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A study of a two-move game with perfect information, such as a move and countermove situation between two firms or economies. This leads to the problem of finding a global minimum of a concave function over a convex domain with the distressing possibility of local minima at every extreme point. It is shown, however, that the global minimum can be obtained by solving a linear-programming system, with side conditions that at least one of certain pairs of variables vanish. The latter problem can be shown to be equivalent to solving a linear-programming problem with some integer-valued variables.
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