An extension of a class of cost sharing methods to the solutions of the class of two-person cooperative games
Two-person games and cost/surplus sharing problems are worth for studying because they are the base for their extending to the classes of such problems with variable population with the help of very powerful consistency properties. In the paper a family of cost-sharing methods for cost sharing problems with two agents is extended to a class of solutions for two-person cooperative games that are larger than both cost-sharing and surplus-sharing problems, since cooperative games have no restrictions on positivity of costs and surpluses. The tool of the extension is a new invariance axiom - self covariance - that can be applied both to cost-sharing methods and to cooperative game solutions. In particular, this axiom replaces the Lower composition axiom which is not applicable to methods for profit sharing problems.
Importance The paper is devoted to analysis of the effectiveness of economic integration of firms. By efficiency I mean the standard requirements for profitability of integration (non-decreasing of total profit) in microeconomics, theory of the firm and the theory of industrial organization, or non-negativity of synergy in the theory of corporate finance and business valuation theory.
Objectives The purpose of the article is to derive the fair value of companies within the economic integration. Its definition is necessary to take into account the effect of external interaction in the competitive environment on the value of the business, to determine the volume of shares exchanged in the merger, the synergy share to pay to the acquired company in the purchase price, for deciding about splitting the business.
Methods Each company aims to increase its own value, which indicates the conflicted nature of the interaction between agents. Thus, this paper proposes the use of tools of the cooperative game theory to determine the profitability of integration for each of the participating firms, taking into account non-decreasing its share in the fair value of the entire integration.
Results The paper formalizes the notion of profitability of economic integration and the fair value of companies with the tools of cooperative game theory. It proofs the interpretation of solution concept of cooperative game as a method of calculating the fair value of companies with regard to its external cooperative interaction with contractors or the purchase price of acquired companies in M&A deals. The paper provides an example of such an analysis for economic integration in the aviation industry.
Conclusions and Relevance The proposed approach to the analysis of economic integration extends the understanding of its nature, making it possible to estimate the contribution of each individual firm. The article is of practical importance for companies to jointly carry out R&D, supply chains, alliances, holdings, M&A deals or investment and consulting companies serving such transactions.
Interval cooperative games are models of cooperative situation where only bounds for payoffs of coalitions are known with certainty. The extension of solutions of classical cooperative games to interval setting highly depends on their monotonicity properties. However. both the prenucleolus and the tau-value are not aggregate monotonic on the class of convex TU games Hokari (2000, 2001). Therefore, interval analogues of these solutions either should be defined by another manner, or perhaps they exist in some other class of interval games. Both approaches are used in the paper: the prenucleolus of a convex interval game is defined by lexicographical minimization of the lexmin relation on the set of joint excess vectors of lower and upper games. On the other hand, the tau-value is shown to satisfy extendability condition on a subclass of convex games -- on the class of totally positive convex games. The interval prenucleolus is determined , and the proof of non-emptiness of the interval \tau-value on the class of interval totally positive games is given.
Non-transferable utility game of oil market is considered. Special approach for defining solution is used. This approach enables to construct a real time models of conflicting processes. Connection between the solution in the game with moving information horizon and solutions on the truncated time intervals is shown.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.