Auctions often involve the sale of many related goods: Treasury, spectrum and electricity auctions are examples. In multi-unit auctions, a bid for one unit may affect payments for other units won, giving rise to an incentive to shade bids differently across units. We establish that such differential bid shading results generically in ex post inefficient allocations in the uniform-price and pay-as-bid auctions. We also show that, in general, the efficiency and revenue rankings for the two formats are ambiguous. However, in settings with symmetric bidders, the pay-as-bid auction often outperforms. In particular, with diminishing marginal utility, symmetric information and linearity, it yields greater expected revenues. We explain the rankings through multi-unit effects, which have no counterparts in auctions with unit demands. We attribute the new incentives separately to multi-unit but constant marginal utility and diminishing marginal utility.JEL classification: D44, D82, D47, L13, L94

Extensive empirical research has shown that in many markets institutional investors have a significant impact on prices and mitigate its adverse effects through their trading strategies. This paper develops a dynamic model of such thin markets, in which the market structure is one of bilateral oligopoly. The paper demonstrates that market thinness qualitatively changes equilibrium properties of prices and dynamic trading strategies, compared to the existing theories of asset pricing. The predictions match a number of empirical facts that are hard to reconcile with the competitive or Cournot-based models. The paper further establishes that the nonstrategic general-equilibrium approach and the strategic approach to trade via Nash in demands are dual representations of a model with endogenous price impact. The proposed approach yields an analytical framework that can be used to study dynamic markets with bilateral market power.

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This paper examines the incentives offered by frictionless markets to innovate asset‐backed securities by owners who maximize the assets' values. Assuming identical preferences across investors with heterogeneous risk‐sharing needs, we characterize economies in which competition provides insufficient incentives to innovate so that, in equilibrium, financial markets are incomplete in all (pure strategy) equilibria, even when innovation is essentially costless. Thus, value maximization does not generally result in complete markets.

Does encouraging trader participation enhance market competitiveness? This paper shows that, when trader preferences are interdependent, trader market power does not necessarily decrease with greater participation, and traders need not become price takers in large markets. Thus, larger markets can be less liquid and associated with lower ex ante welfare. In the linear-normal model, the necessary and sufficient condition on the information structure is provided under which price impact is monotone in market size. A condition is given when the rational expectations equilibrium, which is typically not fully revealing within the considered class of preference interdependencies, is obtained in large markets.