6,625 research outputs found
Two lemmas that changed general equilibrium theory
URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/CESFRamDP2009.htmClassification AMS : 54H25, 47H10, 54C65.Paru dans Games and Economic Behavior, vol.66, issue 2, juillet 2009.Documents de travail du Centre d'Economie de la Sorbonne 2009.52 - ISSN : 1955-611XThis short paper published in Games and Economic Behavior (July 2009) "In Memoriam" of David Gale, emphasizes the seminal role played by two lemmas of David Gale in the development of the foundations of General Equilibrium Theory.Ce cours article, publié dans Games and Economic Behavior (Juillet 2009) "In Memoriam" et en l'honneur de David Gale, analyse l'importance de deux lemmes dûs à David Gale pour le développement de la théorie de l'équilibre général, à ses débuts en 1955 puis vingt ans aprÚs
Optimal equilibria of the best shot game
We consider any network environment in which the "best shot game" is played.
This is the case where the possible actions are only two for every node (0 and
1), and the best response for a node is 1 if and only if all her neighbors play
0. A natural application of the model is one in which the action 1 is the
purchase of a good, which is locally a public good, in the sense that it will
be available also to neighbors. This game typically exhibits a great
multiplicity of equilibria. Imagine a social planner whose scope is to find an
optimal equilibrium, i.e. one in which the number of nodes playing 1 is
minimal. To find such an equilibrium is a very hard task for any non-trivial
network architecture. We propose an implementable mechanism that, in the limit
of infinite time, reaches an optimal equilibrium, even if this equilibrium and
even the network structure is unknown to the social planner.Comment: submitted to JPE
Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise
The study of fluctuations in gene regulatory networks is extended to the case
of Gaussian colored noise. Firstly, the solution of the corresponding Langevin
equation with colored noise is expressed in terms of an Ito integral. Then, two
important lemmas concerning the variance of an Ito integral and the covariance
of two Ito integrals are shown. Based on the lemmas, we give the general
formulae for the variances and covariance of molecular concentrations for a
regulatory network near a stable equilibrium explicitly. Two examples, the gene
auto-regulatory network and the toggle switch, are presented in details. In
general, it is found that the finite correlation time of noise reduces the
fluctuations and enhances the correlation between the fluctuations of the
molecular components.Comment: 10 pages, 4 figure
Risk Aversion Pays in the Class of 2 x 2 Games with No Pure Equilibrium
Simulations indicated that, in the class of 2 x 2 games which only have a mixed equilibrium, payoffs are increased by risk aversion compared to risk neutrality. In this paper I show that the total expected payoff to a player over this class in equilibrium is indeed higher if this player is risk averse than if he is risk neutral provided that all games are played with the same probability. Furthermore, I show that for two subclasses of games more risk aversion is always better, while for a third subclass an intermediate level of risk aversion is preferable.risk aversion; mixed strategy equilibria
Logarithmic and Riesz Equilibrium for Multiple Sources on the Sphere --- the Exceptional Case
We consider the minimal discrete and continuous energy problems on the unit
sphere in the Euclidean space in the presence
of an external field due to finitely many localized charge distributions on
, where the energy arises from the Riesz potential (
is the Euclidean distance) for the critical Riesz parameter if and the logarithmic potential if . Individually, a
localized charge distribution is either a point charge or assumed to be
rotationally symmetric. The extremal measure solving the continuous external
field problem for weak fields is shown to be the uniform measure on the sphere
but restricted to the exterior of spherical caps surrounding the localized
charge distributions. The radii are determined by the relative strengths of the
generating charges. Furthermore, we show that the minimal energy points solving
the related discrete external field problem are confined to this support. For
, we show that for point sources on the sphere, the equilibrium
measure has support in the complement of the union of specified spherical caps
about the sources. Numerical examples are provided to illustrate our results.Comment: 23 pages, 4 figure
License Auctions with Royalty Contracts for (Winners and) Losers
This paper revisits the licensing of a nonâdrastic process innovation by an outside innovator to a Cournot oligopoly. We propose a new mechanism that combines a restrictive license auction with royalty licensing. This mechanism is more profitable than standard license auctions, auctioning royalty contracts, fixedâfee licensing, pure royalty licensing, and two-part tariffs. The key features are that royalty contracts are auctioned and that losers of the auction are granted the option to sign a royalty contract. Remarkably, combining royalties for winners and losers makes the integer constraint concerning the number of licenses irrelevant
Private Matchings and Allocations
We consider a private variant of the classical allocation problem: given k
goods and n agents with individual, private valuation functions over bundles of
goods, how can we partition the goods amongst the agents to maximize social
welfare? An important special case is when each agent desires at most one good,
and specifies her (private) value for each good: in this case, the problem is
exactly the maximum-weight matching problem in a bipartite graph.
Private matching and allocation problems have not been considered in the
differential privacy literature, and for good reason: they are plainly
impossible to solve under differential privacy. Informally, the allocation must
match agents to their preferred goods in order to maximize social welfare, but
this preference is exactly what agents wish to hide. Therefore, we consider the
problem under the relaxed constraint of joint differential privacy: for any
agent i, no coalition of agents excluding i should be able to learn about the
valuation function of agent i. In this setting, the full allocation is no
longer published---instead, each agent is told what good to get. We first show
that with a small number of identical copies of each good, it is possible to
efficiently and accurately solve the maximum weight matching problem while
guaranteeing joint differential privacy. We then consider the more general
allocation problem, when bidder valuations satisfy the gross substitutes
condition. Finally, we prove that the allocation problem cannot be solved to
non-trivial accuracy under joint differential privacy without requiring
multiple copies of each type of good.Comment: Journal version published in SIAM Journal on Computation; an extended
abstract appeared in STOC 201
A sharp stability criterion for the Vlasov-Maxwell system
We consider the linear stability problem for a 3D cylindrically symmetric
equilibrium of the relativistic Vlasov-Maxwell system that describes a
collisionless plasma. For an equilibrium whose distribution function decreases
monotonically with the particle energy, we obtained a linear stability
criterion in our previous paper. Here we prove that this criterion is sharp;
that is, there would otherwise be an exponentially growing solution to the
linearized system. Therefore for the class of symmetric Vlasov-Maxwell
equilibria, we establish an energy principle for linear stability. We also
treat the considerably simpler periodic 1.5D case. The new formulation
introduced here is applicable as well to the nonrelativistic case, to other
symmetries, and to general equilibria
Optimal Equilibria of the Best Shot Game
We consider any network environment in which the âbest shot gameâ is played. This is the case where the possible actions are only two for every node (0 and 1), and the best response for a node is 1 if and only if all her neighbors play 0. A natural application of the model is one in which the action 1 is the purchase of a good, which is locally a public good, in the sense that it will be available also to neighbors. This game will typically exhibit a great multiplicity of equilibria. Imagine a social planner whose scope is to find an optimal equilibrium, i.e. one in which the number of nodes playing 1 is minimal. To find such an equilibrium is a very hard task for any non-trivial network architecture. We propose an implementable mechanism that, in the limit of infinite time, reaches an optimal equilibrium, even if this equilibrium and even the network structure is unknown to the social planner.Networks, Best Shot Game, Simulated Annealing
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Veto players and equilibrium uniqueness in the Baron-Ferejohn model
In political economy, the seminal contribution of the BaronâFerejohn bargaining model constitutes an important milestone for the study of legislative policy making. In this paper, we analyze a particular equilibrium characteristic of this model, equilibrium uniqueness. The BaronâFerejohn model yields a class of payoff-unique stationary subgame perfect equilibria (SSPE) in which playersâ equilibrium strategies are not uniquely determined. We first provide a formal proof of the multiplicity of equilibrium strategies. This also enables us to establish some important properties of SSPE. We then introduce veto players into the original BaronâFerejohn model. We state the conditions under which the new model has a unique SSPE not only in terms of payoffs but also in terms of playersâ equilibrium strategies
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