Long-term implementation of the cooperative solution in a multistage multicriteria game
In order to find an optimal and time consistent cooperative path in multicriteria multistage game the minimal sum of relative deviations rule is introduced. Using this rule one can construct a vector-valued characteristic function that is weakly superadditive. The sustainability of the cooperative agreement is ensured by using an imputation distribution procedure (IDP) based approach. We formulate the conditions an IDP should satisfy to guarantee that the core is strongly time consistent (STC). Namely, if the imputation distribution procedure for the Shapley value satisfies the efficiency condition, the strict balance condition and the strong irrational-behavior-proof condition, given that the Shapley value belongs to the core of each subgame along the cooperative path, it can be used as a “supporting imputation” which guarantees that the whole core is STC. We discuss three payment schedules and check whether they can be used as supporting imputation distribution procedures for the considered multicriteria game.
We use the payment schedule based approach to ensure stable cooperation in multistage games with vector payoffs.
Transport industry in economy had been studied for many years, however, only recently researchers have begun to widely apply concepts of cooperative game theory to optimize costs and profits which are incurred in hauling. Today a wide range of cost/profit allocation methods have become a trend in transport segment, particularly in logistics operations. The most of these methods based on cooperative game theory consider the effect of collaboration (cooperation) which means the integration of companies as a key way to share transportation costs or profits. This study aims to contribute to this area of research by exploring different allocation methods such as the Shapley value, the nucleolus and some other excess based solution concepts of transferable utility game (TU game). In this work we overview existing studies on the subject and consider methodology of cooperative game theory. Further, we calculate numerical example of three shipping companies based on real data. In order to compare profit sharing results we compute the set of allocations and examine the constructive and blocking power of coalitions. The importance and originality of the work are that it explores the new field of application of game theory in logistics which can provide additional insights in this research area
Influence of the assumption about the existence of quantitative coefficients of criteria importance, consistent with the criteria importance order (according to the definitions in the criteria importance theory), on the preference relation, generated by this information, is investigated.
In authors' previous paper published in 2011 in «Control Sciences» journal one example of a bi-criterion decision analysis problem demonstrating that the use of Analytic Hierarchy Process (AHP) may lead to a clearly erroneous result is given. However, the author of another paper published in 2012 in the same journal suggested that he found an error in our use of AHP and, consequently, our criticism of AHP is unsubstantiated. In this new paper the authors show that there was no mistake in the use of AHP in their original counter-example, and provide two further counter-examples that support their original conclusion.
Measuring indirect importance of various attributes is a very common task in marketing analysis for which researchers use correlation and regression techniques. We have listed and illustrated some common problems with widely used latent importance measures. A more theoretically sound approach – the Shapley Value decomposition – was applied to a rich data set of US internet stores. The use of store-level data instead of respondent-level data allowed us to reveal the factors, which are powerful in explaining, why some stores have higher rates of willingness to make repeat purchases than the others. By confronting the indirect importance and performance measures for three different internet stores, we have revealed strengths, weaknesses, attributes that the company should bring customers’ attention to and attributes improvement of which is not of a high priority.
This paper is devoted to modern approaches to the estimation of external conflict in the theory of evidence based on axioms. The conflict measure is defined on the set of beliefs obtained from several sources of information. It is shown that the conflict measure should be a monotone set function with respect to sets of beliefs. Some robust procedures for evaluation of conflict measure that are stable to small changes in evidences are introduced and discussed. The analysis of conflict among forecasts about the value of shares of Russian companies of investment banks is presented. In this analysis the conflict measure estimates inconsistency of recommendations of investment banks, while the Shapley values of this measure on the set of evidences characterize the contribution of each investment bank to the overall conflict. The relationship between conflict and precision of forecasts is also investigated.