704 research outputs found
Welfare and Revenue Guarantees for Competitive Bundling Equilibrium
We study equilibria of markets with heterogeneous indivisible goods and
consumers with combinatorial preferences. It is well known that a
competitive equilibrium is not guaranteed to exist when valuations are not
gross substitutes. Given the widespread use of bundling in real-life markets,
we study its role as a stabilizing and coordinating device by considering the
notion of \emph{competitive bundling equilibrium}: a competitive equilibrium
over the market induced by partitioning the goods for sale into fixed bundles.
Compared to other equilibrium concepts involving bundles, this notion has the
advantage of simulatneous succinctness ( prices) and market clearance.
Our first set of results concern welfare guarantees. We show that in markets
where consumers care only about the number of goods they receive (known as
multi-unit or homogeneous markets), even in the presence of complementarities,
there always exists a competitive bundling equilibrium that guarantees a
logarithmic fraction of the optimal welfare, and this guarantee is tight. We
also establish non-trivial welfare guarantees for general markets, two-consumer
markets, and markets where the consumer valuations are additive up to a fixed
budget (budget-additive).
Our second set of results concern revenue guarantees. Motivated by the fact
that the revenue extracted in a standard competitive equilibrium may be zero
(even with simple unit-demand consumers), we show that for natural subclasses
of gross substitutes valuations, there always exists a competitive bundling
equilibrium that extracts a logarithmic fraction of the optimal welfare, and
this guarantee is tight. The notion of competitive bundling equilibrium can
thus be useful even in markets which possess a standard competitive
equilibrium
Influence Diffusion in Social Networks under Time Window Constraints
We study a combinatorial model of the spread of influence in networks that
generalizes existing schemata recently proposed in the literature. In our
model, agents change behaviors/opinions on the basis of information collected
from their neighbors in a time interval of bounded size whereas agents are
assumed to have unbounded memory in previously studied scenarios. In our
mathematical framework, one is given a network , an integer value
for each node , and a time window size . The goal is to
determine a small set of nodes (target set) that influences the whole graph.
The spread of influence proceeds in rounds as follows: initially all nodes in
the target set are influenced; subsequently, in each round, any uninfluenced
node becomes influenced if the number of its neighbors that have been
influenced in the previous rounds is greater than or equal to .
We prove that the problem of finding a minimum cardinality target set that
influences the whole network is hard to approximate within a
polylogarithmic factor. On the positive side, we design exact polynomial time
algorithms for paths, rings, trees, and complete graphs.Comment: An extended abstract of a preliminary version of this paper appeared
in: Proceedings of 20th International Colloquium on Structural Information
and Communication Complexity (Sirocco 2013), Lectures Notes in Computer
Science vol. 8179, T. Moscibroda and A.A. Rescigno (Eds.), pp. 141-152, 201
Fashion, Cooperation, and Social Interactions
Fashion plays such a crucial rule in the evolution of culture and society
that it is regarded as a second nature to the human being. Also, its impact on
economy is quite nontrivial. On what is fashionable, interestingly, there are
two viewpoints that are both extremely widespread but almost opposite:
conformists think that what is popular is fashionable, while rebels believe
that being different is the essence. Fashion color is fashionable in the first
sense, and Lady Gaga in the second. We investigate a model where the population
consists of the afore-mentioned two groups of people that are located on social
networks (a spatial cellular automata network and small-world networks). This
model captures two fundamental kinds of social interactions (coordination and
anti-coordination) simultaneously, and also has its own interest to game
theory: it is a hybrid model of pure competition and pure cooperation. This is
true because when a conformist meets a rebel, they play the zero sum matching
pennies game, which is pure competition. When two conformists (rebels) meet,
they play the (anti-) coordination game, which is pure cooperation. Simulation
shows that simple social interactions greatly promote cooperation: in most
cases people can reach an extraordinarily high level of cooperation, through a
selfish, myopic, naive, and local interacting dynamic (the best response
dynamic). We find that degree of synchronization also plays a critical role,
but mostly on the negative side. Four indices, namely cooperation degree,
average satisfaction degree, equilibrium ratio and complete ratio, are defined
and applied to measure people's cooperation levels from various angles. Phase
transition, as well as emergence of many interesting geographic patterns in the
cellular automata network, is also observed.Comment: 21 pages, 12 figure
Crises and collective socio-economic phenomena: simple models and challenges
Financial and economic history is strewn with bubbles and crashes, booms and
busts, crises and upheavals of all sorts. Understanding the origin of these
events is arguably one of the most important problems in economic theory. In
this paper, we review recent efforts to include heterogeneities and
interactions in models of decision. We argue that the Random Field Ising model
(RFIM) indeed provides a unifying framework to account for many collective
socio-economic phenomena that lead to sudden ruptures and crises. We discuss
different models that can capture potentially destabilising self-referential
feedback loops, induced either by herding, i.e. reference to peers, or
trending, i.e. reference to the past, and account for some of the phenomenology
missing in the standard models. We discuss some empirically testable
predictions of these models, for example robust signatures of RFIM-like herding
effects, or the logarithmic decay of spatial correlations of voting patterns.
One of the most striking result, inspired by statistical physics methods, is
that Adam Smith's invisible hand can badly fail at solving simple coordination
problems. We also insist on the issue of time-scales, that can be extremely
long in some cases, and prevent socially optimal equilibria to be reached. As a
theoretical challenge, the study of so-called "detailed-balance" violating
decision rules is needed to decide whether conclusions based on current models
(that all assume detailed-balance) are indeed robust and generic.Comment: Review paper accepted for a special issue of J Stat Phys; several
minor improvements along reviewers' comment
Information and ambiguity: herd and contrarian behaviour in financial markets
“The final publication is available at Springer via http://dx.doi.org/10.1007/s11238-012-9334-3”The paper studies the impact of informational ambiguity on behalf of informed traders
on history-dependent price behaviour in a model of sequential trading in nancial markets.
Following Chateauneuf, Eichberger and Grant (2006), we use neo-additive capacities to
model ambiguity. Such ambiguity and attitudes to it can engender herd and contrarian
behaviour, and also cause the market to break down. The latter, herd and contrarian
behaviour, can be reduced by the existence of a bid-ask spread.Research in part funded by ESRC grant RES-000-22-0650
Institutional Herding in Financial Markets: New Evidence Through the Lens of a Simulated Model
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