I think Rym and Luke's point is that the only 100% credible threat is one that leaves no other option. Ripping the steering wheel off leaves no other option. Having your shifter secretly be a joystick that gives you the bare amount of control needed to not die is not 100% credible. If you roll a die or randomly shuffle your cards but still get what you want more often than not, then people will think you're up to something, negating your threat of acting randomly.
If you respond to intentionally signaled threats in a game ever, so threatening you becomes a permanent meta strategy.
By assumption, you're responding only to a person who genuinely follows through with their threats, every time. As such, the "threaten Rym" meta-strategy is only available to that one person, not to everyone.
By never responding to a signaled threat ever, you force your opponent to either harm themselves over time to achieve nothing (maintaining their "reputation") or give up on threatening you.
I could similarly argue that by making my threats and always following through with them, I force you to either harm yourself over time to achieve nothing (maintaining your "reputation") or give up on ignoring my threats.
Among human players in games, I find that all intentional signaling is literally worthless.
Let me bring up a hypothetical scenario:
You, Player 1, play a very long game, which for some reason seems to involve spaceships. You are, and have been, trying to do everything in your power to win the game. The game finally comes to a long-awaited endgame phase. Player 3 initially had the strongest position, but you and Player 2 have ganged up on her and are in the process of shutting her down. However, in the middle of the battle, a freak portal opens up creating a once-in a lifetime opportunity for you and/or Player 2 to backstab one another.
If one of you backstabs the other, the backstabee will be left horribly weakened, with a 5% chance of winning (there's still a chance to get very lucky). Meanwhile, the backstabber will still have a strong position, with a 70% chance to win overall. If you both backstab one another, you'll both be pretty badly hurt, leaving each of you with only a 10% chance of victory. If neither of you backstabs the other, player 3 will be completely eliminated and each of you will be left with a 50% chance.
Of course, at this point, it's obvious that the game is a Prisoner's Dilemma, but since both of you are oh so very rational, you know that for each of you defecting is quite clearly the only rational option, as it's a dominant strategy. If your opponent cooperates you're better off defecting, and if your opponent defects you're still better off defecting. Ideally, you would both be able to come to an agreement where you cooperate, but because you're so "rational" you are simply incapable of anything but cheap talk, and you and your opponent will simply ignore everything you say to one another. What a pity.
Also, you've both noticed that your motherships are very close together. Each mothership has the capacity to self-destruct, which instantly loses you the game. However, since they're so close together, if one of your motherships explodes then your the mothership of your so-called "ally" would explode as well, causing both of you to lose the game. Since you're both so "rational" you both spend a lot of time telling each other about how you're really going to do it, but of course you both know that these are quite trivially incredible threats. There simply is not any in-game mechanism by which you can credibly demonstrate that your mothership will automatically destruct in response to the opponent's attack.
The end result is, of course, inevitable, each of you backstabs the other. Unsurprisingly, the 10% chance doesn't play out for either of you, and Player 3 wins soundly, amused by her good fortune. After the end of the game, you find yourself thinking "If only both our threats had been credible. Hell, if we were both irrational and simply believed each other's threats, we each would have had a 50/50 shot of victory. Or maybe if we had some way of precommiting (e.g. I precommit to cooperate if and only if you make the same precommitment). Ah well, it was just bad luck. It couldn't be helped, the freak meteor shower is to blame. "
So, if Player 1 and Player 2 were supposedly "playing to win", why did they lose? Why did player 3 win? For example, if each of them was the kind of player that did always follow through with their threats, they would both be better off, even though they were threatening one another. This goes directly counter to Rym's hypothetical idea that such scenarios with threats necessarily result in mutual harm.
Similarly, while I agree with the notion that threats should be avoided and/or ignored, what about the opposite of threats---let's call them "promises"? Under the standard game-theoretic reasoning, if you have the capacity to repay someone else for helping you at a very slight cost to yourself, you will never do so. After all, it would simply be "irrational".
You, Player X, play one of your favourite games; in this game, a player can help you at a slight cost to themselves, and immediately afterwards you can repay them at a slight cost to yourself. According to the obvious game-theoretic principle you never repay anyone and, unsurprisingly, you find that almost no one ever helps you. It happens very rarely, typically due to mistakes, or sometimes because you've managed to trick someone.
And yet, if you were the type of person who always repaid people for helping you, and if the other players knew this, you would be strictly better off. After all, the other players would help you in the knowledge that they would be repaid, resulting in both of you being strictly better off (at the detriment of your opponents). In fact, you know several people who do this, but as far as you're concerned those people are simply unfortunate fools who don't know any better.
Of course, it bothers you somewhat that those unfortunate fools tend to win those games more than you do, but you think to yourself "Well, really they're just punishing me for being good at the game. If they were as good as I was they wouldn't do anything silly like helping other people or repaying them for it."
So, if you're taking the former approach rather than the latter, are you really playing optimally? Are you really playing to win every game, when the latter group of people actually win more often than you do?
In your long spaceship story, you already went through the entire thought processes that each player could or should make, even with no communication at all. Depending on the kind of game, I'd attack immediately without warning.
If you want to do some role playing, fun threats and bargaining would fill some time. If there is no in-game mechanic for it, it's just flavor.
Well then we get back to economics because it is a question of, "Does the potential gains from people helping me outweigh the costs of helping them?" and of course "Who do I help?" If you're trying to help the 2nd place player when you're 4th (out of 5) then they might take your help and give you enough to maybe bump you to 3rd. Does that really help in the long run if they get bumped to 1st and no longer feel like helping you because they don't want to lose their seat?
My general point is that, in the majority of games against players who are reasonably good, you gain little to nothing from having the capacity for lying. They will simply recognise your attempts to do so as the background noise that they really are. On the other hand, it can actually be relatively valuable to you if you had the ability to actually and reliably tell the truth.
In the kind of context Rym and Luke propose, in which all players' signals are simply interpreted as cheap talk, a person with a known pathological inability to lie has a strict advantage over a player who does not, except perhaps with regards to deceiving lower-level players or if the game forces them to make specific claims out loud.
Truth telling is a very valuable skill in games that have no mechanism to enforce deals, like Diplomacy. In other game where there is a mechanism or else deals don't matter so much, I don't see its utility. This however, was discussed in an episode of This American Life where the host got tips on playing diplomacy from an actual Ambassador. http://www.thisamericanlife.org/radio-archives/episode/531/got-your-back
In your long spaceship story, you already went through the entire thought processes that each player could or should make, even with no communication at all. Depending on the kind of game, I'd attack immediately without warning.
Of course I went through the thought process, that's the whole point of the story.
My point is that if you and your opponent were both the kinds of players who are willing to follow through with a threat even though it's "incredible", you would both be better off, even though you threatened one another. It's a counter to Rym's argument that being willing to follow through with your threats makes you worse off.
If you are willing to follow up threats and use your power to threaten sparingly, e.g. only in situations like this one, you will be strictly better for it.
My point is that if you and your opponent were both the kinds of players who are willing to follow through with a threat even though it's "incredible", you would both be better off, even though you threatened one another. It's a counter to Rym's argument that being willing to follow through with your threats makes you worse off.
If you and your opponent both throw your steering wheels out you both die.
My point is that if you and your opponent were both the kinds of players who are willing to follow through with a threat even though it's "incredible", you would both be better off, even though you threatened one another. It's a counter to Rym's argument that being willing to follow through with your threats makes you worse off.
If you and your opponent both throw your steering wheels out you both die.
That's a credible threat, not an incredible one. It's also a good reason not to play Chicken in the first place.
In the scenario I posed, each player is individually better off when they are knowably willing to follow through with their threat, and both players are still collectively better off if *both* of them are willing to follow through.
On a different note, in games involving multiple players, or in non-zero-sum games, there can be situations where communication between players is not merely cheap talk and is not at all meaningless. A trivial example is coordination games, but there are also cases in multi-player games where revealing private information can actually be beneficial.
Well then we get back to economics because it is a question of, "Does the potential gains from people helping me outweigh the costs of helping them?"?
By assumption, yes. Otherwise the scenario would be stupid.
However, the point is that despite the fact that you would be better off if they helped you and you helped them back, it's "irrational" to help them back once they have already helped you.
I saw 30 new posts, went crosseyed, and said "maybe I'll come back to this in a future day when I really want to dissect a convo on game mechanisms." Perhaps I will just cross that off my list now.
Anyway, here's the general point I wanted to make, in simpler terms.
Let's assume that you, as a person, have the capability to have this property, and have other people be able to recognize that fact: A: I always follow up on the threats I make, even if it would hurt me to do so.
Now, Rym's response to this point is an important one, and it's one that I completely agree with. He says that you ought to have property B: B: I ignore all threats made by my opponents, even if they are a person with property A.
Indeed, Rym's argument that B counters A is correct. A type-A person playing against a type-B person knows that making the threat is only going to result in both players getting hurt. That being said, this point doesn't mean that the type A player always loses. It just means that the type-A person won't threaten you in the first place, and hence will be in the same situation as people whose "threats" are actually just meaningless noise.
However, if you look closely at the situation, there's something interesting here. If someone really, genuinely is a type-A person, then their threats are actually always credible. Yet, despite that fact, the correct response is still to ignore them. Consequently, this must mean that being a type-B person actually wins out over credible threats.
Of course, it depends on exactly what is meant by the term "credible threat". If player 1 can precommit to a move that will be helpful to player 1 regardless of what player player 2 does, that move isn't a "threat" in the first place; player 1 would've done it even without the commitment device. However, if the credible threat is a move that automatically hurts both player 1 and player 2 if player 2 doesn't give in (e.g. I've wired this bomb to automatically self-destruct and kill us both if you don't do what I'm telling you to do), then if player 2 is a type-B person, player 1 isn't going to make that threat in the first place.
As such, as far as the practical, "how to win every game" part of this discussion is concerned, my suggestion is this: Always ignore all threats made against you, even credible ones, and make sure that everyone knows that this is how you play.
Now, as I've brought up above, there is also an interesting area of discussion here as concerns "promises", which are in some sense the opposite of "threats". Obviously you shouldn't ignore people when they make credible promises, but what if you can be the type of person who will always follow through with a promise, even when a game theorist would claim that your promise is incredible?
As such, as far as the practical, "how to win every game" part of this discussion is concerned, my suggestion is this: Always ignore all threats made against you, even credible ones, and make sure that everyone knows that this is how you play.
As usual I go back to the idea that the credible threat is a commitment to either winning or dying (or coming in first, or taking everyone with you on the way to last). If your opponent metaphorically throws out their steering wheel, and in game terms would force a draw if you don't back down, how do you just 'ignore' that?
You crash into them, and you both die. If you're willing to do that, your opponent would be crazy to throw their steering wheel out against you, would they not?
Also, if the result of you both "crashing" is a draw, that's not equivalent to the game of Chicken. The consequences of crashing have to be disastrous.
Comments
You, Player 1, play a very long game, which for some reason seems to involve spaceships. You are, and have been, trying to do everything in your power to win the game. The game finally comes to a long-awaited endgame phase. Player 3 initially had the strongest position, but you and Player 2 have ganged up on her and are in the process of shutting her down. However, in the middle of the battle, a freak portal opens up creating a once-in a lifetime opportunity for you and/or Player 2 to backstab one another.
If one of you backstabs the other, the backstabee will be left horribly weakened, with a 5% chance of winning (there's still a chance to get very lucky). Meanwhile, the backstabber will still have a strong position, with a 70% chance to win overall.
If you both backstab one another, you'll both be pretty badly hurt, leaving each of you with only a 10% chance of victory.
If neither of you backstabs the other, player 3 will be completely eliminated and each of you will be left with a 50% chance.
Of course, at this point, it's obvious that the game is a Prisoner's Dilemma, but since both of you are oh so very rational, you know that for each of you defecting is quite clearly the only rational option, as it's a dominant strategy. If your opponent cooperates you're better off defecting, and if your opponent defects you're still better off defecting. Ideally, you would both be able to come to an agreement where you cooperate, but because you're so "rational" you are simply incapable of anything but cheap talk, and you and your opponent will simply ignore everything you say to one another. What a pity.
Also, you've both noticed that your motherships are very close together. Each mothership has the capacity to self-destruct, which instantly loses you the game. However, since they're so close together, if one of your motherships explodes then your the mothership of your so-called "ally" would explode as well, causing both of you to lose the game. Since you're both so "rational" you both spend a lot of time telling each other about how you're really going to do it, but of course you both know that these are quite trivially incredible threats. There simply is not any in-game mechanism by which you can credibly demonstrate that your mothership will automatically destruct in response to the opponent's attack.
The end result is, of course, inevitable, each of you backstabs the other. Unsurprisingly, the 10% chance doesn't play out for either of you, and Player 3 wins soundly, amused by her good fortune. After the end of the game, you find yourself thinking
"If only both our threats had been credible. Hell, if we were both irrational and simply believed each other's threats, we each would have had a 50/50 shot of victory. Or maybe if we had some way of precommiting (e.g. I precommit to cooperate if and only if you make the same precommitment).
Ah well, it was just bad luck. It couldn't be helped, the freak meteor shower is to blame.
"
So, if Player 1 and Player 2 were supposedly "playing to win", why did they lose? Why did player 3 win?
For example, if each of them was the kind of player that did always follow through with their threats, they would both be better off, even though they were threatening one another. This goes directly counter to Rym's hypothetical idea that such scenarios with threats necessarily result in mutual harm.
You, Player X, play one of your favourite games; in this game, a player can help you at a slight cost to themselves, and immediately afterwards you can repay them at a slight cost to yourself. According to the obvious game-theoretic principle you never repay anyone and, unsurprisingly, you find that almost no one ever helps you. It happens very rarely, typically due to mistakes, or sometimes because you've managed to trick someone.
And yet, if you were the type of person who always repaid people for helping you, and if the other players knew this, you would be strictly better off. After all, the other players would help you in the knowledge that they would be repaid, resulting in both of you being strictly better off (at the detriment of your opponents). In fact, you know several people who do this, but as far as you're concerned those people are simply unfortunate fools who don't know any better.
Of course, it bothers you somewhat that those unfortunate fools tend to win those games more than you do, but you think to yourself
"Well, really they're just punishing me for being good at the game. If they were as good as I was they wouldn't do anything silly like helping other people or repaying them for it."
So, if you're taking the former approach rather than the latter, are you really playing optimally? Are you really playing to win every game, when the latter group of people actually win more often than you do?
If you want to do some role playing, fun threats and bargaining would fill some time. If there is no in-game mechanic for it, it's just flavor.
In the kind of context Rym and Luke propose, in which all players' signals are simply interpreted as cheap talk, a person with a known pathological inability to lie has a strict advantage over a player who does not, except perhaps with regards to deceiving lower-level players or if the game forces them to make specific claims out loud.
http://www.thisamericanlife.org/radio-archives/episode/531/got-your-back
Also, the skill of truth-telling is trivially easy to acquire - just don't ever lie.
My point is that if you and your opponent were both the kinds of players who are willing to follow through with a threat even though it's "incredible", you would both be better off, even though you threatened one another. It's a counter to Rym's argument that being willing to follow through with your threats makes you worse off.
If you are willing to follow up threats and use your power to threaten sparingly, e.g. only in situations like this one, you will be strictly better for it. There is an in-game mechanic for following through with a threat; you can self-destruct your mothership.
In the scenario I posed, each player is individually better off when they are knowably willing to follow through with their threat, and both players are still collectively better off if *both* of them are willing to follow through.
However, the point is that despite the fact that you would be better off if they helped you and you helped them back, it's "irrational" to help them back once they have already helped you.
Let's assume that you, as a person, have the capability to have this property, and have other people be able to recognize that fact:
A: I always follow up on the threats I make, even if it would hurt me to do so.
Now, Rym's response to this point is an important one, and it's one that I completely agree with. He says that you ought to have property B:
B: I ignore all threats made by my opponents, even if they are a person with property A.
Indeed, Rym's argument that B counters A is correct. A type-A person playing against a type-B person knows that making the threat is only going to result in both players getting hurt. That being said, this point doesn't mean that the type A player always loses. It just means that the type-A person won't threaten you in the first place, and hence will be in the same situation as people whose "threats" are actually just meaningless noise.
However, if you look closely at the situation, there's something interesting here. If someone really, genuinely is a type-A person, then their threats are actually always credible. Yet, despite that fact, the correct response is still to ignore them. Consequently, this must mean that being a type-B person actually wins out over credible threats.
Of course, it depends on exactly what is meant by the term "credible threat". If player 1 can precommit to a move that will be helpful to player 1 regardless of what player player 2 does, that move isn't a "threat" in the first place; player 1 would've done it even without the commitment device. However, if the credible threat is a move that automatically hurts both player 1 and player 2 if player 2 doesn't give in (e.g. I've wired this bomb to automatically self-destruct and kill us both if you don't do what I'm telling you to do), then if player 2 is a type-B person, player 1 isn't going to make that threat in the first place.
As such, as far as the practical, "how to win every game" part of this discussion is concerned, my suggestion is this:
Always ignore all threats made against you, even credible ones, and make sure that everyone knows that this is how you play.
Now, as I've brought up above, there is also an interesting area of discussion here as concerns "promises", which are in some sense the opposite of "threats". Obviously you shouldn't ignore people when they make credible promises, but what if you can be the type of person who will always follow through with a promise, even when a game theorist would claim that your promise is incredible?
Also, if the result of you both "crashing" is a draw, that's not equivalent to the game of Chicken. The consequences of crashing have to be disastrous.