Order dispatching and driver repositioning (also known as fleet management) in the face of spatially and temporally varying supply and demand are central to a ride-sharing platform marketplace. Hand-crafting heuristic solutions that account for the dynamics in these resource allocation problems is difficult, and may be better handled by an end-to-end machine learning method. Previous works have explored machine learning methods to the problem from a high-level perspective, where the learning method is responsible for either repositioning the drivers or dispatching orders, and as a further simplification, the drivers are considered independent agents maximizing their own reward functions. In this paper we present a deep reinforcement learning approach for tackling the full fleet management and dispatching problems. In addition to treating the drivers as individual agents, we consider the problem from a system-centric perspective, where a central fleet management agent is responsible for decisionmaking for all drivers.

We compute the complete RO(G)-graded coefficients of "ordinary" cohomology with coefficients in Z/2 for G = (Z/2) n . IntroductionThe notion of a cohomology theory graded by elements of the real representation ring (RO(G)-graded cohomology) is a key concept of equivariant stable homotopy theory of a finite or compact Lie group G. Like much of stable homotopy theory, perhaps one of the first known example was K-theory. Atiyah and Singer [4] introduced equivariant Ktheory of a compact Lie group G and proved that it is naturally RO(G)graded. In fact, Bott periodicity identifies many of the "dimensions" in RO(G), and relates others to "twistings" (see Karoubi [6] and, for a more recent treatment, Freed, Hopkins and Teleman [8]). Pioneered by Adams and Greenlees [9], the general RO(G)-graded stable homotopy theory theory found firm foundations in the fundamental book of Lewis, May and Steinberger [21].Despite the clear importance of the concept, beyond K-theory, calculations of RO(G)-graded cohomology are few and far in between. Perhaps the most striking case is "ordinary" RO(G)-graded cohomology. Bredon [5] discovered Z-graded G-equivariant cohomology associated with a coefficient system which is "ordinary" in the sense that the cohomology of a point is concentrated in a single dimension. It was later discovered ([20]) that such a theory becomes RO(G)-graded when the coefficient system enjoys the structure of a Mackey functor [7], which means that it allows building in an appropriate concept of transfer. Strikingly, the RO(G)-graded coefficients were not known in any single non-trivial case.Complete calculations of RO(Z/2)-graded coefficients, however, are important in Real-oriented stable homotopy theory, because they exhibit the analogy with the complex-oriented case. Real orientation was, once again, discovered first by Atiyah in the case of K-theory [3], and

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