5,127 research outputs found
On Nash Dynamics of Matching Market Equilibria
In this paper, we study the Nash dynamics of strategic interplays of n buyers
in a matching market setup by a seller, the market maker. Taking the standard
market equilibrium approach, upon receiving submitted bid vectors from the
buyers, the market maker will decide on a price vector to clear the market in
such a way that each buyer is allocated an item for which he desires the most
(a.k.a., a market equilibrium solution). While such equilibrium outcomes are
not unique, the market maker chooses one (maxeq) that optimizes its own
objective --- revenue maximization. The buyers in turn change bids to their
best interests in order to obtain higher utilities in the next round's market
equilibrium solution.
This is an (n+1)-person game where buyers place strategic bids to gain the
most from the market maker's equilibrium mechanism. The incentives of buyers in
deciding their bids and the market maker's choice of using the maxeq mechanism
create a wave of Nash dynamics involved in the market. We characterize Nash
equilibria in the dynamics in terms of the relationship between maxeq and mineq
(i.e., minimum revenue equilibrium), and develop convergence results for Nash
dynamics from the maxeq policy to a mineq solution, resulting an outcome
equivalent to the truthful VCG mechanism.
Our results imply revenue equivalence between maxeq and mineq, and address
the question that why short-term revenue maximization is a poor long run
strategy, in a deterministic and dynamic setting
Numerical Study of the Aerodynamics of DLR-F6 Wing-Body in Unbounded Flow Field and in Ground Effect
The main focus of this thesis is on the simulation of flow past a three-dimensional wing-body configuration (DLR-F6) in ground effect; a complex 3D wing-body configuration in ground effect has never been analyzed in the aerodynamics literature to date. For the purpose of validation of the simulation approach, computations are performed for the DLR-F6 wing-body in unbounded flow and are compared with the experimental data. The commercial CFD solver ANSYS FLUENT is employed for computations. Compressible Reynolds-Averaged Navier-Stokes (RANS) equations in conjunction with Spalart-Allmaras (SA) and - Shear Stress Transport (SST) turbulence models are solved. The validated code is employed to calculate the flow field in ground effect; the effects of flight heights above the ground and angle of attack on the aerodynamic properties and flow field are analyzed
On Revenue Maximization with Sharp Multi-Unit Demands
We consider markets consisting of a set of indivisible items, and buyers that
have {\em sharp} multi-unit demand. This means that each buyer wants a
specific number of items; a bundle of size less than has no value,
while a bundle of size greater than is worth no more than the most valued
items (valuations being additive). We consider the objective of setting
prices and allocations in order to maximize the total revenue of the market
maker. The pricing problem with sharp multi-unit demand buyers has a number of
properties that the unit-demand model does not possess, and is an important
question in algorithmic pricing. We consider the problem of computing a revenue
maximizing solution for two solution concepts: competitive equilibrium and
envy-free pricing.
For unrestricted valuations, these problems are NP-complete; we focus on a
realistic special case of "correlated values" where each buyer has a
valuation v_i\qual_j for item , where and \qual_j are positive
quantities associated with buyer and item respectively. We present a
polynomial time algorithm to solve the revenue-maximizing competitive
equilibrium problem. For envy-free pricing, if the demand of each buyer is
bounded by a constant, a revenue maximizing solution can be found efficiently;
the general demand case is shown to be NP-hard.Comment: page2
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