Games of Prediction of Periodic Sequences
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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In the paper several infinite two-person games are studied, all having the following common structure Player 1 Emitter produces a binary periodic sequence Player 2 Predictor observes some initial segment of this sequence and then tries to predict the next digit. The payoff to Emitter is zero if the prediction is a correct one. The games differ in additional assumptions--those are in particular Predictor required to make his prediction after observing a prescribed number of digits of the sequence Predictor allowed to observe any number of digits but earning a decreasing amount for each correct prediction as the number increases The period of the emitted sequence being chosen by random from some fixed distribution Emitter allowed to choose the period but being paid a decreasing amount for incorrect prediction as the period increases. Combining these assumptions two zero-sum and two nonzero-sum games are obtained. It is shown that all these games possess a solution, some are at least partially solved and their further properties investigated.
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