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1. Originally Posted by The_Liquid_Laser
The end result is that C will get between 1-100 coins, but the exact amount depends on the negotiating ability of the two pirates.
Are you sure? I'd think C would always accept 1 coin and A has little reason to offer more. If C refuses A's offer, then B gets all the money.

Realistically, C could vote A down just out of spite but it's already defined in the question that the pirates value gold, not murder. C can't give up the option of 1 coin just to kill A and then realize 0 coins.

2. Originally Posted by Feops
Are you sure? I'd think C would always accept 1 coin and A has little reason to offer more. If C refuses A's offer, then B gets all the money.

Realistically, C could vote A down just out of spite but it's already defined in the question that the pirates value gold, not murder. C can't give up the option of 1 coin just to kill A and then realize 0 coins.
If you are taking this as a purely mathematical construct, then we can assume that C will accept only one gold coin. However we can also consider that most people in this situation would feel insulted by only being offered one coin. In this case C might just vote to have A thrown overboard.

I do agree that A has the advantage here, since A is the one making the proposal. For example if 20 gold coins is equal to about a year's pay for a normal person, then A could be fairly confident that C would accept a 20/80 split. Being able to propose the offer does have a big advantage, but technically negotiations could go either way. All we can say for sure is that C will receive between 1-100 coins and A will receive the rest.

3. Originally Posted by Blank
That's all well and good, but I'm just saying within this particular example, it can be equated to two guys robbing someone else with a gun pointed to their head and asking that person to divvy up their money in a favorable way amongst the three.

Chances are, someone's brain is going to get splattered onto a wall.
no, completely different because we're talking very different power dynamics there... there's no immediate loss for the robbers if the man doesn't make a decision that they like and they blow his brains out, there IS a loss for pirate C

though if the robbers get caught, they might get put in a prisoner's dilemma

4. Originally Posted by Blank
I've recently begun to study game theory, and stumbled into the Pirate's Game, and I would like to challenge the common-held solution to the game. Feel free to discuss.
You're right. Something is, ahem, fishy.

Suppose pirates 2 & 3 agree that the offer of zero and one gold coin by pirate 1 is ludicrous.

They reject it among themselves, throw pirate 1 in the sea and have 50 coins each.

These "irrational agents" would be 50 and 49 coins respectively better off and will have punished the greedy pirate for his lack of ethics and brazen cheek. Punishing greed is surprisingly satisfying although, strictly speaking, not very productive.

In maximising their payoffs in an equitable manner and punishing selfish behaviour, they have surely acted rationally? For pirate 3 being "rational" and accepting one coin is irrational because the outcome, as defined by the game, is better achieved by using a cooperative strategy where he gets 50 coins.

So a rational choice of strategy might include completely irrational strategies. Such as cooperation.

5. If A dies then C dies if he doesn't accept Bs offer (regardless of any promise from B which B will immediately break after A is dead if it results in less than all of the gold for him). Thus A can take all of the gold less one as long as C values life above gold or whatever other value. There is no value placed on honor so all contracts/agreements between B and C are illusory/unenforceable [thus no cooperation strategy]. As long as A knows the rules of the game as a certainty his life is never in danger and can take all less one.

A single coin will always be enough to appease C because the alternative is nothing or death (at the second stage if A dies)

One the other hand if A is unaware of all of the rules [pirates always value life first and gold 2nd] It would be the most logical for him to give all of the gold to B or C with the simple goal to save his hide. In other words it depends on whether the pirates know all of the rules and follow them strictly(no variables can anticipate what the other pirates will do or what x equals)

6. I don't know; I still think we're downplaying the importance of how one would try to preserve his/her life. Pirate A knows Pirate B is against him no matter what (unless if B were to get all of the gold, but B could still opt to kill Pirate A for no reason,) leaving his life in Pirate C's hands.

Pirate C should therefore theoretically know that Pirate A values his life more than his gold, thus, based on that logic, Pirate A would be obligated to give all of his gold to either Pirates B or C to save his life. To say that C should be happy with whatever he receives is a bit insulting to C's intelligence, imo, and A's need to perpetuate his existence as well.

7. C needs to perpetuate his existence too and A knows this is a strict given. A's greed for gold above everything else besides his own life will outweigh any bonus coin to C beyond one. Any choice above one gold piece from A to C is merely a gratuity and conflicts with As second priority/mandate.

C knows if A dies he gets nothing from B thus his greed and logic (i.e. rule of the invariable values if known as is apparently presumed) will force him to take anything given to him by A as long as its not nothing (because then he has nothing to lose and can still preserve his life by the mere act of agreeing with Bs distribution once A is dead even if it is (which it will be under the rules/logic) 100 to B and nothing to C.

With fixed variable each other knows what cards the others hold and there is no logical basis to be taken in by a bluff/unenforceable negotiation. Even without A knowledge of the other pirates mandate (the life/greed value hierarchy) in retrospect the results would play out the same as long as A gives C at least one coin or B getting all of the gold if C is capable of acting illogically during the first tier of negotiations.

The question also appears to assume that this single distribution is the beginning and end of all negotiations. Assuming there are other subsequent negotiations resulting in similar distributions, or reasonable likelihood thereof, I personally would choose "no gold today" over "one gold piece today" because precedent and reputation for exercising the option of outside the logical lock-box (the inability to resist immediate gratification) in itself has value for future negotiations. A value I would estimate which is worth more than one gold piece. Professional poker players know this when they play at multiple game sittings often choosing to play contrary to strict mathematical logic of the odds of wining to gain the benefit of applying variables.

8. Pirate's Gold is a convoluted version of the Ultimatum game, played with 2 agents. In practice nobody acts "rationally" and accepts a dollar while the other guy gets \$99. IRL you'd tell Mr \$99 to fuck himself and walk away.

Even after the rules are explained, most people seldom take less than 20% of the pot and reject the offer, creating lose-lose scenarios.

And some Asian countries the split can be a very equitable - and apparently irrational - 50%.

9. I think some of you are fudging the rules a bit to make your point. Look at the rule parameters again. If things have to play according to the rules, then 1) C is in no danger of losing his life, as he would never really get to the point of proposing anything, 2) If pirates order of value is Life > Gold > Nothing, then the original scenario of A getting 99 coins and C getting one coin will occur.

C bargaining with A for more coins than 1 would go against the stated parameters of the scenario. If C votes NO on any proposal made by A, he gets nothing, because B would get it all in the 2nd round. So unless A offers C nothing, it is to C's advantage to vote yes to anything more than zero coins that A offers him.

Now if you want to argue that C would vote NO to spite A in case of a very low offer to C, that is fine and probably more realistic in life, but again that violates the parameters of the game. If you think C would hold A hostage for an offer of all coins, that too goes against the stated parameters.

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