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In this paper, we are concerned with the problem of determining the existenceof multiple equilibria in economic models. We propose a general and completeapproach for identifying multiplicities of equilibria in semi-algebraiceconomies, which may be expressed as semi-algebraic systems. The approach isbased on triangular decomposition and real solution classification, twopowerful tools of algebraic computation. Its effectiveness is illustrated bytwo examples of application.

Computing Equilibria of Semi-algebraic Economies Using Triangular Decomposition and Real Solution Classification