Antiduality in exact partition games
This note shows that the egalitarian Dutta and Ray (1989) solution for transferable utility games is self-antidual on the class of exact partition games. By applying a careful antiduality analysis, we derive several new axiomatic characterizations. Moreover, we point out an error in earlier work on antiduality and repair and strengthen several related characterizations on the class of convex games.
This study identifies how country differences on a key cultural dimension—egalitarianism— influence the direction of different types of international investment flows. A society's cultural orientation toward egalitarianism is manifested by intolerance for abuses of market and political power and a desire for protecting the weak and less powerful actors. We show egalitarianism to be based on exogenous factors including social fractionalization, dominant religion circa 1900, and war experience from the 19th century era of state formation. Controlling for a large set of competing explanations, we find a robust influence of egalitarianism distance on cross-national investment flows of bond and equity issuances, syndicated loans, and mergers and acquisitions. An informal cultural institution largely determined a century or more ago, egalitarianism exercises its effect on international investment via an associated set of consistent contemporary policy choices. But even after controlling for these associated policy choices, egalitarianism continues to exercise a direct effect on cross-border investment flows, likely through its direct influence on managers’ daily business conduct.
This paper axiomatically studies the equal split-off set (cf. Branzei et al. (Banach Center Publ 71:39–46, 2006)) as a solution for cooperative games with transferable utility which extends the well-known Dutta and Ray (Econometrica 57:615–635, 1989) solution for convex games. By deriving several characterizations, we explore consistency of the equal split-off set on the domains of exact partition games and arbitrary games.
Drawing on the neo-institutional approach in organizational theory and global strategy, we advance a theory on the impact that differences in cultural egalitarianism have on multinational firms’ decision of where to engage in foreign direct investment (FDI) across the globe. Egalitarianism expresses a society’s cultural orientation with respect to intolerance for abuses of market and political power; it shapes the ways in which firms holding power interact with different stakeholders. After presenting a series of case illustrations, we find a strong negative impact of egalitarianism distance on FDI flows in a broad sample of nations and for different entry modes. Our results are robust to a broad set of competing accounts, including effects from other cultural dimensions, major features of the legal and regulatory regimes, other features of the institutional system, and economic development. These results hold while controlling for origin and host country factors through a fixed-effects specification as well as by using instruments for egalitarianism. We also find that other cultural influences are important as well. Differences in cultural harmony are actually positively associated with increased FDI flows, likely because multinational firms seek countries with lower societal support for entrepreneurship. FDI further tends to flow from high embeddedness to low embeddedness countries, and we link this in part to international regulatory arbitrage on environmental protection regimes.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.