Using oriented volume to prove Sperner’s lemma

Brown, A.B., Cairns, S.S.: Strengthening of Sperner’s lemma applied to homology theory. Proc. Natl. Acad. Sci. USA 47, 113–114 (1961)

Kannai, Y.: An elementary proof of the no-retraction theorem. Am. Math. Monthly 88, 264–268 (1981)

Kannai, Y.: The core and balancedness. In: Aumann, R.J., Hart, S. (eds.) Handbook of Game Theory with Economic Applications, pp. 355–395. Elsevier, Amsterdam (1992)

McLennan, A., Tourky, R.: Using volume to prove Sperner’s lemma. Econom. Theory 35, 593–597 (2008)

Meunier, F.: Combinatorial Stokes formulae. Eur. J. Combin. 29, 286–297 (2008)

Milnor, J.: Analytic proofs of the “hairy ball theorem” and the Brouwer fixed-point theorem. Am. Math. Monthly 85, 521–524 (1978)

Scarf, H.E.: The computation of equilibrium prices: an exposition. In: Arrow, K.J., Intriligator, M.D. (eds.) Handbook of Mathematical Economics, pp. 1007–1061. North-Holland, Amsterdam (1982)

Seifert, H., Threlfall, W.: Seifert and Threlfall: A Textbook of Topology. Academic Press, Eng. Trnas (1980)

Shapley, L.S.: On balanced games without side payments. In: Mathematical programming, pp. 261–290. Academic Press, San Diego (1973)

Shapley, L.S., Vohra, R.: On Kakutani’s fixed point theorem, the K-K-M-S theorem and the core of a balanced game. Econom. Theory 1(1991), 108–116 (1991)

Spanier, E.H.: Algebraic Topology. McGraw-Hill, New York (1966)

Sperner, E.: Neuer beweis für die invarianz der dimensionszahl und des gebietes. Abh. Math. Sem. Univ. Hamburg 6, 265–272 (1928)