Cooperative games under bubbly uncertainty

Weber, Gerhard Wilhelm
The allocation problem of rewards/costs is a basic question for players, namely, individuals and companies that are planning cooperation under uncertainty. The involvement of uncertainty in cooperative game theory is motivated by the real world in which noise in observation and experimental design, incomplete information and vagueness in preference structures and decision-making play an important role. In this study, a new class of cooperative games, namely, the cooperative bubbly games, where the worth of each coalition is a bubble instead of a real number, is presented. Furthermore, a new solution concept, the bubbly core, is defined. Finally, the properties and the conditions for the non-emptiness of the bubbly core are given. The paper ends with a conclusion and an outlook to related and future studies.


On dominance core and stable sets for cooperative ellipsoidal games
ALPARSLAN GÖK, Sırma Zeynep; Weber, Gerhard Wilhelm (Informa UK Limited, 2013-10-01)
The allocation problem of rewards or costs is a central question for individuals and organizations contemplating cooperation under uncertainty. The involvement of uncertainty in cooperative games is motivated by the real world where noise in observation and experimental design, incomplete information and further vagueness in preference structures and decision-making play an important role. The theory of cooperative ellipsoidal games provides a new game theoretical angle and suitable tools for answering this...
Solving optimal investment problems with structured products under CVaR constraints
Korn, Ralf; Zeytun, Serkan (Informa UK Limited, 2009-01-01)
We consider a simple investment problem where besides stocks and bonds the investor can also include options (or structured products) into the investment portfolio. The aim of the investor is to maximize the expected return under a conditional value-at-risk (CVaR) constraint. Due to possible intermediate payments, we have to deal with a re-investment problem which turns the original one-period problem into a multi-period one. For solving this problem, an iterative scheme based on linear optimization is deve...
Heuristic methods for the capacitated stochastic lot-sizing problem under the static-dynamic uncertainty strategy
Randa, A. Cem; Dogru, Mustafa K.; İyigün, Cem; Ozen, Ulas (Elsevier BV, 2019-09-01)
We consider a lot-sizing problem in a single-item single-stage production system facing non-stationary stochastic demand in a finite planning horizon. Motivated by common practice, the set-up times need to be determined and frozen once and for all at the beginning of the horizon while decisions on the exact lot sizes can be deferred until the setup epochs. This operating scheme is referred to as the static dynamic uncertainty strategy in the literature. It has been shown that a modified base stock policy is...
Optimal lot-sizing/vehicle-dispatching policies under stochastic lead times and stepwise fixed costs
Alp, O; Erkip, NK; Gullu, R (Institute for Operations Research and the Management Sciences (INFORMS), 2003-01-01)
We characterize optimal policies of a dynamic lot-sizing/vehicle-dispatching problem under dynamic deterministic demands and stochastic lead times. An essential feature of the problem is the structure of the ordering cost, where a fixed cost is incurred every time a batch is initiated (or a vehicle is hired) regardless of the portion of the batch (or vehicle) utilized. Moreover, for every unit of demand not satisfied on time, holding and backorder costs are incurred. Under mild assumptions we show that the ...
Incorporating wealth information into a multiple criteria decision making model
Karasakal, Esra (Elsevier BV, 2003-10-01)
We describe how a multiple criteria decision making (MCDM) modelling framework can be extended to account for one of the behavioral ramifications of a decision making activity, namely, the decision maker's (I)M's) perception of his/her current wealth status, referred to as decisional wealth. Within the MCDM framework, decisional wealth reflects the relative achievements of each of the objectives in a given efficient solution. It is our argument that a DM's preferences and the importance of his/her objective...
Citation Formats
O. PALANCI, S. Z. ALPARSLAN GÖK, and G. W. Weber, “Cooperative games under bubbly uncertainty,” MATHEMATICAL METHODS OF OPERATIONS RESEARCH, pp. 129–137, 2014, Accessed: 00, 2020. [Online]. Available: