the definition of the normal form game you cited explicitly says that the payoffs are in the form of cardinal or ordinal utilities. Which is distinct from in-game payouts.
No. In that article, the only spot where ‘utility’ appears is identifying utility with the player’s payoffs/payouts. (EDIT: but perhaps I don’t get what you mean by ‘in-game payouts’?)
that player’s set of payoffs (normally the set of real numbers, where the number represents a cardinal or ordinal utility—often cardinal in the normal-form representation)
To reiterate: I’m not talking about VNM-utility, derived by taking a preference ordering-over-lotteries and back out a coherent utility function. I’m talking about the players having payoff functions which cardinally represent the value of different outcomes. We can call the value-units “squiggles”, or “utilons”, or “payouts”; the OP’s question remains.
Also, too, it sounds like you agree that the strategy your counterparty uses can make a normal form game not count as a “stag hunt” or “prisoner’s dillema” or “dating game”
No. In that article, the only spot where ‘utility’ appears is identifying utility with the player’s payoffs/payouts. (EDIT: but perhaps I don’t get what you mean by ‘in-game payouts’?)
To reiterate: I’m not talking about VNM-utility, derived by taking a preference ordering-over-lotteries and back out a coherent utility function. I’m talking about the players having payoff functions which cardinally represent the value of different outcomes. We can call the value-units “squiggles”, or “utilons”, or “payouts”; the OP’s question remains.
No, I don’t agree with that.