Price Controls, Non-Price Quality Competition, and the Nonexistence of Competitive Equilibrium

We investigate how price ceilings and floors affect outcomes in continuous time, double auction markets with discrete goods and multiple qualities. When price controls exist, the existence of competitive equilibria is no longer guaranteed; hence, we investigate the nature of non-price competition and how markets might evolve in its presence. We develop a quality competition model based on matching theory. Equilibria of the quality competition model always exist in such price-constrained markets; moreover, they naturally correspond to competitive equilibria when competitive equilibria exist. Additionally, we characterize the set of equilibria of the quality competition model in the presence of price restrictions. In a series of experiments, we find that market outcomes closely conform to the predictions of the model. In particular, price controls induce non-price competition between agents both in theory and in the experimental environment; market behaviors result in allocations close to the predictions of the model

Understanding Price Controls and Non-Price Competition with Matching Theory

We develop a quality competition model to understand how price controls affect market outcomes in buyer-seller markets with discrete goods of varying quality. While competitive equilibria do not necessarily exist in such markets when price controls are imposed, we show that stable outcomes do exist and characterize the set of stable outcomes in the presence of price restrictions. In particular, we show that price controls induce non-price competition: price floors induce the trade of inefficiently high quality goods, while price ceilings induce the trade of inefficiently low quality goods

Extreme Walrasian Dynamics: The Gale Example in the Lab

We study the classic Gale (1963) economy using laboratory markets. Tatonnement theory predicts prices will diverge from an equitable interior equilibrium towards infinity or zero depending only on initial prices. The inequitable equilibria determined by these dynamics give all gains from exchange to one side of the market. Our results show surprisingly strong support for these predictions. In most sessions one side of the market eventually outgains the other by more than twenty times, leaving the disadvantaged side to trade for mere pennies. We also find preliminary evidence that these dynamics are sticky, resisting exogenous interventions designed to reverse their trajectories

On the Efficiency of the Walrasian Mechanism

Central results in economics guarantee the existence of efficient equilibria for various classes of markets. An underlying assumption in early work is that agents are price-takers, i.e., agents honestly report their true demand in response to prices. A line of research in economics, initiated by Hurwicz (1972), is devoted to understanding how such markets perform when agents are strategic about their demands. This is captured by the \emph{Walrasian Mechanism} that proceeds by collecting reported demands, finding clearing prices in the \emph{reported} market via an ascending price t\^{a}tonnement procedure, and returns the resulting allocation. Similar mechanisms are used, for example, in the daily opening of the New York Stock Exchange and the call market for copper and gold in London. In practice, it is commonly observed that agents in such markets reduce their demand leading to behaviors resembling bargaining and to inefficient outcomes. We ask how inefficient the equilibria can be. Our main result is that the welfare of every pure Nash equilibrium of the Walrasian mechanism is at least one quarter of the optimal welfare, when players have gross substitute valuations and do not overbid. Previous analysis of the Walrasian mechanism have resorted to large market assumptions to show convergence to efficiency in the limit. Our result shows that approximate efficiency is guaranteed regardless of the size of the market

Modeling Electricity Auctions

The recent debates over discriminatory versus uniform-price auctions in the UK and elsewhere have revealed an incomplete understanding of the limitations of some popular auction models when applied to real-world electricity markets. This has led certain regulatory authorities to prefer discriminatory auctions on the basis of reasoning from models which are not directly applicable to any existing electricity market. Vickrey auctions, although often recommended by economists, have also been ignored in these debates. This article describes the approach which we believe should be taken to analyzing these issues

Computing Equilibria in Markets with Budget-Additive Utilities

We present the first analysis of Fisher markets with buyers that have budget-additive utility functions. Budget-additive utilities are elementary concave functions with numerous applications in online adword markets and revenue optimization problems. They extend the standard case of linear utilities and have been studied in a variety of other market models. In contrast to the frequently studied CES utilities, they have a global satiation point which can imply multiple market equilibria with quite different characteristics. Our main result is an efficient combinatorial algorithm to compute a market equilibrium with a Pareto-optimal allocation of goods. It relies on a new descending-price approach and, as a special case, also implies a novel combinatorial algorithm for computing a market equilibrium in linear Fisher markets. We complement these positive results with a number of hardness results for related computational questions. We prove that it is NP-hard to compute a market equilibrium that maximizes social welfare, and it is PPAD-hard to find any market equilibrium with utility functions with separate satiation points for each buyer and each good.Comment: 21 page

The Complexity of Non-Monotone Markets

We introduce the notion of non-monotone utilities, which covers a wide variety of utility functions in economic theory. We then prove that it is PPAD-hard to compute an approximate Arrow-Debreu market equilibrium in markets with linear and non-monotone utilities. Building on this result, we settle the long-standing open problem regarding the computation of an approximate Arrow-Debreu market equilibrium in markets with CES utility functions, by proving that it is PPAD-complete when the Constant Elasticity of Substitution parameter \rho is any constant less than -1