Matroids are Immune to Braess Paradox

The famous Braess paradox describes the following phenomenon: It might happen that the improvement of resources, like building a new street within a congested network, may in fact lead to larger costs for the players in an equilibrium. In this paper we consider general nonatomic congestion games and give a characterization of the maximal combinatorial property of strategy spaces for which Braess paradox does not occur. In a nutshell, bases of matroids are exactly this maximal structure. We prove our characterization by two novel sensitivity results for convex separable optimization problems over polymatroid base polyhedra which may be of independent interest.Comment: 21 page

International Trade and Income Distribution: A Reconsideration

The postwar expansion of trade among the industrial countries has not had the strong distributional effects which standard models of trade would have led us to expect. This paper develops a model which attempts to explain this observation, while at the same time making sense of some other puzzling empirical aspects of world trade. The basis of the model is a distinction between two kinds of trade: "Heckscher-Ohlin" trade, based on differences in factor proportions, and "intraindustry" trade, based on scale economies and product differentiation. To incorporate intraindustry trade into the model it is necessary to drop the usual assumptions of constant returns to scale and perfect competition; instead the paper deals with a world where economies of scale are pervasive and all firms possess some monopoly power. Surprisingly, it is nonetheless possible to develop a fully-worked-out general equilibrium model which remains simple and can be used to compare autarky and free trade. Two main results emerge from the analysis. First, the nature of trade depends on how similar countries are in their factor endowments. As countries become more similar, the trade between them will increasingly become intra-industry in character. Second, the effects of opening trade depend on its type. If intraindustry trade is sufficiently dominant the advantages of extending the market will outweigh the distributional effects, and the owners of scarce as well as of abundant factors will be made better off.

Hierarchical Trade and Endogenous Price Distortions

We study the allocation of commodities through a two-stage hierarchy of competitive markets. Groups or countries trade at global prices while individuals within a group trade at local prices. We identify the free trade and the autarky equilibrium as polar cases. We show that no other two-stage market equilibria exist if the commodity space is two-dimensional. An example demonstrates that other, so-called intermediate equilibria exist for three-dimensional commodity spaces. The example also exhibits endogenous price distortions in third countries when some countries follow distortionary trade policies. We give two existence proofs for intermediate equilibria in higher dimensions. Each proof provides an explicit construction of special classes of intermediate equilibria.