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The notion of arbitrage is predominantly used as a conceptual framework in finance and economics for studying equilibrium as well as pricing relations of asset markets. The consequences of equilibrium analysis based upon arbitrage, however, do not apply to the case with nontransitive preferences simply because the literature assumes the transitivity of preferences. We propose a weak notion of arbitrage which provides a sufficient condition for the existence of equilibrium of the economy where preferences need be neither transitive nor complete and the consumption sets need not be bounded from below.


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Short-Selling, Nontransitive Preferences, Arbitrage, Competitive Equilibrium