This is Kaushik Basu describing 'Traveler's dilemma'
Lucy and Pete, returning from a distant Pacific island, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them
Why the fuck would he do that? He should deny any and all liability. Why would a rational person agree to hand out money? Either there is fear of litigation or there is a 'reputational effect' in which case this is not a 'memoryless game' and therefore the folk theorem of repeated games has purchase. The solution will converge to the substantive or Muth Rational solution. Incidentally, perfect information means perfect knowledge of game theory, economics, the law, etc. It also means that the Airline Manager knows the exact amount both actually paid. Otherwise 'backward induction' can't provide the solution.
I suppose, if the Airline manager is all powerful, he can say 'I will pay one of you one cent with some unknown non-zero probability, if you will sign a piece of paper saying you never owned any antiques and also that you smell bad and your Mummy hates you'. Basu type rationality would arrive at the conclusion that both will immediately sign the paper for a non-zero expected payoff.
but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it.
So, he will ask an independent expert or better yet get a quote from a dealer (i.e. a market maker in antiques) for his 'spread' (i.e. buy or sell price)
Instead he devises a more complicated scheme. He asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together.
No he won't. Either they have no pre-compact, in which case it is enough to just ask them to name their price of purchase, or else there is a pre-compact such that they split the winnings in some 'Shapley value' determined manner no matter who gets the bigger pay-out.
Thus, suppose one traveler is an ugly, elderly man like me. The other appears a pretty, somewhat promiscuous, young girl- which, indeed, is how Basu appeared to Lesbians back when we were both at the LSE.
The manager- assuming he is all powerful and can act arbitrarily- may pay 100- after all, it is isn't his money!- so as to get a chance to sleep with the Basu lookalike, but will pay nothing for the chance to fuck a fat bastid wot looks like me.
Still there is an incentive for both to have a pre-compact such that the elderly man says 'look, I know you won't pay me a dime, but I truthfully tell you I got this for a thousand bucks. I know there was an identical one which a pretty girl had picked up before me. She too paid a thousand coz the vendor was a total bender. So am I. Is there any chance that you too go in occasionally for a 'bit of brown'? As Nathanael West observed, there's nothing quite like a clean old man.'
I'm not saying the girl will split 50-50 with the old geezer. 'Shapley Values' will determine the outcome. This is the Muth Rational, Schelling focal, solution- i.e. it is the one smart peeps will hit on even if there was no pre-compact.
If both write the same number, he will take that to be the true price, and he will pay each of them that amount.
Why? Antiques are the sort of thing people haggle over. It is highly unlikely that two customers pay exactly the same price for such an object. Firstly there is 'value discrepancy'- the cognoscenti will pay more- and secondly there is 'local monopoly' and socio-temporal market segmentability- i.e when you buy and who you appear to be when you buy affects expectations and thus Supply elasticity.
But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating.
If he wants the actual price, this is a bad 'mechanism' for inducing its revelation. The proper way to proceed is to threaten prosecution for fraud if a false claim is made.
In that case, he will pay both of them the lower number along with a bonus and a penalty—the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment.
This is foolish. Suppose one gives a lower figure than the other. You then threaten the other with a criminal prosecution for fraud unless they drop their claim.
For instance, if Lucy writes 46 and Pete writes 100, Lucy will get $48 and Pete will get $44.
Why give him anything? Tell him your company will prosecute the shit out of him and get a criminal conviction. Lucy is your witness against his outrageous claim.
What numbers will Lucy and Pete write? What number would you write?
This scenario only works if the remote Pacific island has been blown up by a volcano and no expert on its antiquities has survived. Also, there can't have been an invoice or recorded monetary or other transaction. Even so, only if the antiques in question have been damaged beyond all recognition would an independent valuation be impossible.
Assuming this is the case, I would write down 100 iff this was close to the value or else I didn't want the trouble and expense of litigation. So would any one else who is rational. Why? If the airline manager pays a lower amount to at least one person, he has admitted liability. A court would approve my claim that the other person 'low-balled' the value in return for a bigger pay-out. In other words, I can show that the other person had an incentive to lie about the amount we both must actually have paid.
In Game theory, you need to mention all the alternatives available to players. In this case, I would not play the game at all. Why? Evidence that the manager made this offer is enough to show liability. A court may decide that this liability is for a much higher amount than is covered by the Airline's insurance policy.
The other party too should decline to participate in the game save for immediate, unequivocal, consideration- i.e. a bribe.
This is the Muth rational solution. It is Schelling focal- i.e. does not depend on communication. The correct Economic theory states that where a legal claim to compensation exists, you should only accept a settlement which is at least as good as the net expected benefit from litigation. The airline, for its part, should make no offer whatsoever because that admits liability. As a matter of fact, it may use terms like 'without prejudice' or 'without any admission of liability' in making the offer. But just because you say something you say isn't to be taken to be what it obviously fucking is, this does not mean that a court will take your word for it.
Basu does not understand game theory. He thinks the payoff matrix is what he himself- a stupid shithead- thinks it would be. So his 'Traveler's dilemma' or 'paradox' amounts to this- 'if travellers were as stupid as me, they'd drop their claim for compensation in return for the chance to suck off the airline manager iff the alternative, according to him, was sucking him off while he shits on your tits.
The question is why this manager would bother mentioning the suitcases or offering any money whatsoever. If people are stupid enough to believe the two alternatives you present to them are their only alternatives why not offer them a choice between being your slave and being your slave while poking themselves very painfully in the eye?
Scenarios of this kind, in which one or more individuals have choices to make and will be rewarded according to those choices, are known as games by the people who study them (game theorists).
Smart game theorists, like Binmore, made billions for the Exchequer through clever auction design. Basu was by no means smart. Still he was brown and came from a Commie shithole. Also, he was actually stupider than Amartya Sen.
I crafted this game, “Traveler’s Dilemma,” in 1994 with several objectives in mind: to contest the narrow view of rational behavior
Muth rationality prevails. People follow the prediction of the correct economic theory. In this case, these guys say 'you've admitted liability. See ya in Court. My Uncle's a High Court Judge while my sister-in-law works for Fox. We will fucking crucify you.'
and cognitive processes taken by economists and many political scientists, to challenge the libertarian presumptions of traditional economics and to highlight a logical paradox of rationality. Traveler’s Dilemma (TD) achieves those goals because the game’s logic dictates that 2 is the best option, yet most people pick 100 or a number close to 100—both those who have not thought through the logic and those who fully understand that they are deviating markedly from the “rational” choice. Furthermore, players reap a greater reward by not adhering to reason in this way.
Basu must have been the only economist in the world not to have known of John Muth's theory of Rational Expectations which predicts that people will assume others people are rational and know the correct economic theory. The odd thing is that Basu wasn't from some little village in Bihar. He had lived all his life in big Cities with plenty of dynamite litigators who were always on the look-out for a suit against a big Corporation with deep pockets or even a small airline whose one or two aircraft can be seized to settle the debt arising from a Court judgement.
Consider the following-
To see why 2 is the logical choice, consider a plausible line of thought that Lucy might pursue: her first idea is that she should write the largest possible number, 100, which will earn her $100 if Pete is similarly greedy.
Rational- not greedy. Basu is a buddhijivi. He thinks it is vulgar to want proper compensation. You should demand to suck off the airline manager in return for his kicking you in the bollocks. Asking for money is swinish behavior.
(If the antique actually cost her much less than $100, she would now be happily thinking about the foolishness of the airline manager’s scheme.) Soon, however, it strikes her that if she wrote 99 instead, she would make a little more money, because in that case she would get $101. But surely this insight will also occur to Pete,
who will want to signal that he is a reliable ally to Lucy. After all, the fact that the airline pays 100 does not exhaust the claim both have. Indeed, the offer is an admission of liability. Suppose either 'low-balls'. It is now in the interest of the other party to allege fraud and conspiracy. The fact is, if you do stupid shit, other people can always gain by alleging that you tried to harm them. Chances are, you are too stupid to defend your own reputation.
and if both wrote 99, Lucy would get $99. If Pete wrote 99, then she could do better by writing 98, in which case she would get $100.
Says who? Why believe some 'Airline Manager' who has an incentive to make you look like a lying toe-rag?
Yet the same logic
i.e. Basu level stupidity. No wonder Calcutta sank and sank throughout the course of the Twentieth Century.
would lead Pete to choose 98 as well.
No. At this point it is obvious that it is not rational to try to game the system for the chance to earn a couple of extra bucks. Only if you think the other person is irrational would you yourself be tempted down the same path. But why stop there? If the other guy really is irrational and impulsive, he might also suddenly smash in your skull and start eating your brains. You'd better kill him before he has a chance to kill you.
Rationality does not involve assuming other people are crazy cannibals even if there is some small probability that such is the case. On the contrary, Rationality is about applying the correct economic theory- not some shite a brown Bengali monkey pulled out of his arse.
In that case, she could deviate to 97 and earn $99. And so on. Continuing with this line of reasoning would take the travelers spiraling down to the smallest permissible number, namely, 2.
No it would not. Backward induction concerns a feasible and optimal state. In this case, it is getting the highest compensation possible. It isn't Basu's slow-witted shite. Backward induction says 'don't trust a cunt who tells you your only two alternatives are to suck his cock or suck his cock while he shits on your tits'. Equally, rationality does not say you should kill everybody you see just in case they are completely irrational cannibals who want to eat your brains.
Sadly, the extremely intellectually backward regime of Manmohan appointed this nutter 'Chief Economic Advisor'. The markets sighed a breath of relief when the paralytic Sardar and his Bengali puppet were swept off the stage.
It may seem highly implausible that Lucy would really go all the way down to 2 in this fashion.
It is mad. Still, because you were a brown monkey, who was part of a powerful citation cartel of Bengali bhadralok blathershites, you were useful to Academia to signal that certain sorts of Game Theory were as useless as axiomatic 'Social Choice' shite.
That does not matter (and is, in fact, the whole point)—this is where the logic leads us.
Logic leads Bengali buddhijivis to slit their own fucking throats. How soon will they have to flee West Bengal, just as they fled the East?
Game theorists commonly use this style of analysis, called backward induction.
Kaushik should have explicitly said that he wanted buddhijivis to be given not just 'Educationally Backward' Status but that they be granted affirmative action on the basis that they were brain, fucking, dead. However, us Iyers deserve priority.
Backward induction predicts that each player will
refuse to play the Airline Manager's game. They will also refuse to suck his dick if, he tells them, the alternative is that they suck his dick while he shits on their tits.
write 2 and that they will end up getting $2 each (a result that might explain why the airline manager has done so well in his corporate career). Virtually all models used by game theorists predict this outcome for TD—the two players earn $98 less than they would if they each naively chose 100 without thinking through the advantages of picking a smaller number. Traveler’s Dilemma is related to the more popular Prisoner’s Dilemma, in which
both parties are guilty of something. There is a legal claim against them. Also, there is the notion that criminals have low 'time preference' and high 'impulsivity' and that 'there is no honor amongst thieves'. As a matter of fact, a vicious nutcase may gain pleasure from being tortured provided he knows his best pal is receiving yet more severe punishment.
Basu, cretin that he is, doesn't get that if you are not a criminal, you have no reason to play anybody's game. The District Attorney is a public servant. His proffer is the proffer of the State. It is likely to be more lenient than what a Court would inflict. The Airline Manager's proffer is nothing of the sort.
two suspects who have been arrested for a serious crime are interrogated separately and each has the choice of incriminating the other (in return for leniency by the authorities) or maintaining silence (which will leave the police with inadequate evidence for a case, if the other prisoner also stays silent). The story sounds very different from our tale of two travelers with damaged souvenirs,
It is. If you have been arrested, your menu of choice is circumscribed. The Police/Prosecution has a monopoly of a particular type of coercion. This is not the case with 'torts'- e.g. an Airline losing your luggage- as opposed to statutory crimes.
but the Dilemma is identical to that of a variant of TD in which each player has the choice of only 2 or 3 instead of every integer from 2 to 100.
Nonsense! No proffer by a D.A can make you rich. At best you escape jail. In the one case, the dominant strategy is to refuse to incriminate yourself. In the other, if you have a counterpart who is crazy enough to admit liability- go to town on his ass!
Game theorists
are as stupid as shit.
analyze games without all the trappings of the colorful narratives by studying each one’s so-called payoff matrix
which this cunt is too fucking stupid to be able to specify even in a 'lost luggage' type scenario.
—a square grid containing all the relevant information about the potential choices and payoffs for each player [see box on opposite page]. Lucy’s choice corresponds to a row of the grid and Pete’s choice to a column;
Fuck off! Knightian Uncertainty obtains. Both use a Regret Minimizing strategy- e.g. don't fucking agree to play a game save for up-front consideration.
the two numbers in the selected square specify their rewards. Despite their names, Prisoner’s Dilemma and the two-choice version of Traveler’s Dilemma present players with no real dilemma.
Yes they do. In 'Prisoners' you know you've done something wrong and could be made the scapegoat. In 'Travelers' you know that the Airline Manager is a shithead whom you can fuck over- if you have the time and the money to make is worthwhile.
This is the difference between having to suck off a guy who saw you kill your wife and kicking a guy in the slats if he says he will only give you the Pizza you paid for if you suck him off.
Basu offers this little anthropological apercu.
I heard this tale in India. A hat seller, on waking from a nap under a tree, found that a group of monkeys had taken all his hats to the top of the tree. In exasperation he took off his own hat and flung it to the ground. The monkeys, known for their imitative urge, hurled down the hats,
this was a stochastic outcome.
which the hat seller promptly collected. Half a century later his grandson, also a hat seller, set down his wares under the same tree for a nap.
But, because he had 'memory', he'd have secured his hats appropriately. Hat sellers may get lucky once, even twice, but the Regret Minimising strategy requires taking precautions against unexpected- i.e. Knightian Uncertain- outcomes.
On waking, he was dismayed to discover that monkeys had taken all his hats to the treetop.
The monkeys had also bitten his fucking goolies off.
Then he remembered his grandfather’s story, so he threw his own hat to the ground. But, mysteriously, none of the monkeys threw any hats, and only one monkey came down. It took the hat on the ground firmly in hand, walked up to the hat seller, gave him a slap and said, “You think only you have a grandfather?”
This may be buddhijivi humor. The fact is, so long as the British ruled, these fucking brown monkeys had to pretend to be intelligent. Then, after Independence, they could slap each other silly saying 'you think only you have a comprador grandfather? Let me tell you, my family was totes rooting for the Islamists who ethnically cleansed us, while you- you stupid cunt- were cheering for Japanese Imperialism or Chairman Mao's tender mercies.'
This story illustrates an important distinction between ordinary decision theory and game theory.
No. It illustrates the stupidity of the Bengali buddhijivi. Some forty or fifty years ago, Sen had published a shite 'Game theory' type paper co-authored with a fucking British Viscount. So the good little coprophagous cunts at D.Skool started pretending they knew from Game theory. Come to think of it, my pal from St.Columba- Rajiv Sarin- is an 'inert game theorist'. Fuck him. He is useless.
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