Marakulin, V.

equilibrium price non-standard equilibria dividend hierarchic agent budget vector p i l non-standard prices non-standard dividend equilibria theorem proof economy non-standard dividend equilibrium 1 q 1 condition proposition number consumption element hierarchic price allocation manifold mapping walrasian equilibrium agent i definition system coalition component restriction function assumption utility coupon section result walrasian endowment representation hierarchic equilibria survival assumption bread i supp market allocation x x polyhedral transversal economy e value dividend equilibria rejective core lemma consumer florig subset survival prices p consumption sets x i l hierarchic price q p / p coupons equilibrium paper proposition 3.6 y i pi non-standard equilibria utility functions face f finitenes existence dimension model marakulin example space preference analysis