9 research outputs found
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
Bounded incentives in manipulating the probabilistic serial rule
The Probabilistic Serial mechanism is valued for its fairness and efficiency in addressing the random assignment problem. However, it lacks truthfulness, meaning it works well only when agents' stated preferences match their true ones. Significant utility gains from strategic actions may lead self-interested agents to manipulate the mechanism, undermining its practical adoption. To gauge the potential for manipulation, we explore an extreme scenario where a manipulator has complete knowledge of other agents' reports and unlimited computational resources to find their best strategy. We establish tight incentive ratio bounds of the mechanism. Furthermore, we complement these worst-case guarantees by conducting experiments to assess an agent's average utility gain through manipulation. The findings reveal that the incentive for manipulation is very small. These results offer insights into the mechanism's resilience against strategic manipulation, moving beyond the recognition of its lack of incentive compatibility
Nash Social Welfare Approximation for Strategic Agents
The fair division of resources is an important age-old problem that has led
to a rich body of literature. At the center of this literature lies the
question of whether there exist fair mechanisms despite strategic behavior of
the agents. A fundamental objective function used for measuring fair outcomes
is the Nash social welfare, defined as the geometric mean of the agent
utilities. This objective function is maximized by widely known solution
concepts such as Nash bargaining and the competitive equilibrium with equal
incomes. In this work we focus on the question of (approximately) implementing
the Nash social welfare. The starting point of our analysis is the Fisher
market, a fundamental model of an economy, whose benchmark is precisely the
(weighted) Nash social welfare. We begin by studying two extreme classes of
valuations functions, namely perfect substitutes and perfect complements, and
find that for perfect substitutes, the Fisher market mechanism has a constant
approximation: at most 2 and at least e1e. However, for perfect complements,
the Fisher market does not work well, its bound degrading linearly with the
number of players.
Strikingly, the Trading Post mechanism---an indirect market mechanism also
known as the Shapley-Shubik game---has significantly better performance than
the Fisher market on its own benchmark. Not only does Trading Post achieve an
approximation of 2 for perfect substitutes, but this bound holds for all
concave utilities and becomes arbitrarily close to optimal for Leontief
utilities (perfect complements), where it reaches for every
. Moreover, all the Nash equilibria of the Trading Post mechanism
are pure for all concave utilities and satisfy an important notion of fairness
known as proportionality
Wages and Utilities in a Closed Economy
The broad objective of this paper is to propose a mathematical model for the
study of causes of wage inequality and relate it to choices of consumption, the
technologies of production, and the composition of labor in an economy. The
paper constructs a Simple Closed Model, or an SCM, for short, for closed
economies, in which the consumption and the production parts are clearly
separated and yet coupled. The model is established as a specialization of the
Arrow-Debreu model and its equilibria correspond directly with those of the
general Arrow-Debreu model. The formulation allows us to identify the
combinatorial data which link parameters of the economic system with its
equilibria, in particular, the impact of consumer preferences on wages. The SCM
model also allows the formulation and explicit construction of the consumer
choice game, where expressed utilities of various labor classes serve as
strategies with total or relative wages as the pay-offs. We illustrate, through
examples, the mathematical details of the consumer choice game. We show that
consumer preferences, expressed through modified utility functions, do indeed
percolate through the economy, and influence not only prices but also
production and wages. Thus, consumer choice may serve as an effective tool for
wage redistribution
Price Competition in Networked Markets: How do monopolies impact social welfare?
We study the efficiency of allocations in large markets with a network
structure where every seller owns an edge in a graph and every buyer desires a
path connecting some nodes. While it is known that stable allocations in such
settings can be very inefficient, the exact properties of equilibria in markets
with multiple sellers are not fully understood even in single-source
single-sink networks. In this work, we show that for a large class of natural
buyer demand functions, we are guaranteed the existence of an equilibrium with
several desirable properties. The crucial insight that we gain into the
equilibrium structure allows us to obtain tight bounds on efficiency in terms
of the various parameters governing the market, especially the number of
monopolies M. All of our efficiency results extend to markets without the
network structure.
While it is known that monopolies can cause large inefficiencies in general,
our main results for single-source single-sink networks indicate that for
several natural demand functions the efficiency only drops linearly with M. For
example, for concave demand we prove that the efficiency loss is at most a
factor 1+M/2 from the optimum, for demand with monotone hazard rate it is at
most 1+M, and for polynomial demand the efficiency decreases logarithmically
with M. In contrast to previous work that showed that monopolies may adversely
affect welfare, our main contribution is showing that monopolies may not be as
`evil' as they are made out to be; the loss in efficiency is bounded in many
natural markets. Finally, we consider more general, multiple-source networks
and show that in the absence of monopolies, mild assumptions on the network
topology guarantee an equilibrium that maximizes social welfare.Comment: To appear in Proceedings of WINE 2015: 11th Conference on Web and
Internet Economic
Incentive Ratios of Fisher Markets
Abstract. In a Fisher market, a market maker sells m items to n potential buyers. The buyers submit their utility functions and money endowments to the market maker, who, upon receiving submitted information, derives market equilibrium prices and allocations of its items. While agents may benefit by misreporting their private information, we show that the percentage of improvement by a unilateral strategic play, called incentive ratio, is rather limited—it is less than 2 for linear markets and at most e 1/e ≈ 1.445 for Cobb-Douglas markets. We further prove that both ratios are tight.