
a novel combinatorial algorithm for computing a market equilibrium in linear
Fisher markets. We complement these positive results with a number of hardness
results for related computational questions. We prove that it is NP-hard to
compute a market equilibrium that maximizes social welfare, and it is PPAD-hard
to find any market equilibrium with utility functions with separate satiation
points for each buyer and each good.
