Algorithm for constructing a locally optimal strategy for the first player in a linear game problem with forbidden situations

A linear game problem for two players is considered. The two players alternately choose their strategies from the corresponding sets. First, the first player chooses their strategy, then, knowing the first player’s strategy, the second player chooses their strategy. The strategy sets of the second player depend on the strategy of the first player. The first player is forbidden from selecting a strategy that results in the strategy sets of the second player being empty. The objective of the first player is to maximize a convex and piecewise-linear function (the minimum function over the second player’s strategy). The objective of the second player is to minimize a linear function. An algorithm is proposed that allows for constructing a locallyoptimal strategy for the first player. An example is provided to illustrate how the algorithm works.

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