Quote: Or maybe we’re playing a game in which the stag hunt matrix describes some sort of payouts that are not exactly utilities. E.g., we’re in a psychology experiment and the experimenter has shown us a 2x2 table telling us how many dollars we will get in various cases—but maybe I’m a billionaire and literally don’t care whether I get $1 or $10 and figure I might as well try to maximize your payout, or maybe you’re a perfect altruist and (in the absence of any knowledge about our financial situations) you just want to maximize the total take, or maybe I’m actually evil and want you to do as badly as possible.
So, if the other player is “always cooperate” or “always defect” or any other method of determining results that doesn’t correspond to the payouts in the matrix shown to you, then you aren’t playing “prisoner’s dillema” because the utilities to player B are not dependent on what you do. In all these games, you should pick your strategy based on how you expect your counterparty to act, which might or might not include the “in game” incentives as influencers of their behavior.
In static games of complete, perfect information, a normal-form representation of a game is a specification of players’ strategy spaces and payoff functions.
You are playing prisoner’s dilemma when certain payoff inequalities are satisfied in the normal-form representation. That’s it. There is no canonical assumption that players are expected utility maximizers, or expected payoff maximizers.
because the utilities to player B are not dependent on what you do.
Noting that I don’t follow what you mean by this: do you mean to say that player B’s response cannot be a constant function of strategy profiles (ie the response function cannot be constant everywhere)?
Um… 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.
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”
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”
Quote: Or maybe we’re playing a game in which the stag hunt matrix describes some sort of payouts that are not exactly utilities. E.g., we’re in a psychology experiment and the experimenter has shown us a 2x2 table telling us how many dollars we will get in various cases—but maybe I’m a billionaire and literally don’t care whether I get $1 or $10 and figure I might as well try to maximize your payout, or maybe you’re a perfect altruist and (in the absence of any knowledge about our financial situations) you just want to maximize the total take, or maybe I’m actually evil and want you to do as badly as possible.
So, if the other player is “always cooperate” or “always defect” or any other method of determining results that doesn’t correspond to the payouts in the matrix shown to you, then you aren’t playing “prisoner’s dillema” because the utilities to player B are not dependent on what you do. In all these games, you should pick your strategy based on how you expect your counterparty to act, which might or might not include the “in game” incentives as influencers of their behavior.
Here is the definition of a normal-form game:
You are playing prisoner’s dilemma when certain payoff inequalities are satisfied in the normal-form representation. That’s it. There is no canonical assumption that players are expected utility maximizers, or expected payoff maximizers.
Noting that I don’t follow what you mean by this: do you mean to say that player B’s response cannot be a constant function of strategy profiles (ie the response function cannot be constant everywhere)?
Um… 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.
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.