This paper introduces a model of preferences, in which, given beliefs about uncertain outcomes, an individual evaluates an action by a quantile of the induced distribution. The choice rule of Quantile Maximization unifies maxmin and maxmax as maximizing the lowest and the highest quantiles of beliefs distributions, respectively, and offers a family of less extreme preferences. Taking preferences over acts as a primitive, we axiomatize Quantile Maximization in a Savage setting. Our axiomatization also provides a novel derivation of subjective beliefs, which demonstrates that neither the monotonicity nor the continuity conditions assumed in the literature are essential for probabilistic sophistication. We characterize preferences of quantile maximizers towards downside risk. We discuss how the distinct properties of the model, robustness and ordinality, can be useful in studying choice behaviour for categorical variables and in economic policy design. We also offer applications to poll design and insurance problems.

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.

Large institutional investors dominate many financial markets. This paper develops a consumption-based model of markets in which all institutional traders recognize their impact on prices. Bilateral (buyer and seller) market power changes efficiency and arbitrage properties of equilibrium. Predictions match temporary and permanent price effects of supply shocks, order breakup, limits to arbitrage, nonneutrality of trading frequency, and real effects of shocks and announcements in periods other than event dates. Maximizing welfare and stabilizing liquidity through disclosure of information about fundamentals presents a trade-off. Equilibrium representation as "trading against price impact" provides a link with the industry's practice.

This paper investigates the effects of market size on the ability of price to aggregate traders' private information. To account for heterogeneity in correlation of trader values, a Gaussian model of double auction is introduced that departs from the standard information structure based on a common (fundamental) shock. The paper shows that markets are informationally efficient only if correlations of values coincide across all bidder pairs. As a result, with heterogeneously interdependent values, price informativeness may not increase monotonically with market size. As a necessary and sufficient condition for the monotonicity, price informativeness increases with the number of traders if the implied reduction in (the absolute value of) an average correlation statistic of an information structure is sufficiently small.

This article reviews the theory of imperfectly competitive financial markets, with special attention to recent contributions and rapidly growing areas of research. We highlight the methodological advances that have led to a unified analytic framework for static, dynamic, centralized, and decentralized markets. Accounting for imperfect competition has not only reshaped our understanding of financial market data but also underscored the importance of market structure, motivated novel policy tools and objectives, and opened new avenues for market design. We identify areas where new models and techniques could enable further progress on equilibrium and market design analyses for markets with large players.

Most assets clear independently rather than jointly. This paper presents a model based on the uniform‐price double auction which accommodates arbitrary restrictions on market clearing, including independent clearing across assets (allowed when demand for each asset is contingent only on the price of that asset) and joint market clearing for all assets (required when demand for each asset is contingent on the prices of all assets). Additional trading protocols for traded assets—neutral when the market clears jointly—are generally not redundant innovations, even if all traders participate in all protocols. Multiple trading protocols that clear independently can be designed to be at least as efficient as joint market clearing for all assets. The change in price impact brought by independence in market clearing can overcome the loss of information, and enhance diversification and risk sharing. Except when the market is competitive, market characteristics should guide innovation in trading technology.

Decentralized trading motivates financial innovation, making synthetic products like derivatives nonredundant, even when all traders trade all assets. This nonredundancy arises because derivatives affect cross-security inference (information) and, in markets with large traders, equilibrium price impact (liquidity). The efficient securities differ from the underlying assets. While the market index/mutual funds are efficient in decentralized markets with competitive investors, heterogeneous portfolios that balance index tracking with liquidity transformation become efficient in markets with large traders. Efficient securities facilitate the trading of all fundamental risks but generally forgo hedging all contingencies to minimize the price impact costs associated with risk sharing and diversification.

When selling goods like wireless spectrum or electricity contracts, designers often opt for core-selecting mechanisms—i.e. those that induce outcomes in the core—in order to balance revenue and efficiency goals. But increasingly, auctions—such as the Federal Communications Commission’s Incentive Auction and those explored for natural resources—seek to reallocate goods, not just sell them. We show that when bidders can both buy and sell, substitutability among goods is no longer sufficient or necessary for core selection. In particular, in these environments, core selection can fail even with a single good and positive revenue, and can succeed even when some or all bidders view goods as complements. Instead, we show that the key feature that determines core selection is heterogeneity among the bidders. With too much heterogeneity, reallocation mostly realises pre-existing gains from trade among the bidders, and core selection fails. With limited heterogeneity, most gains from trade among the bidders are created by the quantity auctioned, and a core-selecting mechanism is possible.

In this paper, we show that stable outcomes exist in matching environments with complementarities, such as social media platforms or markets for patent licenses. Our results apply to both nontransferable and transferable utility settings, and allow for multilateral agreements and those with externalities. In particular, we show that stable outcomes in these settings are characterized by the largest fixed point of a monotone operator, and so can be found using an algorithm; in the nontransferable utility case, this is a one‐sided deferred acceptance algorithm, rather than a Gale–Shapley algorithm. We also give a monotone comparative statics result as well as a comparative static on the effect of bundling contracts together. These illustrate the impact of design decisions, such as increased privacy protections on social media, or the use of antitrust law to disallow patent pools, on stable outcomes.

Most assets are traded in multiple interconnected trading venues. This paper develops an equilibrium model of decentralized markets that accommodates general market structures with coexisting exchanges. Decentralized markets can allocate risk among traders with different risk preferences more efficiently, thus realizing gains from trade that cannot be reproduced in centralized markets. Market decentralization always increases price impact. Yet, markets in which assets are traded in multiple exchanges, whether they are disjoint or intermediated, can give higher welfare than the centralized market with the same traders and assets. In decentralized markets, demand substitutability across assets is endogenous and heterogeneous among traders.