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The main objects here are games in which players mainly compete but nonetheless collaborate on some subsidiary activities. Play assumes a two-stage nature in that first-stage moves presume coordination of some subsequent tasks. Specifically, we consider instances where second-stage coordination amounts to partial cost sharing, anticipated and sustained as a core solution. Examples include regional Cournot oligopolies with joint transportation. We define and characterize equilibria, and inquire about their existence. [Copyright &y& Elsevier]