If utility functions can always be affinely transformed to yield strict competition without loss of strategic content, then the claim that 'actual preferences' break strict competitiveness is an artifact of the chosen representation, not a deep feature of the game.
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Players' evaluations of outcomes or processes that go beyond material pay-offs, may relate to the process of play itself, and may contain irreducibly subjective elements
representation(Schopenhauer's Kantian framework; the empirical/phenomenal side of reality)
The world as it appears to a knowing subject; objects as they are given through the subject's cognitive forms
utility function(Used to explain why utilitarians must identify each person separately when utility functions differ across the population)
A function describing the relationship between goods or policies received by an individual and the utility (welfare or satisfaction) that individual derives from them, which may differ across individuals