Cardinal-Utility Matching Markets: The Quest for Envy-Freeness, Pareto-Optimality, and Efficient Computability
CoRR(2024)
摘要
Unlike ordinal-utility matching markets, which are well-developed from the
viewpoint of both theory and practice, recent insights from a computer science
perspective have left cardinal-utility matching markets in a quandary. The
celebrated pricing-based mechanism for one-sided cardinal-utility matching
markets due to Hylland and Zeckhauser, which had long eluded efficient
algorithms, was finally shown to be PPAD-complete.
This led us to ask the question: is there an alternative, polynomial time,
mechanism for one-sided cardinal-utility matching markets which achieves the
desirable properties of HZ, i.e. (ex-ante) envy-freeness (EF) and
Pareto-optimality (PO)? In this paper we show:
1. The problem of finding an EF+PO lottery in a one-sided cardinal-utility
matching market is PPAD-complete.
2. A (2 + ϵ)-approximately envy-free and (exactly) Pareto-optimal
lottery can be found in polynomial time using Nash bargaining.
We also present several results on two-sided cardinal-utility matching
markets, including non-existence of EF+PO lotteries as well as existence of
justified-envy-free and weak Pareto-optimal lotteries.
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