290,082 research outputs found
Mechanism Design via Optimal Transport
Optimal mechanisms have been provided in quite general multi-item settings [Cai et al. 2012b, as long as each bidder's type distribution is given explicitly by listing every type in the support along with its associated probability. In the implicit setting, e.g. when the bidders have additive valuations with independent and/or continuous values for the items, these results do not apply, and it was recently shown that exact revenue optimization is intractable, even when there is only one bidder [Daskalakis et al. 2013]. Even for item distributions with special structure, optimal mechanisms have been surprisingly rare [Manelli and Vincent 2006] and the problem is challenging even in the two-item case [Hart and Nisan 2012]. In this paper, we provide a framework for designing optimal mechanisms using optimal transport theory and duality theory. We instantiate our framework to obtain conditions under which only pricing the grand bundle is optimal in multi-item settings (complementing the work of [Manelli and Vincent 2006]), as well as to characterize optimal two-item mechanisms. We use our results to derive closed-form descriptions of the optimal mechanism in several two-item settings, exhibiting also a setting where a continuum of lotteries is necessary for revenue optimization but a closed-form representation of the mechanism can still be found efficiently using our framework.Alfred P. Sloan Foundation (Fellowship)Microsoft Research (Faculty Fellowship)National Science Foundation (U.S.) (CAREER Award CCF-0953960)National Science Foundation (U.S.) (Award CCF-1101491)Hertz Foundation (Daniel Stroock Fellowship
Strong Duality for a Multiple-Good Monopolist
We characterize optimal mechanisms for the multiple-good monopoly problem and
provide a framework to find them. We show that a mechanism is optimal if and
only if a measure derived from the buyer's type distribution satisfies
certain stochastic dominance conditions. This measure expresses the marginal
change in the seller's revenue under marginal changes in the rent paid to
subsets of buyer types. As a corollary, we characterize the optimality of
grand-bundling mechanisms, strengthening several results in the literature,
where only sufficient optimality conditions have been derived. As an
application, we show that the optimal mechanism for independent uniform
items each supported on is a grand-bundling mechanism, as long as
is sufficiently large, extending Pavlov's result for items [Pavlov'11]. At
the same time, our characterization also implies that, for all and for all
sufficiently large , the optimal mechanism for independent uniform items
supported on is not a grand bundling mechanism
Energy-scales convergence for optimal and robust quantum transport in photosynthetic complexes
Underlying physical principles for the high efficiency of excitation energy
transfer in light-harvesting complexes are not fully understood. Notably, the
degree of robustness of these systems for transporting energy is not known
considering their realistic interactions with vibrational and radiative
environments within the surrounding solvent and scaffold proteins. In this
work, we employ an efficient technique to estimate energy transfer efficiency
of such complex excitonic systems. We observe that the dynamics of the
Fenna-Matthews-Olson (FMO) complex leads to optimal and robust energy transport
due to a convergence of energy scales among all important internal and external
parameters. In particular, we show that the FMO energy transfer efficiency is
optimum and stable with respect to the relevant parameters of environmental
interactions and Frenkel-exciton Hamiltonian including reorganization energy
, bath frequency cutoff , temperature , bath spatial
correlations, initial excitations, dissipation rate, trapping rate, disorders,
and dipole moments orientations. We identify the ratio of \lambda T/\gamma\*g
as a single key parameter governing quantum transport efficiency, where g is
the average excitonic energy gap.Comment: minor revisions, removing some figures, 19 pages, 19 figure
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