Arantza Estévez-Fernández
Home
Teaching
Research
Co-authors
CV
Phone: +31 20 598 5483
Fax: +31 20 598 6020
E-mail
|
| |
 |
| Research |
|
|
Thesis
Estévez-Fernández, A. (2006) "Cooperative Behavior, Competition and
Operations Research", PhD thesis, Tilburg University, The Netherlands.
(Abstract)
(CentER Ph.D. Thesis Series)
| |
Game theory is the mathematical tool to study cooperation and
competition. Since the beginnings of operations research and game theory
both fields have been closely related. This thesis further investigates
this relationship. Costs or rewards sharing problems arising from
scheduling problems, traveling salesman problems and project management
are investigated within the framework of game theory. Refinements of the
set of optimal solutions of linear programming problems are studied by
making use of the relationship betweenof linear programming problems,
linear complementarity problems, and matrix games. Finally, competitive
environments, i.e. bimatrix games for which some appealing properties of
matrix games are kept, are analyzed. |
|
|
Publications
-
Apt, K., Estévez-Fernández, A. (2009)
"Sequential pivotal mechanisms for public project problems " In:
Algorithmic Game Theory (Eds. Mavronicolas, M. and Papadoupoulou, V.G.), 85-96.
(Abstract)
(
Link)
| |
It is well-known that
for several natural decision problems no budget balanced Groves
mechanisms exist. This has motivated recent research on designing
variants of feasible Groves mechanisms (termed as ‘redistribution of
VCG (Vickrey-Clarke-Groves) payments’) that generate reduced deficit.
With this in mind, we study sequential mechanisms and consider optimal
strategies that could reduce the deficit resulting under the
simultaneous mechanism. We show that such strategies exist for the
sequential pivotal mechanism of the well-known public project problem.
We also exhibit an optimal strategy with the property that a maximal
social welfare is generated when each player follows it. Finally, we
show that these strategies can be achieved by an implementation in
Nash equilibrium. |
|
-
Borm, P., Estévez-Fernández, A., and Fiestras-Janiero, M.G. (2009)
"Competitive environments and protective behaviour"
Games and Economic Behavior 67, 245-252.
(Abstract) (Earlier
CentER DP 2006-43)
| |
The class of two-person competition games is introduced
and analyzed. For any game in this class the set of Nash equilibria is
convex and all Nash equilibria lead to the same payoff vector. Competition
games are compared to other competitive environments such as unilaterally
competitive games and rivalry games. Moreover, protective behaviour within
competitive environments is analyzed. For matrix games it is known that
protective strategies profiles exactly correspond to proper equilibria. It is
shown that this result can be extended to the class of unilaterally
competitive games. |
|
Estévez-Fernández, A., Borm, P., Meertens, M., and Reijnierse,
H. (2009) "On the core of routing games with revenues",
International Journal of Game Theory 38, 291-304.
(Abstract) (Earlier
CentER DP 2006-43)
| |
Traveling salesman problems with revenues form a
generalization of traveling salesman problems. Here, next to travel costs
an explicit revenue is generated by visiting a city. We analyze routing
problems with revenues, where a predetermined route on all cities
determines the tours along subgroups. Corresponding routing games with
revenues are analyzed. It is shown that these games have a nonempty core
and a complete description of the core is provided. |
|
-
Estévez-Fernández, A., Mosquera. M.A.,
Borm, P., and Hamers, H. (2008) "Proportionate flow shop games",
Journal of Scheduling 11, 433-447.
(Abstract) (Earlier
CentER DP 2006-63)
| |
In a proportionate flow shop problem several jobs have
to be processed through a fixed sequence of machines and the processing
time of each job is equal on all machines. By identifying jobs with
agents, whose costs linearly depend on the completion time of their jobs,
and assuming an initial processing order on the jobs, we face two problems:
the first one is how to obtain an optimal order that minimizes the total
processing cost, the second one is how to allocate the cost savings obtained
by ordering the jobs optimally. In this paper we focus on the allocation
problem. PFS games are defined as cooperative games associated to
proportionate flow shop problems. It is seen that PFS games have a nonempty
core. Moreover, it is shown that PFS games are convex if the jobs are
initially ordered in decreasing urgency. For this case an explicit game
independent expression for the Shapley value is provided. |
|
-
Estévez-Fernández, A., Borm, P., Calleja,
P., and Hamers, H. (2008) "Sequencing games with repeated players",
Annals of Operations Research
158, 189-203.
(Abstract) (Earlier
CentER DP 2004-128)
| |
Two classes of one machine sequencing situations are
considered in which each job corresponds to exactly one player but a
player may have more than one job to be processed, so called RP (repeated
player) sequencing situations. In max-RP sequencing situations it is
assumed that each player's cost function is linear with respect to the
maximum completion time of his jobs, whereas in min-RP sequencing situations
the cost functions are linear with respect to the minimum completion times.
For both classes, following explicit procedures to go from the initial
processing order to an optimal order for the coalition of all players, equal
gain splitting rules are defined. It is shown that these rules lead to core
elements of the associated RP sequencing games. Moreover, it is seen that
min-RP sequencing games are convex. |
|
-
Estévez-Fernández, A., Borm, P., and Hamers, H. (2007)
"Project games", International Journal of Game Theory
36, 149-176.
(Abstract) (Earlier
CentER DP 2005-91)
| |
This paper studies situations in which a project
consisting of several activities is not executed as planned. It is
divided into three parts. The first part analyzes the case where the
activities may be delayed; this possibly induces a delay on the project
as a whole with additional costs. Associated delayed project games are
defined and are shown to have a nonempty core. The second part considers
the case where the activities may be expedited; this possibly induces an
expedition of the project as a whole creating profits. Corresponding
expedited project games are introduced and are shown to be convex. The
third and last part studies situations where some activities may be delayed
and some activities may be expedited. Related project games are defined and
shown to have a nonempty core. |
|
-
Calleja, P., Estévez-Fernández, A., Borm, P., and Hamers, H.
(2006) "Job scheduling, cooperation and control", OR Letters
34, 22-28.
(Abstract) (Earlier
CentER DP 2004-65)
| |
This paper studies one machine job scheduling situations
where clients can have more than one job to be processed and where a job
can be of interest for different players. Corresponding cooperative games
are introduced and a result on balancedness is provided. |
|
-
Estévez-Fernández, A., Borm, P., and Hamers, H. (2006)
"On the core of multiple longest traveling salesman games",
European Journal of Operational Research 174, 1816-1827.
(Abstract) (Earlier
CentER DP 2003-127)
| |
In this paper we introduce multiple longest traveling
salesman (MLTS) games. An MLTS game arises from a network in which a
salesman has to visit each node (player) precisely once, except to his
home location, in such an order that maximizes the total reward. First
it is shown that the value of a coalition of an MLTS game is determined
by taking the maximum of suitable combinations of one and two person
coalitions. Secondly it is shown that MLTS games with five or less
players have a nonempty core. However, a six player MLTS game may have
an empty core. For the special instance in which the reward between a
pair of nodes is equal to 0 or 1, we provide relations between the
structure of the core and the underlying network. |
|
-
Estévez-Fernández, A. and Fiestras-Janiero, M.G. (2004)
"On properties of several refinements of optimal solutions in Linear
Programming", Journal of Optimization Theory and Applications
122, 41-62.
(Abstract)
| |
In this paper we investigate the properties of the
optimal solutions we obtain when we translate the concepts of perfect,
proper and weakly proper solutions from the context of Linear
Complementary into the framework of Linear Programming. |
|
|
Research reports
|
Estévez-Fernández, A. (2009)
"A game theoretical approach to sharing penalties and rewards in projects",
TI 2009-090/1.
(Abstract)
| |
This paper analyzes situations in which a
project consisting of several activities is not realized
according to plan. If the project is expedited, a reward arises.
Analogously, a penalty arises if the project is delayed. This paper
considers the case of arbitrary monotonic reward and penalty
functions on the total expedition and delay, respectively. Attention
is focused on how to divide the total reward (penalty) among the
activities: the core of a corresponding cooperative project game
determines a set of stable allocations of the total reward (penalty).
In the definition of project games,surplus (cost) sharing mechanisms
are used to take into account the specific characteristics of the reward
(penalty) function at hand. It turns outs that project games are related
to bankruptcy and taxation games. This relation allows us to establish
the nonemptiness of the core of project games. |
|
Estévez-Fernández, A., Borm, P., Hamers, H., and Voorneveld, M. (2008)
"The museum pass game and its value "revisited"",
CentER DP 2004-07
(new version, pdf, 164 Kb).
(Abstract)
| |
This paper discusses the problem in which a group of service
providers offers a passepartout that allows its owners the use of their
services an unlimited number of times during a fixed period of time. The
problem we address is how to share the total joint revenues of this
passepartout system among the providers. Arguments are provided to model
this problem within the framework of bankruptcy. |
|
|
Working papers
|
"Chinese postman problems and related games"
(with Marloes Gerichhausen and Herbert Hamers).
"On generalizations of the Talmud rule"
(with Peter Borm).
"Generalization of bankruptcy problems".
|
|
|
|