Many economic-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Such assumptions introduce a conceptual problem, as results that rely on finiteness are often implicitly nonrobust; for example, they may rely on edge effects or artificial boundary conditions. Here, we present a unified method that enables us to remove finiteness assumptions, such as those on datasets, market sizes, and time horizons. We then apply our approach to a variety of revealed preference, matching, and exchange economy settings.<\/p>\n
The key to our approach is Logical Compactness, a core result from Propositional Logic. Building on Logical Compactness, in a revealed-preference setting, we reprove Reny\u2019s infinitedata version of Afriat\u2019s theorem and (newly) prove an infinite-data version of McFadden and Richter\u2019s characterization of rationalizable stochastic datasets. In a matching setting, we reprove large-market existence results implied by Fleiner\u2019s analysis, and prove both the strategyproofness of the man-optimal stable mechanism in infinite markets, and an infinite-market version of Nguyen and Vohra\u2019s existence result for near-feasible stable matchings with couples. In a trading-network setting, we prove that the Hatfield et al. result on existence of Walrasian equilibria extends to infinite markets. Finally, we prove that Pereyra\u2019s existence result for dynamic two-sided matching markets extends to a doubly-infinite time horizon.<\/p>\n","protected":false},"excerpt":{"rendered":"
Many economic-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Such assumptions introduce a conceptual problem, as results that rely on finiteness are often implicitly nonrobust; for example, they may rely on edge effects or artificial boundary conditions. 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