| On the optimal strategy in a random game (2004) | |||||||||||
Abstract | |||||||||||
| Consider a two-person zero-sum game played on a random n by n matrix where the entries are iid normal random variables. Let Z be the number of rows in the support of the optimal strategy for player I given the realization of the matrix. (The optimal strategy is a.s. unique and Z a.s. coincides with the number of columns of the support of the optimal strategy for player II.) Faris an Maier (see the references) make simulations that suggest that as n gets large Z has a distribution close to binomial with parameters n and 1/2 and prove that P(Z=n) < 2-(k-1). In this paper a few more theoretically rigorous steps are taken towards the limiting distribution of Z: It is shown that there exists a | |||||||||||
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