2021/08/15 by В. И. Данилов, Danilov, Vladimir I., Gleb Koshevoy +1
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Combinatorics (math.CO) #Economic theories and models #FOS: Mathematics #Game Theory and Voting Systems
paper · pdf · doi:10.48550/arxiv.2108.06786
openalex publication_date 2021/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We revisit the problem of existence of stable systems of contracts with arbitrary sets of contracts. We show that stable sets of contracts exists if choices of agents satisfy path-independence. We call such choice functions Plott functions. Our proof is based on application of Zorn lemma to a special poset of semi-stable pairs. Moreover, we construct a dynamic process on the poset (generalizing algorithm Gale and Shapley) steady states of which are stable sets. In Appendix we discuss Lehmann hyper-orders and establish a bijection between the set of Lehmann hyper-orders and the set of Plott functions.