Abstract
The best guaranteed results in games where "others'" control actions influence not only the utility function but also the admissibility set of each participant are analyzed and compared. The research is conducted without a formal reduction to classical games on direct products of rigid admissibility sets by means of penalized extension of the utility function. By the example of the generalized Cournot duopoly, it is shown that, for a chosen participant, his right to be the first to use common scarce resources might be more important than awareness of previous choices of his competitors. This means the possibility of violating the fundamental inequality of the classical game theory which states that the max-min of the utility function does not exceed its min-max, established for games on direct products of sets of admissible control actions.
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