I mean it’s not plain CDT, it’s variant of CDT with ratification? I’m not sure how it should work, it’s weird. You are like, searching over belief states that will lead to desirable conclusion?
E.g. your skillful opponent already made the move, but it’s unknown to you, and there are 4 buttons: Rock, Paper, Scissors, Random_Choice.
It’s obvious that at least one of Rock, Paper, Scissors has more CDT expected utility than Random_Choice, given that the opponent’s move is already fixed and you have to have some belief about its actual state, and no matter how small the difference in your belief in its state, it breaks the tie.
I mean it’s not plain CDT, it’s variant of CDT with ratification?
Ratification just means a solution to a decision theory problem. A problem that is ratifiable is a problem that has a stable solution. Scroll up and he discussing ratification as a concept more.
Joyce is not talking about some other form of CDT.
It’s obvious that at least one of Rock, Paper, Scissors has more CDT expected utility than Random_Choice
That is the case if and only if you believe one option is more likely to have been played then the others. If you think there is a 70% chance your opponent played scissors, then in that situation you should always play rock. In that situation, playing rock is ratifiably the best choice.
In the case where you are playing another rational agent in a normal-form game, the only ratifiable solution is for both players to have equal chances of playing rock paper or scissors, i.e. they adopt a mixed strategy.
If you think there is a 70% chance your opponent played scissors, then in that situation you should always play rock.
Any, however small divergence from equal credences on your opponent’s fixed move, leads you to playing the counter, instead of pressing random move button.
But good opponents are making moves that are in fact dependent on your move, and as you drop that EDT style update, where after making move your estimate of opponents move would change to the counter to yours, and utility along it, you get screwed.
CDT thinks it’s very small positive utility, but EDT correctly thinks it’s large negative utility.
Any, however small divergence from equal credences on your opponents fixed move, leads you to playing the counter
Not however small, it depends on the payouts as to the mixed strategy you should adopt, just like what any game theorist would say. It you have a greater than not odds, yes you should play the move that you expect to win. If there is a dominant pure strategy, CDT recommends that.
But good opponents are making moves that are in fact depended on your move,
If your opponent is also a rational agent, the only stable solution is for both players to randomly select rock-paper-scissors with equal frequency.
But good opponents are making moves that are in fact depended on your move
They are making moves dependent on what they expect you to do. Unless they are time travelers. You know they make moves depending on what you do, and they know you know that and so on. If it is a normal-form game, that means that any solution other than randomly picking is not a stable solution. Your only stable solution is to pick randomly.
If you see patterns in their behavior, you can predict them, and they would be foolish to play with you, unless by pressing random_choice. If they see patterns in your behavior they can predict you, and you would be foolish to play with them, unless by pressing random_choice.
If you use CDT, and press random_choice against imperfect agent, you leave money on the table, according to CDT.
Rational agents is a required assumption for any decision theory.
If you see patterns in their behavior, you can predict them, and they would be foolish to play with you, unless by pressing random_choice
If you are a rational agent and your opponent is not, it is possoble for a stable solution where you win more often than not. The only way to get you to pick something that would have you losing more often than not (w/o playing with payoffs) is if your expectations about the outcomes are wrong. The agent with wrong predictions losing to the one with better predictions is unremarkable.
Rational agents is a required assumption for any decision theory
No? CDT definition makes no references to agents, nor rational agents. It sees the world, and itself, and makes no distinction of dumb matter and agents.
No? CDT definition makes no references to agents, nor rational agents. It sees the world, and itself, and makes no distinction of dumb matter and agents.
What do you think decision theories are? The entire point of a decision theory is to describe what decisions rational agents aught to make. If there is no agent to make a decision, there is no decision theory. You can see page 5 of the book i previously linked for a decent definition of decision theory. Or the section on decision theory beginning on page 351.
I mean it’s not plain CDT, it’s variant of CDT with ratification? I’m not sure how it should work, it’s weird. You are like, searching over belief states that will lead to desirable conclusion?
E.g. your skillful opponent already made the move, but it’s unknown to you, and there are 4 buttons: Rock, Paper, Scissors, Random_Choice.
It’s obvious that at least one of Rock, Paper, Scissors has more CDT expected utility than Random_Choice, given that the opponent’s move is already fixed and you have to have some belief about its actual state, and no matter how small the difference in your belief in its state, it breaks the tie.
Ratification just means a solution to a decision theory problem. A problem that is ratifiable is a problem that has a stable solution. Scroll up and he discussing ratification as a concept more.
Joyce is not talking about some other form of CDT.
That is the case if and only if you believe one option is more likely to have been played then the others. If you think there is a 70% chance your opponent played scissors, then in that situation you should always play rock. In that situation, playing rock is ratifiably the best choice.
In the case where you are playing another rational agent in a normal-form game, the only ratifiable solution is for both players to have equal chances of playing rock paper or scissors, i.e. they adopt a mixed strategy.
Any, however small divergence from equal credences on your opponent’s fixed move, leads you to playing the counter, instead of pressing random move button.
But good opponents are making moves that are in fact dependent on your move, and as you drop that EDT style update, where after making move your estimate of opponents move would change to the counter to yours, and utility along it, you get screwed.
CDT thinks it’s very small positive utility, but EDT correctly thinks it’s large negative utility.
Not however small, it depends on the payouts as to the mixed strategy you should adopt, just like what any game theorist would say. It you have a greater than not odds, yes you should play the move that you expect to win. If there is a dominant pure strategy, CDT recommends that.
If your opponent is also a rational agent, the only stable solution is for both players to randomly select rock-paper-scissors with equal frequency.
They are making moves dependent on what they expect you to do. Unless they are time travelers. You know they make moves depending on what you do, and they know you know that and so on. If it is a normal-form game, that means that any solution other than randomly picking is not a stable solution. Your only stable solution is to pick randomly.
I mean, where do you see perfect agents?
If you see patterns in their behavior, you can predict them, and they would be foolish to play with you, unless by pressing random_choice. If they see patterns in your behavior they can predict you, and you would be foolish to play with them, unless by pressing random_choice.
If you use CDT, and press random_choice against imperfect agent, you leave money on the table, according to CDT.
Rational agents is a required assumption for any decision theory.
If you are a rational agent and your opponent is not, it is possoble for a stable solution where you win more often than not. The only way to get you to pick something that would have you losing more often than not (w/o playing with payoffs) is if your expectations about the outcomes are wrong. The agent with wrong predictions losing to the one with better predictions is unremarkable.
No? CDT definition makes no references to agents, nor rational agents. It sees the world, and itself, and makes no distinction of dumb matter and agents.
What do you think decision theories are? The entire point of a decision theory is to describe what decisions rational agents aught to make. If there is no agent to make a decision, there is no decision theory. You can see page 5 of the book i previously linked for a decent definition of decision theory. Or the section on decision theory beginning on page 351.