Abstrakt: |
There are nindependent Bernoulli random variables with parameters pithat are observed sequentially. We consider the following sequential two-person zero-sum game. Two players, A and B, act in turns starting with player A. The game has nstages, at stage k, if Ik=1, then the player having the turn can choose either to keep the turn or to pass it to the other player. If the Ik=0, then the player with the turn is forced to keep it. The aim of the game is not to have the turn after the last stage: that is, the player having the turn at stage nwins if In=1and, otherwise, he loses. We determine the optimal strategy for the player whose turn it is and establish the necessary and sufficient condition for player A to have a greater probability of winning than player B. We find that, in the case of nBernoulli random variables with parameters 1 / n, the probability of player A winning is decreasing with ntoward its limit 12-12e2=0.4323323…. We also study the game when the parameters are the results of uniform random variables, U[0,1]. |