Estévez-Fernández, A. (2006) "Cooperative Behavior, Competition and Operations Research", PhD thesis, Tilburg University, The Netherlands.
(Abstract) (CentER Ph.D. Thesis Series)

1. 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.

   
   

2. 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.

   
   

3. 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.

   
   

4. 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.

   
   

5. 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.

   
   

6. 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.

   
   

7. 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.

   
   

8. 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.

   
   

9. 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.

   
   

Estévez-Fernández, A. (2009) "A game theoretical approach to sharing penalties and rewards in projects", TI 2009-090/1.
(Abstract)

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)

"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".