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| JORSJ Vol.54-1 Abstract and Keywords |
1. Pairwise Stability in
a Two-Sided Matching Market with Indivisible Goods
and Money
Yasir Ali and Rashid Farooq (National Univ. of Sciences
and Technology, Pakistan)
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- Abstract
- We consider a two-sided matching
market in which the traders are partitioned into
two sets; the set of sellers and the set of buyers.
Each seller owns at most one indivisible good and
each buyer owns a certain amount of money. Money
is assumed to be an integer variable. Each trader
can trade with at most one trader of the opposite
side. The marriage model of Gale and Shapley is
a special case of our model. We give a constructive
proof to show the existence of a pairwise stable
outcome.
- Keywords
- Game theory, stable matching, marriage
model, indivisible goods
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2. Solution of Nonsmooth
Generalized Complementarity Problems
Mohamed Aly Tawhid (Thompson Rivers University Canada) |
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- Abstract
- We consider an unconstrained minimization
reformulation of the generalized complementarity
problem GCP$(f,g)$ when the underlying functions
$f$ and $g$ are $H$-differentiable. We describe
$H$-differentials of some GCP functions based on
the min function and the penalized Fischer-Burmeister
function, and their merit functions. Under appropriate
semimonotone (${\bf E_0}$), strictly semimonotone
(${\bf E}$) regularity-conditions on the $H$-differentials
of $f$ and $g$, we show that a local/global minimum
of a merit function (or a `stationary point' of
a merit function) is coincident with the solution
of the given generalized complementarity problem.
When specialized GCP$(f,g)$ to the nonlinear complementarity
problems, our results not only give new results
but also extend/unify various similar results proved
for $C^1$, semismooth, and locally Lipschitzian.
- Keywords
- Optimization, generalized complementarity
problem, merit function, regularity conditions,
locally Lipschitzian, semismooth-functions, $H$-differentiability
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3. An Inspection Game with Smuggler's
Decision on the Amount of Contraband
Ryusuke Hohzaki (National Defense Academy) |
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- Abstract
- This paper deals with an inspection
game of Customs and a smuggler. Customs has two
options: patrol or no-patrol. The smuggler makes
a decision on the amount of contraband to smuggle.
In a given period of days, Customs has a limited
number of opportunities to patrol while the smuggler
can ship any amount of contraband as long as he
has not exhausted this supply. When both players
take action, there are some possibilities that Customs
captures the smuggler and there are also possibilities
that the smuggler is successful. If the smuggler
is captured or there remains no day for playing
the game, the game ends. In this paper, we formulate
the problem as a multi-stage two-person zero-sum
stochastic game, derive a closed form of equilibrium
in a specific case and investigate the properties
of the optimal strategies for the players. Nearly
all past research has studied the smuggler's strategy
with the two choices of smuggling or no-smuggling.
This paper focuses on the smuggler's decision as
to the amount of contraband.
- Keywords
- Game theory, inspection game, multi-stage
stochastic game, two-person zero-sum
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4.
Asymptotic Behavior for MArP/PH/2 Queue with Join
the Shortest Queue Discipline
Yutaka Sakuma (Tokyo University of Science)
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- Abstract
- This paper considers a parallel queueing
model with two servers, where arriving customers
join the shortest queue. In \cite{SMZ 2006}, we
studied a similar queueing model, and obtained the
tail decay rate of the stationary distribution by
using the matrix analytic approach. The main objectives
of this paper are to extend the result in \cite{SMZ
2006} to a more general model, and to clarify difficulty
when we apply similar techniques as in \cite{SMZ
2006}. In this paper, we study a MArP/PH/$2$ queue
with join the shortest queue discipline, and show
that the geometric tail asymptotics of the stationary
distribution is obtained under a certain condition
on the service time distribution.
- Keywords
- Queue, Markovian arrival process,
join the shortest queue discipline, phase type distribution,
tail decay rate, quasi-birth-and-death process
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