Том 8

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Last time moment optimality in uniform 1-bullet silent duel with scaled exponentially-convex accuracy
(2025) Romanuk, Vadym
The uniform 1-bullet silent duel with scaled exponentially-convex accuracy of payoffs is a symmetric matrix game whose optimal value is 0, and each of the duelists has the same optimal behavior, whether it is in pure or mixed strategies. Such duels model two-side competitive interaction, where the purpose is to gain a reward by making the best possible decision through quantized time. It is proved that the last time moment is optimal in the duel with N time moments only when the accuracy factor does not exceed marginal value e−e N−2 / N−1 / N−2 e N−1 −1. If the accuracy factor is dropped below this marginal value, then the last time moment is single optimal. If the accuracy factor is exactly equal to the marginal value, the duelist has two optimal time moments: the penultimate and last one. The conditions of the last time moment optimality can be set to force the duelist to act the latest possible, which is quite useful in some blockchain settings, where participants (e. g., validators or miners) choose when to attempt block proposal or transaction insertion under uncertainty.