If player preferences are fully formalizable as payoff functions—as standard expected utility theory demands—then they are already constitutive elements of the game form, not supplements to it.

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Expected utility theory(as used in decision theory and economics): A theory that says when people make decisions under uncertainty, they should choose the option that gives them the highest average (expected) satisfaction, weighing each possible outcome by how likely it is to happen.
Payoff function(in game theory, representing what players care about): A mathematical formula that assigns a score or reward to each possible outcome, showing how much a player values different results.
Supplements(describing what preferences would be if they were NOT part of the game's basic structure): Additional things added on top of something that aren't essential to it—extras that enhance but don't define the core.
constitutive(an alternative type of relationship the grounding relation might be): Describes how something is made up of or formed from basic components that define its essential nature.

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