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Thread: The travellers' dilemma

  1. #33
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    Re: The travellers' dilemma

    Quote Originally Posted by peterb View Post
    I did wonder what the effect would be if the reward or penalty was different, but it actually does make no difference - its the psychology of potential reward that is supposed to govern the choice.
    I'm not getting through here am I..... There are 3 things at play in this problem: maths/game theory, logic (in this case, the two are distinct) and psychology. The psychology side of it is not particularly interesting or difficult. Would I rather make more money, or screw over my opponent? Of course, any sane person would choose to make more money, rather than screw over his opponent. That's not even worthy of comment. The point here is that there is a mathematical, game-theoretically sound argument for $2 being the optimal choice. Logically, it's stupid - the aim of the game, as several people have noted, is not to screw over your opponent, and by taking the game-theoretical approach, we end up minimizing our payout. Simple logic trumps the maths. That, to me, is the interesting side.

    In terms of the psychology, this, rather than the prisoners' dilemma, is more akin to all sorts of conflicts and negotiations, whereby we go in with mindsets of it being a zero-sum-game, and that it's more important (for reasons, perhaps, of personal pride, or political pressure) not to get the best deal for yourself, but to get a better deal than your opponents, or at least to feel like you've done them over. We can all see this, right? In terms of global politics, game theory suggests tactics very similar to north korea, and, currently, theresa mays' brexit negotiations stance, i.e., appear unpredictable, and make your opponents think you're ready to blow yourself up as well as them, if you don't get what you want. If you'll pardon my french, c'est évidemment bolloques. The psychology of the problem is only interesting insofar as to the parallels with real life.

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    Re: The travellers' dilemma

    Quote Originally Posted by wazzickle View Post
    I'm not getting through here am I.....
    Nope.

    Quote Originally Posted by wazzickle View Post
    The psychology side of it is not particularly interesting or difficult. Would I rather make more money, or screw over my opponent? Of course, any sane person would choose to make more money, rather than screw over his opponent. That's not even worthy of comment.
    Depends on both the opponent and the amount of money, as well as what could be gained by allowing the opponent an equal or even greater amount of money.

    Quote Originally Posted by wazzickle View Post
    The point here is that there is a mathematical, game-theoretically sound argument for $2 being the optimal choice.
    Well... no... there isn't... not that I can see, anyway....

    Quote Originally Posted by wazzickle View Post
    Game theory suggests the answer is $2 - assuming you start with $100, as the other traveller is entirely rational, he will be looking to maximise his own return and select $99.
    Will he?
    That's not only an assumption, but also psychology...

    Quote Originally Posted by wazzickle View Post
    The key here is that bidding $2 does not maximize returns, but, rather, minimizes them, through the logic simply of trying to beat the other guy.
    So now the game has changed from maximising return (your own or that for the both of you), to minimising returns (again, your own, your oppo's or even both of yours)....?

    Quote Originally Posted by wazzickle View Post
    Which is pretty stupid imo.
    Yep, so far I'm thinking this is a pretty dumb puzzle and wondering why you're taking such great pains to explain it to us and have us understand (with great respect) exactly what you're trying to get at...
    It's stupid... where's the interesting part?

    Quote Originally Posted by wazzickle View Post
    the aim of the game, as several people have noted, is not to screw over your opponent, and by taking the game-theoretical approach, we end up minimizing our payout.
    The aim as given, or as assumed?
    This is why the psychology matters and why we can't trust AI to run our nuke programs yet... Not only are there so many additional variables in dealing with humans, but the variables are subjective and even subject to change.

    Quote Originally Posted by wazzickle View Post
    Simple logic trumps the maths. That, to me, is the interesting side.
    No, it trumps the game theory, as described... However, I disagree with the theory.

    Quote Originally Posted by wazzickle View Post
    In terms of the psychology, this, rather than the prisoners' dilemma, is more akin to all sorts of conflicts and negotiations, whereby we go in with mindsets of it being a zero-sum-game, and that it's more important (for reasons, perhaps, of personal pride, or political pressure) not to get the best deal for yourself, but to get a better deal than your opponents, or at least to feel like you've done them over.
    We can all see this, right?
    We cannot all see this, no... not entirely and not me, anyway, which is where my problem comes in.
    For example, who says I have to do over my opponent at all? If I secure us both a top end deal, they might even become allies instead. That's way better than equalising with or beating them...

    However, I know naff-all about game theory and all that, but still here are a couple of ideas...

    Quote Originally Posted by wazzickle View Post
    If one names lower than the other, however, that amount will be taken to be the correct amount. That traveller will receive an 'honesty bonus' of $2 more than that price; the other traveller is taken to be a liar, though, and will receive $1 less than that amount.
    So with ^that in mind:
    Quote Originally Posted by wazzickle View Post
    What amount of money should you claim is the price of the artefact?
    I say: 6) else
    I say it it entirely worthless. No value. £0. Nil points...
    You cannot get lower than nothing, so if he claims the same we walk away even... but if he claims a single cent more, then I still get $2 and he now owes them $1. That's logic and maths, used together.
    How's THAT for game theory!!

    I feel all smart, now.....


    Alternatively, you claim it is worth $100.
    Anything he claims will either be equal or lower.
    Payouts are then issued.
    Whatever is paid, you then go occupy his place of residence, kill him and install yourself as governor of that residence, take the money and walk off far richer, while retaining the option to govern the residence and enslave anyone else still living there.
    Not only does that work just as well, it's also kinda how various empires seemed to do it with notable successes throughout history...

    OK, really feeling smart, after that!!


    Aside from being obvious that I don't do game theory and stuff, or play wargames, etc.... How does that all sound?

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    Re: The travellers' dilemma

    Quote Originally Posted by Ttaskmaster View Post
    How does that all sound?
    It sounds like you don't understand the problem as I described it, which must be at least partly my fault.

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    Re: The travellers' dilemma

    I recall the usual advice is to take plenty of water and some Imodium.

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  8. #37
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    Re: The travellers' dilemma

    Now, the thing to keep in mind is that both items are Valuable!
    You ask for $100.
    Then, you hit the guy on the head with your valuable item. You steal his $100 and his valuable item.



    And,
    then you tie him up and leave him in your basement until his rich employer or family pays you ransom. So, you just made a 3 X profit

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    Re: The travellers' dilemma

    Quote Originally Posted by OilSheikh View Post
    Now, the thing to keep in mind is that both items are Valuable!
    You ask for $100.
    Then, you hit the guy on the head with your valuable item. You steal his $100 and his valuable item.
    And then fence it on Ebay?
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    Re: The travellers' dilemma

    Quote Originally Posted by wazzickle View Post
    ....

    In any case. Game theory suggests the answer is $2 - assuming you start with $100, as the other traveller is entirely rational, he will be looking to maximise his own return and select $99. Knowing that will be his strategy, you underbid him with $98, and he changes with $97, all the way until $2.

    ...
    That interpretation of a game theory rational response only works if the object of the exercise is to beat the other guy, no matter at what cost. Relax that imperative and a rational person, aware that the other is rational, would state the true value of the item, aware that whether you end up with €99 ... sorry, $99, $100 or $101, any are way better than $2. It is not rational for rational people go end up at $2.

    However, the rationale has at least three major flaws. First, since when have people been, let alone always act, entirely rationally? Second, in relation to the subject that inspired it, there are WAY more than two reward systems involved. Three, not all the reward systems are monetary. Four, both sides have red lines leading them to impose some rules they will declare to the other side but cross, and some they will declare to the other side but not cross. Working out which is which is tricky.

    And five, they also likely both have rules they will not declare, or admit to, but also will not cross.

    And six, sometimes the best strategy in a game is to not play in the first place. Such as, just claim on vour own insurance which, for a valuable item, any rational person would have in place.


    Okay, I did say "more than" three reasons.

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    Re: The travellers' dilemma

    Quote Originally Posted by wazzickle View Post
    Please read through your post again and ask yourself whether there are any inconsistencies.

    Change the levels of the penalty or bonus if you want, it doesn't matter. This is a theoretical question whereby improving your results by a small amount is the goal, if you can't improve your results by a bigger amount. "Not worth it" is not part of this equation.
    At no point does it state that you HAVE to maximise your gain to the nth degree. Therefore we are dealing with a subjective situation and as a consequence the bonus and penalty does matter. Rationally you want to get reasonably close to the maximum amount to recoup your losses. So when the likelihood is that the other traveller will bid high as well a loss of 2 versus >90 isn't significant. However, if the loss was 50 you'd apply different logic as potentially only gaining half your recompense wouldn't be favourable.
    If Wisdom is the coordination of "knowledge and experience" and its deliberate use to improve well being then how come "Ignorance is bliss"

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    Re: The travellers' dilemma

    That's all well and dandy. I don't know how to explain the same thing in different ways, and I don't want to repeat myself, so I'll say for the final time: the game theoretical solution (as I've stated, not the correct one) is 2. The correct solution is 99 or 100. We're not arguing here. You can claim game theory is wrong. You'd be agreeing with me.

    My overall point was that where personal pressures (dislike of the other side, your own side wanting a win rather than maximisation) apply, this sort of logic often becomes front and centre. I.E. the threat to the EU by TM that we'd be ok with shooting ourselves in the foot as long as the other side got both feet shot at the same time.

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    Re: The travellers' dilemma

    Quote Originally Posted by wazzickle View Post
    That's all well and dandy. I don't know how to explain the same thing in different ways, and I don't want to repeat myself, so I'll say for the final time: the game theoretical solution (as I've stated, not the correct one) is 2. The correct solution is 99 or 100. We're not arguing here. You can claim game theory is wrong. You'd be agreeing with me.

    My overall point was that where personal pressures (dislike of the other side, your own side wanting a win rather than maximisation) apply, this sort of logic often becomes front and centre. I.E. the threat to the EU by TM that we'd be ok with shooting ourselves in the foot as long as the other side got both feet shot at the same time.
    The problem is, in relation to the EU, that we would be shooting oyrselves in the foot.

    In any comparison between "no deal" and "bad deal", dismissing the notion of no deal being inferior requires assumptions about the nature of "bad deal".

    That's where Brexiters and remainers tend to disagree. You assume ANY deal is better than no deal and Brexiters do not. Which is better for the uK, long term, depends ENTIRELY on the detsil if "bad deal" and as we don't currently know what dsal is on offer, assuming no deal must be worse is a dogmatic assumption that ANY deal the EU offers must always be better than no deal, an assumption that pztently is untrue, when the EU keeps plucking ever larger ludicrous sums for our "bill" without even discussing trade and everthing else.

    Besides, what does game theory tell you about negotiated outvomes when you let the other side know all your red lines without knowing theirs?

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    Re: The travellers' dilemma

    Quote Originally Posted by Saracen View Post
    The problem is, in relation to the EU, that we would be shooting oyrselves in the foot.

    In any comparison between "no deal" and "bad deal", dismissing the notion of no deal being inferior requires assumptions about the nature of "bad deal".

    That's where Brexiters and remainers tend to disagree. You assume ANY deal is better than no deal and Brexiters do not. Which is better for the uK, long term, depends ENTIRELY on the detsil if "bad deal" and as we don't currently know what dsal is on offer, assuming no deal must be worse is a dogmatic assumption that ANY deal the EU offers must always be better than no deal, an assumption that pztently is untrue, when the EU keeps plucking ever larger ludicrous sums for our "bill" without even discussing trade and everthing else.

    Besides, what does game theory tell you about negotiated outvomes when you let the other side know all your red lines without knowing theirs?
    That sometimes it doesn't matter. In poker we learn that, in certain situations, you could turn your cards over and it wouldn't make a difference to you or your opponents' decisions that are yet to come. There were also situations with a sever information deficit. E.G. I was on tv playing poker more than once, and consequently occasionally was recognised. For other people it was much more of a problem. They'd been seen playing the highest stakes poker they'd ever played, a number of times, with a particular style. They were very much a known quantity. They were playing unknowns, and could assume nothing about their playing style, except for the fact that the other side knew how they played. What do you do? You adjust your strategy a little. It's not a particularly tough adjustment.

    I was also briefly a negotiator for Barclays. In a bunch of consumer-company negotiations, their is a significant information deficit. As the consumer, I'm usually the one at the raw end of that exchange. You can compensate very easily. Lay your cards on the table, and make believable threats. 'This is my situation. If you offer me this, I can stay. I know you have the power to offer this, as a friend has told me you will.' That is often a bluff - I don't know their redlines. I make a believable threat, like 'Sky are offering a good deal, can you match it or beat it?' You find out their red lines by making believable threats. The fact that we've muddied the waters about ours - whether a genuine redline or not - the rest of the EU clearly don't, nor should, believe that we'd be willing to go from being part of the EU, the vast majority of our trade either way with them, offering access to the rest of our trading partners, to 'out on our collective behinds'. I sure as hell hope our position of 'I'M NUTS DON'T TEST ME I'LL GODDAMN DO IT' is just bluster, and not genuine political madness.

    I would refer to another gambling situation for the 'no deal better than a bad deal' discussion. In blackjack, with perfect strategy the odds are against us assuming we play perfect strategy - by something like 50.3 to 49.7% I believe. We could card-count to beat that deficit; alternatively, we could, for whatever reason, play to lose harder. In roulette you can't - for every £1 you put down, you on average lose ~5p every time, which is fixed. In blackjack, you could play to give yourself 0% chance in certain situations (hitting on a 21), and minimize.

    In other words. Yes, we could do worse than no deal. We'd have to try pretty hard to get there though.

    Of course, this is just my opinion on 'where we are now' vs 'where we could be with a good deal' vs WTO. You have your own opinion. If it really looks like our negotiators are so crap that they can't get a better deal than WTO - a pretty horrendously awful baseline - they should be fired, and we should get more time to renegotiate. I say again: WTO is a baseline, a fallback, a last resort. To do worse than that would take some effort. IMO

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    Re: The travellers' dilemma

    Quote Originally Posted by wazzickle View Post
    It sounds like you don't understand the problem as I described it, which must be at least partly my fault.
    Entirely your fault. The onus is on you to explain your position to your audience, tailoring it however necessary.

    Quote Originally Posted by wazzickle View Post
    You can claim game theory is wrong.
    Of course it's wrong. That's why they call it theory - The real world, in practice, clearly works differently, for starters!

    Quote Originally Posted by wazzickle View Post
    My overall point was that where personal pressures (dislike of the other side, your own side wanting a win rather than maximisation) apply, this sort of logic often becomes front and centre. I.E. the threat to the EU by TM that we'd be ok with shooting ourselves in the foot as long as the other side got both feet shot at the same time.
    Well.... yeah.... that's human nature.
    You see this all the time in martial arts and combative sport - People instinctively sacrifice their own safety in order to try and score a winning hit, half the time through ignorance of their position, the other half through just being mindlessly hellbent on winning. This from otherwise perfectly rational people, too...

    Quote Originally Posted by wazzickle View Post
    In other words. Yes, we could do worse than no deal. We'd have to try pretty hard to get there though.
    Depends... No Deal with Europe still leaves us options with those not in Europe.
    However, given some of the egoes involved in this little game of politics, I would not be surprised to find us getting the worst imaginable deal on purpose if it meant the person doing the negotiating later benefited from it. In fact, that's exactly what a previous CEO did to our company and both we're and our customers are still paying the price over a decade later...

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    Re: The travellers' dilemma

    Quote Originally Posted by Ttaskmaster View Post
    Entirely your fault. The onus is on you to explain your position to your audience, tailoring it however necessary.
    Well that's nice and gentle of you, but other people have understood it, as I have explained it, first time, so I would say that it would be unfair for me to shoulder all the blame.

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    Re: The travellers' dilemma

    Just because money is involved, it doesn't make this a mathematical problem. It's a people problem.

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    Re: The travellers' dilemma

    Quote Originally Posted by wazzickle View Post
    Well that's nice and gentle of you, but other people have understood it, as I have explained it, first time, so I would say that it would be unfair for me to shoulder all the blame.
    Well... if you're just going to just dismiss my whole line of reasoning and enquiry like that, in a single sentence proclaiming my utter ignorance, then surely you expect the same in return?

    Based on your posts so far and the similar responses to/from others far smarter than me, you must have wanted something very specific, but did not specifically ask for it... so it is still down to you to articulate clearly what you want from us...

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      • Cooler Master HAF XB
      • Operating System:
      • Windows 8.1 64Bit
      • Monitor(s):
      • Samsung 2032BW, 1680 x 1050
      • Internet:
      • 16Mb Plusnet

    Re: The travellers' dilemma

    It's dead simple, the insurance company follows the data protection act and never even mentions that there's another party with an identical claim. Therefore both recieve $100 for the item because frankly, who doesn't pad their insurance claim if there's a certaintity of getting away with it.

    (\___/) (\___/) (\___/) (\___/) (\___/) (\___/) (\___/)
    (='.'=) (='.'=) (='.'=) (='.'=) (='.'=) (='.'=) (='.'=)
    (")_(") (")_(") (")_(") (")_(") (")_(") (")_(") (")_(")


    This is bunny and friends. He is fed up waiting for everyone to help him out, and decided to help himself instead!

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