Models and Methods for Interval-Valued Cooperative Games in by Deng-Feng Li

By Deng-Feng Li

This e-book proposes numerous usual interval-valued resolution techniques of interval-valued cooperative video games with transferable application. It completely investigates those options, thereby constructing the houses, versions, tools, and purposes. the 1st bankruptcy proposes the interval-valued least sq. strategies and quadratic programming types, equipment, and houses. subsequent, the satisfactory-degree-based non-linear programming versions for computing interval-valued cores and corresponding bisection set of rules are defined. eventually, the ebook explores numerous simplification tools of interval-valued ideas: the interval-valued equivalent department and equivalent surplus department values; the interval-valued Shapley, egalitarian Shapley, and discounted Shapley values; the interval-valued team spirit and generalized team spirit values; and the interval-valued Banzhaf worth.

This ebook is designed for people from varied fields and disciplines, resembling selection technology, video game conception, administration technology, operations examine, fuzzy units or fuzzy arithmetic, utilized arithmetic, business engineering, finance, utilized economics, professional procedure, and social financial system in addition to man made intelligence. additionally, it's appropriate for lecturers, postgraduates, and researchers from diversified disciplines: choice research, administration, operations study, fuzzy arithmetic, fuzzy process research, utilized arithmetic, structures engineering, undertaking administration, offer chain administration, commercial engineering, utilized economics, and hydrology and water resources.

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Extra info for Models and Methods for Interval-Valued Cooperative Games in Economic Management

Example text

3. ’s method [19] may obtain negative interval-valued Shapley-like values ∗ À 00 Á of players, which are not rational. 2, ϕ1 υ is not a positive interval even if all coalitions’ values are positive intervals. However, the quadratic programming methods always assures that the interval-valued least square solutions are positive if all coalitions’ values are positive intervals. 4. 2, according to the method proposed by Han et al. [19], the interval lengths of the interval-valued Shapley-like values of players are identical.

40)) can be directly applied to compute the intervalvalued least square solutions of interval-valued cooperative games. ’s method [19] is respectively used to compute the interval-valued Shapley-like value of each player. 2. In the quadratic programming methods, the distance is used to measure the differences between interval-valued payoffs and interval-type values of coalitions. Thus, we can effectively avoid the magnification of uncertainty resulted from the subtraction of intervals. ’s method [19] may not overcome this disadvantage.

Cent Eur J Oper Res. 2011;19:523–32. 22. Alparslan G€ ok SZ, Branzei O, Branzei R, Tijs S. Set-valued solution concepts using intervaltype payoffs for interval games. J Math Econ. 2011;47:621–6. 23. Peleg B, Sudh€ olter P. Introduction to the theory of cooperative games, Series C: game theory, mathematical programming and operations research, vol. 34. 2nd ed. Berlin: Springer; 2007. 24. Branzei R, Dimitrov D, Tijs S. Models in cooperative game theory: crisp, fuzzy, and multichoice games, Lecture notes in economics and mathematical systems, 556.

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