Catan - Use GAME THEORY to counter Extortion!
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- เผยแพร่เมื่อ 19 ก.ย. 2024
- #catan #colonist #catantournament #strategy #gametheory
Let's use GAME THEORY to avoid being extorted during Settler's of Catan!
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I really like the Golden Balls analogy. I had seen that video many times but never considered that the idea changed the game theory equation for the other player.
Right! Before, I had never thought to try to change the payout for the other player! Things I need to continue looking out for!
I'm beyond relieved you mention this.............because I've been saying for a while now that when extortion-heavy strategic players are denied and pushed back upon, they suddenly become disoriented and exposed at best, tilted at worst.
I just can't stress enough how important it is, if you're playing a tournament, to try and research your opponents in advance. For example, Dylighted is a decisively extortion and trade-heavy sort of player who is certainly skilled and knows the game, but is nonetheless a more exposed, inconsistent player when opponents recognize his play style as is easy to identify just by analyzing some of his previous matches...............and counter with "Golden Balls" as you put it and trade embargoes.
The bottom line is: extortion unmistakably has its place in Catan, but so does channeling your inner-trade protectionist and summoning the courage to look your opponent in your eye when one threatens you with an aggressive knight and say, "Try me! A one-in-four chance to pick up that resource is still only a 25% chance!"
Great content as always, thanks sooooooooo much! =)
Zara! I always look forward to your comment :)
Love this take, i agree! I definitely am starting to keep better track of catan players tendancies :)
Nice video! I have a used a related approach to counter extortion that I call an "anti-extortion" agreement. This agreement is designed to penalize the extorter instead of the other players.
Player 1 tries to extort player 2. Players 2-4 make a gentleman's agreement to an anti-extortion agreement. The terms are: "regardless of who player 1 robs, the next player (among players 2-4) who rolls a 7 agrees to rob player 1 and give the robbed resource (via a 2:1 1:1 trade) to the player who player 1 robbed.". Effectively, it becomes like player 1 is robbing himself (in terms of cards lost) and removes his ability to control who is losing a card (the source of his power to extort), because the robbed player gets a card back on the next 7. The person losing a card is randomized by the next 7 dice roll.
I like this agreement because it has a bit of poetic justice -- it is basically doing the same thing the extorter is doing (using threats of future robberies and agreements to trade) to nullify the ability to extort. Plus it feels roughly fair to the other players.
Note that players 3 and 4 are incentivized to make the anti-extortion agreement, because if player 2 agreed to be extorted, players 3 and 4 a have high probability of being robbed and losing a card.
@@moocow6 It's not optimal for player 2. Player 2 should always just agree to be extorted, then lie and not actually trade the promised resource to player 1 unless he otherwise actually wants to do it anyway. This is better for player 2. No player is incentivized to agree to your above proposed deal because the optimal strategy would be to not actually give away the free resource once it came down to that moment. The optimal strategy would be to rob the ideal person to rob and then keep the resource for yourself, thus meaning that optimal players would always do so. In fact, that is always the optimal strategy when stealing: Simply pick the person who is optimal to steal from, block the optimal spot to block for them, then steal from them. Every deal made can always be broken, so it's completely pointless to try to make them.
All of the above, of course, is trying to consider the Nash equilibrium strategy, which is what the video was about (despite failing to actually capture the Nash equilibrium approach and completely overlooking the much better strategy than the one he was employing in the video).
@@Ohrami The problem in practice with your proposed approach of agreeing to be extorted and lying about trading is that it is viewed as scummy and players will punish you by future blocks or trade embargoes, making it really bad in practice. The concept of Nash equilibria or game theoretically optimal is not practical for games like Catan, where computing the optimal play involves computing an exponentially large game tree of all possible dice-roll/turn action sequences(and their associated probabilities) until the game finishes to completion.
This is not close to being tractable for humans or computers, so players are obviously not agents operating according to an optimal strategy. When people make promises of future actions, it is used by other players as a proxy to computing this intractably large game tree, allowing them to more effectively predict/approximate what's going to happen in the future. Psychologically, people don't like lying because it invalidates this prediction process. They are willing to punish liars even if it involves suboptimal play.
As Catan is played in current communities, players get a significant advantage by using extortion and this shouldn't be the case (i.e., if people played optimally, extortion wouldn't be effective). I think my example gives a practical approach to countering it that works in most situations.
@@moocow6 You can very easily determine the Nash equilibrium of these individual scenarios without determining the Nash equilibrium of the entire game. I explained it in another comment, but imagine the Golden Balls game was played as a turn-based game, with Nick revealing he had chosen "Split" to his opponent without his opponent having acted yet. Nothing Nick can do should ever be able to convince his opponent to pick anything but "Steal" if he is playing rationally.
In Catan, supposing you already calculated the optimal block spot, the optimal steal, and what trades are optimal for your opponents to make, and you then pick a suboptimal block spot, steal from a suboptimal opponent, and then propose a trade that is not optimal for your opponent to make, he will always decline regardless of whatever nonsense you or he said previously. Your bargaining power as the extorter comes from the placement of the robber and your steal target. Once this robber has been placed and you have already chosen who to steal from, you have no leverage at all anymore.
I see no reason in particular why human players would tend toward colluding against people who lie any more than colluding against people who extort people. Extortion can be viewed as an aggressive action, and a person lying to trick that person can be viewed as justice. It depends a lot on the group you are playing with, and particularly how much they care about winning or playing optimally. Your assumptions can be applied to literally any action. You could just as easily argue that taking the best spot while going first means the second place player will collude against you all game to try to make sure you don't win. You could argue that you should say nothing because people who speak are targeted much more heavily than those who don't. (This is the case on Colonist more often than not.)
Catan as a whole actually has no Nash equilibrium, as it is not a finite game. Still, determining what is the optimal strategy or Nash equilibrium in many of these individual scenarios is very doable given you make some assumptions, which are already assumptions being made by all players regardless.
@@Ohrami Your argument for being able to compute the Nash equilibrium for an individual turn is hypothetical; it's based on the unrealistic assumption that 1) you're able to compute the optimal spot to rob, optimal trades to make, exact probabilities of each player winning, etc. and 2) the other players are also able to compute this and have the exact same beliefs. This isn't close to being realistic in practice because it involves computing that exponentially large game tree over all possible game outcomes.
A Nash equilibrium strategy isn't even optimal (in terms of maximizing your probability of winning) if your opponents are not following an optimal strategy (which they are not). Since lying is relatively uncommon in most communities, you do actually get useful information from table talk to be able to better model what your opponents strategies are.
When people try to extort in practice, it often works because you have little to no knowledge of how they perceive who is in the lead and how they trade that off with the relative utility and probability of each resource that they could rob from each person. You yourself only have an inexact estimate of the probability of each player winning. The extorter is able to convince you that their decision on who to rob is mostly based on what resources you have.
What a coincidence I just went to a game theory lecture yesterday what a interesting concept I was thinking about possible Catan strategy applications of this theory and then I see your video the next day what a coincidence great work Hakuna Matata catan keep up the contact
If you're taking a class on game theory or are interested in it, try to prove that extortion is generally ineffective in the game of Catan. It's something the video's uploader neglected and his suggestions are misapplying game theory, or at least the concept of Nash equilibrium.
@@Ohrami yes he just talks about the advantages of tracking… Game theory is great for settlement picks; table talk there could be a place for expansion
Thanks Sean! Crazy coincidence!! XD
I am glad you enjoyed the video!
I am impressed there is way the apply a basic prisoner's dilemma to a game of Catan. Good job, thank you for sharing it. This is something I could definitely start applying in my games.
Thanks Andro! I am glad you liked it! Good luck!
Some of the best catan advice I've ever seen
Thank you Jack! so nice!!
Very interesting take on counter extortions principles. Thanks!
Thanks for the nice comment ! :)
This video is incredible
Thank you Ben!!!! Means a lot!
You're best video so far!
Wow! Thank you Franky!!! I'm glad you liked it :)
love your videos. keep it up my guy
Thanks Jiyuan! I'm glad you enjoyed it!!!
what a fantastic video! super interesting and well edited!
the only problem in a practical scenario is having to assume your opponents are rational😹
hahahah! very true! Some times players act very irrational XD
Love this high level analysis
If only I could type this fast online hahah
Thanks braden!!
And no kidding haha! I generally enjoy playing online in Catan Champs league - that way I can voice chat with other players since I am such a slow typer haha
The link is in the description if you want to join!
Great stuff!
Thanks Treeck!
So good gonna apply this to my game
Thanks Dominic!! Good luck! Let me know if you get any interesting results :)
Great video! It makes sense that there is a time and place to push back on extortion-heavy players. Thanks for the well-edited content!
Thanks hubbsy!!
Nick's IQ over 9000
HES THE GOAT!
Just remember to use your Golden Balls!
If youre looking to join a FREE online catan league, check out Catan Champs: bit.ly/catanchampionshipleague
nice explanation and all but not applicable at all in Real Life in a Colonist Game. You will find better spots for Product Placement than here ;)
Agreed! Automatches on colonist can be hard to communicate with other players.
I mainly play in the Catan Championship league, where players play on colonist but also voice chat in discord! Makes these strategies a lot more feasible :D
You are making a mistake with your analysis in the Catan examples. It is always possible to lie in Catan about future promises, and after the player moves the robber in a way that's favorable for you, if trading him a wool isn't the optimal play, you have no incentive to do so from a game theory perspective. This is because, from a game theory perspective, everyone should behave rationally, and perform each individual action in the way that optimizes their own results. There is no way that trading a guy a wool for an ore when you have a settlement in your hand is almost ever the optimal strategy.
Prisoner's dilemma is a game in standard form, where all actions are performed simultaneously. Catan is a game where all actions are performed consecutively, in turn. This is why the analogy is not applicable. A more accurate analogy would be if the Golden Balls was a turn-based game, and Nick was going first. If he had shown that he had chosen "Split" to his opponent, since he went first, absolutely nothing he could ever do should be able to convince his opponent, who goes after him, to pick anything but "Steal". The same applies here in Catan. Your opponent already moved the robber onto a spot that is favorable for you. Absolutely nothing he does should be able to convince you to trade away your precious wool for cheap. He can't backtrack anymore, so his threats hold zero weight and he has no bargaining power. The only way this would work would be if players were allowed to trade while holding the robber and before placing it. If you traded them something that then made it irrational for them to ever steal from you, they wouldn't ever steal from you after that, and extortion would be effective.
The main issue with applying game theory, and specifically Nash equilibrium, to Catan is that Catan is a potentially infinite game, thus meaning it has no Nash equilibrium. Still, in these individual scenarios, you can see the optimal strategy is almost always to lie, thus meaning extortion stops being effective and nobody does it anymore since everyone lies after being extorted.
Finally, let's consider how real humans will play, which is not rationally, especially on Colonist. If you type all of those things in a game of Colonist, the responses will be something like, "who asked 😂" or "this guy's annoying, he talks a lot" followed by being blocked repeatedly for no reason while in last place. I doubt anyone would even be able to fully comprehend or understand what you are saying or even calculate why it's good for them. When playing specifically against random opponents in Colonist, I think these suggestions are completely worthless and your best bet is usually to say nothing for the entire game.
Im gonna explain to you the basic.Catan is way more competitive then you think.There are discords servers with pro Catan players. You don't hear a lot about extorsion with random in ranked cause the skill gap is low and so is the communication skill. Meanwhile we voice chat in the discord server so table talk is really an asset that help you covince people. If someone roll the Robber people always debate where it's going. Catan online with randomn is a totaly different game.
@@maazzzable Pro Catan players? So they make a career off of competing in Catan, and support their livelihoods through winning tournaments or other competitions involving Catan?
Nobody in Catan plays at a pro level. It's not a game that can be played at a pro level. There's no money in it. Regardless, everything I said is true.
@@Ohrami Okay, noone can do Catan as a Job, But the Community is huge enough, that there are at least small prizes for the winners in the Range of 20-200$. And it is quite competitive, the people there tryhard for the fun, If you don't know it, really Check Out Catan Champs, thats the place where Hakuna Is Admin, and where Those Strategies really come to use.
@@darthskixx2263 Perhaps they take it seriously and it's cool but I don't find playing on Colonist, which has differing rules from the regular Catan game and a terrible trading method, is really worth playing in any serious competition.
@@Ohrami I don't know what youre talking about? Colonist Tries to Simulate the regular Catan Game as good as possible, the Rules are exactly the Same. Also the Trading system is fantastic imo, I wouldnt know a way how to Improve that.