161,526 research outputs found
Bundling Equilibrium in Combinatorial auctions
This paper analyzes individually-rational ex post equilibrium in the VC
(Vickrey-Clarke) combinatorial auctions. If is a family of bundles of
goods, the organizer may restrict the participants by requiring them to submit
their bids only for bundles in . The -VC combinatorial auctions
(multi-good auctions) obtained in this way are known to be
individually-rational truth-telling mechanisms. In contrast, this paper deals
with non-restricted VC auctions, in which the buyers restrict themselves to
bids on bundles in , because it is rational for them to do so. That is,
it may be that when the buyers report their valuation of the bundles in
, they are in an equilibrium. We fully characterize those that
induce individually rational equilibrium in every VC auction, and we refer to
the associated equilibrium as a bundling equilibrium. The number of bundles in
represents the communication complexity of the equilibrium. A special
case of bundling equilibrium is partition-based equilibrium, in which
is a field, that is, it is generated by a partition. We analyze the tradeoff
between communication complexity and economic efficiency of bundling
equilibrium, focusing in particular on partition-based equilibrium
A Note on the Dynamics of Incentive Contracts
Laffont and Tirole [3] show that when the uncertainty about the agent's ability is small, the equilibrium must involve a large amount of pooling, but it is not necessary to be a partition equilibrium. They construct a nonpartition continuation equilibrium for a given first-period menu of contracts and conjecture that this continuation equilibrium need not be suboptimal for the whole game under small uncertainty. We show that, irrespective of the amount of uncertainty, this nonpartition continuation equilibrium generates a smaller payoff for the principal than a different menu of contracts with a partition continuation equilibrium. In this sense, Laffont and Tirole's menu of contracts, giving rise to a nonpartition continuation equilibrium, is not optimal. An intuition behind this result is provided that may shed some light on the problem of dynamic contracting without commitment.Incentive Contracts; Dynamic Contracting; Commitment; Partition Equilibrium; Ratchet Effect; Bunching
Implementation of the Recursive Core for Partition Function Form Games
In partition function form games, the recursive core (r-core) is implemented by a modified version of Perry and Reny’s (1994) non-cooperative game. Specifically, every stationary subgame perfect Nash equilibrium (SSPNE) outcome is an r-core outcome. With the additional assumption of total r-balancedness, every r-core outcome is an SSPNE outcome.REcursive Core, Nash Equilibrium, Partition Function Form Games
Thermodynamic Analysis of Interacting Nucleic Acid Strands
Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality
Deuterated hydrogen chemistry: Partition functions, Equilibrium constants and Transition intensities for the H3+ system
H3+ and the deuterated isotopomers are thought to play an important role in
interstellar chemistry. The partition functions of H3+, D2H+ and D3+ are
calculated to a temperature of 800 K by explicitly summing the ab initio
determined rotation-vibration energy levels of the respective species. These
partition functions are used to calculate the equilibrium constants for nine
important reactions in the interstellar medium involving H3+ and its deuterated
isotopomers. These equilibrium constants are compared to previously determined
experimental and theoretical values. The Einstein A coefficients for the
strongest dipole transitions are also calculated
Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions
Following up on recent work in the context of ordinary fluids, we study the
equilibrium partition function of a 3+1 dimensional superfluid on an arbitrary
stationary background spacetime, and with arbitrary stationary background gauge
fields, in the long wavelength expansion. We argue that this partition function
is generated by a 3 dimensional Euclidean effective action for the massless
Goldstone field. We parameterize the general form of this action at first order
in the derivative expansion. We demonstrate that the constitutive relations of
relativistic superfluid hydrodynamics are significantly constrained by the
requirement of consistency with such an effective action. At first order in the
derivative expansion we demonstrate that the resultant constraints on
constitutive relations coincide precisely with the equalities between
hydrodynamical transport coefficients recently derived from the second law of
thermodynamics.Comment: 46 page
Constraints on Fluid Dynamics from Equilibrium Partition Functions
We study the thermal partition function of quantum field theories on
arbitrary stationary background spacetime, and with arbitrary stationary
background gauge fields, in the long wavelength expansion. We demonstrate that
the equations of relativistic hydrodynamics are significantly constrained by
the requirement of consistency with any partition function. In examples at low
orders in the derivative expansion we demonstrate that these constraints
coincide precisely with the equalities between hydrodynamical transport
coefficients that follow from the local form of the second law of
thermodynamics. In particular we recover the results of Son and Surowka on the
chiral magnetic and chiral vorticity flows, starting from a local partition
function that manifestly reproduces the field theory anomaly, without making
any reference to an entropy current. We conjecture that the relations between
transport coefficients that follow from the second law of thermodynamics agree
to all orders in the derivative expansion with the constraints described in
this paper.Comment: Typos corrected, References adde
- …