Poly-time 1/e-approx algorithm for general HZ equilibria via stratification reduction to bi-valued case, plus 5x5 counterexample showing irrational exact equilibria for tri-valued utilities.
Vazirani and Mihalis Yannakakis , title =
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Approximation and Irrationality in Hylland--Zeckhauser Equilibria
Poly-time 1/e-approx algorithm for general HZ equilibria via stratification reduction to bi-valued case, plus 5x5 counterexample showing irrational exact equilibria for tri-valued utilities.