Showing posts with label Game Theory. Show all posts
Showing posts with label Game Theory. Show all posts

Friday, April 13, 2012

Talk is Trash


I recently studied a few cheap talk models, beginning with the seminal paper by Crawford and Sobel in 1982. By “cheap talk”, most economists really mean free talk. A cheap talk game is one where one agent can send a message without incurring any exogenous cost: the only cost incurred is endogenous, i.e. it affects the sender’s payoff by influencing the receiver’s action choice. In short, cheap talk is a costless signal.

From a linguistic perspective, the “talk is cheap” maxim is traditionally taken to mean that the words in a message could be meaningless and need not be supported by truth, actions or evidence. The rising popularity of sarcasm should lend some added meaning to the phrase: what is said is very different from what is meant because the inherent meaning of our words is often diluted by how we say it.

So is the game theoretic use of the phrase cheap talk itself cheap talk? No! Economists are nothing if not precise. But it is possible that calling an entire subset of signalling games “Cheap Talk” is an attempt to make it sound a lot more interesting than it really is. If cheap talk is enough to make a paper sound interesting, imagine how much more intriguing a trash talk model would seem. Measuring the cost of indulging in trash talk and weighing it against the psychological advantage it confers could help us calculate whether being courteous is worthwhile at all. Children waste much of their childhood learning social conventions and much of their adult life brimming with resentment as they teach their children to fight their instinct to be frank.

Such a model might do to social relations what the prisoner’s dilemma did to gang loyalty – although it is socially optimal for all of us to be nice and the outcome is Pareto superior to any other, if each of us acts in a self-interested manner, being nasty would be a dominant strategy unless social ostracism outweighs the personal gain from feeling smug. However, if the psychological cost of courtesy is greater than its social benefit, we could adjust social structures to eliminate the rationale for teenage rebellion and angst altogether. It would be fascinating to see teenagers rebel by being excessively nice to everyone because their parents were so blunt all the time. Gandhi would be so proud. 


Tuesday, March 13, 2012

Man Up, Wall Street


I can’t say I’ve been following the Occupy Wall Street protests with bated breath. For one, I don’t know what the protest is about and it seems, nor does anybody else – not the protesters, not the reporters, not those who approve or disapprove of the movement – in short, nobody.  A protest that’s not against something definite is not a protest so much as it is a public forum for airing self-pity. I thought the internet was enough for that. 


I'm a bit confused about what they expect to achieve and how they will do so. But I suppose most protesters are and that's really a secondary issue. Personally, I’m a big fan of protests. It gives everyone a few days off work. The media finally has something to report. There’s always something to watch on TV. And it’s indicative of a populace that is trying to think about the state of the world.

Unfortunately, Occupy Wall Street is running out of funds. Apparently, it’s difficult to draw attention to how poor you are unless someone gives you the money to do so. No, no. No irony at all. It’s time for Wall Street to be a man and do the right thing. It must fund the protests, thereby negating the premise of the protest altogether. It’s a win-win. 

Saturday, March 3, 2012

Picketing, Pocketing


Suppose each of your pockets can be picked with an equal probability on any given day. I’m going to take a conservative estimate of 10% and assume that the probabilities are independently and identically distributed. You have some money, say Rs. 500 that you would like to carry. Would you prefer to distribute them across both pockets so that the probability of you having nothing is minimised, or would you prefer to keep it in a single pocket to maximise the probability of getting to keep all your money? To put it another way, by putting your money in a lot of different pockets, are you actually raising the probability of at least something getting stolen?

Is it correct to say that the probability of each pocket being picked is independent? We could argue in favour of this assumption because it is unlikely that pickpockets would take the risk of checking all the pockets of the same person once they’ve found something. But if the assumption is correct, then you should be indifferent between the distributions (250, 250) and (499, 1), which you are not. So let us further simplify by assuming that the money is equally divided between all pockets.

Let’s calculate what you should do, shall we? If you put all your money in one pocket, the expected value of the money that you can expect to have at the end of the day is 0.9 * 500 = Rs. 450. Since we assume that the probability of the first pocket being picked is completely unrelated to the probability of the second pocket being picked, the intersection of the events should simply be the product of the two probabilities. So the probability both pockets being picked is 0.1 * 0.1 = 0.01. If you equally distribute your money over both pockets, the expected value will be 500 – P(AUB) = 0.1*250 + 0.1+250 – 0.01*500 = Rs. 455. While the amount you put in each pocket doesn’t affect the expected value, the number of pockets will. So it’s rather rational to keep your money in many different pockets if you’re an average person.

But there could be pickpockets who grab opportunities with both hands. Assuming a probability distribution over all pockets instead of conditioning it on the individual does not allow for a fantastically unlucky individual who has all pockets picked on a single metro ride. Let’s just say nobody likes that guy too much anyway so we aren’t relaxing any assumptions for him. This also means that we don’t think a person’s pocket is more likely to be picked just because he has a lot of them. I’m forced to concede that this, too, isn’t very unrealistic. Where will the pickpocket look in a pair of Dockers?

So even without accounting for risk aversion, our model shows that it is indeed rational not to put all your eggs in one basket. In any case, the preference for not losing everything is probably stronger than the preference for not losing anything. But extend this concept to too many pockets and regardless of what the calculations tell you, you should know that you will end up losing at least some money just by forgetting about it (true story). It is reasonable to say that there is an upper bound to the number of pockets you will split your money across: just as it would be embarrassing to find out that you are broke because your pocket has been picked, it would be rather awkward to have to fish out tenners from four different pockets to pay for a doughnut. The answer, my friend, is moderation. 

Sunday, February 26, 2012

Oh Fudge


How does one fudge an interview? I have no idea. Perhaps I should give it my best shot because the company sulks and leaves without recruiting anybody whenever I do so. When I try to come off dumb, I appear to become irresistibly desirable as an employee. If I was feminist enough, I would probably call it chauvinism. As a placement coordinator who never sat for placements, I wondered why students had so much trouble making a choice. But things are rather different on the other side of the glass door. Especially for me. I doubt that people think as much about getting married to someone as I do about interviewing for a job. Accepting one job means forfeiting the opportunity to apply for all the others. Given that my preferences are not at all aligned with the rest of the batch, are nearly the reverse of the order in which companies were scheduled and that I don’t have complete information about the companies that will turn up in the future, I find it incredibly difficult to make a decision. The process is further complicated by chance variables and sudden changes in factors that were hitherto assumed fixed, and I’m just not equipped with sufficiently sophisticated modelling techniques to solve that sort of problem. I end up tossing more coins than most cricket umpires do in their entire careers.

By turning up for an interview and performing well, you are choosing a job that acts as a safety net over the opportunity to get a job that you really like. If the former choice is more realistic and rational, then I probably should have applied to more companies than I did. Rationality always lands me in knee-deep shit.

Showing up for an interview and “fudging it” amounts to insulting the interviewer’s intelligence. I already have enough issues with all the Catberts without incurring their wrath.

By not showing up for an interview, you’re honest about your intentions. But you risk pissing off your placement cell, your batch mates and the company you applied to. You also maintain your status quo as an unemployed person.

Three roads diverged in a yellow wood, all pointing to certain doom. 

Sunday, February 19, 2012

Lie Your Heart Out


Is it rational to be honest if you know you'll get into trouble? From the point of view of behavioural economics, there are three types of people: rational (they make an action choice in the first time period and stick to it), quasi-hyperbolic naive (they change their mind when the time comes to act on their choices) and quasi-hyperbolic sophisticated (they know that they are unlikely to stick to their original choice so they make arrangements to prevent themselves from deviating from the chosen strategy). 

I'm given to understand that rationalists are nasty, lying reprobates who act entirely in self-interest. I suppose they will lie every chance they get. Never trust a true rationalist. The quasi-hyperbolic sophisticated person wants to lie but knows that there's a good chance that he will end up telling the truth so he will make arrangements to commit himself to lying, say, by extinguishing the truth, brainwashing himself, testing himself to see if he holds up under torture: the sophisticated guy is classic contract killer material. 

A quasi-hyperbolic naive person is a spineless, useless creature. Being naive, he will want to lie but helplessly blabber the truth when the time comes. He is clearly the most lovable one of the three. 

Friday, February 10, 2012

Stage Fright


I’ve always been pretty good at taking notes. If there was an award for the most photocopied notebooks in school, I would most certainly get it. This was partly due to my obsessive need for record keeping and partly because my school was the sort where I was unlikely to find anybody else who bothered to bring a notebook at all.

As a Master’s student with no background in economics, I make notes that are too detailed even by my standards. I rationalise this to myself by arguing that what is obvious to people who have already studied economics for three years is not obvious at all to me. But lately I’ve been suffering from stage fright because of all the photocopying my registers undergo. I’m very acutely aware of the fact that everything I write will be read by people other than me so I try to sound more authoritative, I double-check my grammar, I avoid scribbling in the margins like I would otherwise. Self-censorship. It makes me quite uncomfortable and I only find solace in the fact that I’m not writing anything even mildly interesting anyway.

Any prospective employers finding my blog would be bad news for me. My posts put together suggest that I’m awful at making decisions and interpret theories as I please but I have a pretty handwriting and I’m good at taking notes. I would almost certainly wind up as a secretary. 

Monday, January 30, 2012

Embracing my Indianness


The exchange students in my college last semester complained about how everything in India happens “tomorrow.” I chuckled like I always do when I hear jokes that I don’t believe are at my expense. “Oh how Indian!” I thought to myself. What I’ve come to realise lately is that I’m more Indian than I think I am. I have been meaning to study “tomorrow” for the last 15 years and I’m yet to get around to it of my own accord. What’s a 2-month delay in installing an internet connection compared to that? I also unnecessarily add “only” at the end of each sentence, as if my conversations are really chequebooks. I use present continuous tense where simple present would suffice. I have no notion of punctuality. 

I remember having watched one of Russell Peters’ shows where he said that Indians probably don’t find jokes with the Indian accent offensive because they don’t think they have it. “They think there’s one guy in the country with that accent!” I think that logic can be extended for most Indian stereotypes. We are a part of the crowds we so detest. We’re exasperated that nobody stands in line although we always break it. I think we consider it okay to break the rules. We complain because everyone else breaks them at the same time and that inconveniences us. It’s as if we think we’ve landed up, quite by accident, in a place that’s so full of people who don’t behave as we would like them to. That we’re one of them is immaterial. 

Sunday, January 29, 2012

Tipping my Imaginary Hat to old Astrology


I have decided to get a job by accumulating good karma. I’m helping a very dear friend with her university applications. I’m looking for a word that would convey the exact opposite of nostalgia but I haven’t been able to find it. Usually when people look back at things they smile and say, “Oh some things never change.” Now picture me saying the same thing but throwing my hands up and shaking my head wistfully as I speak. That’s exactly what I do when I look at the questions in such applications.

Everybody’s favourite question is, “Describe your strengths and weaknesses.” This is a rather dumb question to ask, because self-evaluation will almost always seek to mislead. It’s not that the candidate can’t help disclosing some useful information. No, not at all. When you include this question in your application, you reduce all your candidates to a single strength and a single weakness: they are all liars. They bend or stretch the truth. Some may take the liberty of extinguishing the truth altogether. Poor truth, everyone discriminates against it.

Not that my friend is a liar. I may be one, but she’s an absolute gem of a person. I couldn’t think of any weakness that would seem acceptable, so I googled weaknesses. It wasn’t very useful. But for the first time ever, astrology came to my rescue. I looked up weaknesses for different zodiac signs and astrologers are just so good at cushioning the blow, you don’t need to do anything more! I’m convinced that all these “What’s your personality type” and “Do you know your ruling planet” tests were devised expressly to help with application forms. I tip my hat to you, astrology. 

Tuesday, January 24, 2012

The Waiting Game


I’m not the sort of person who is usually on time. I have a rare condition. I once arrived so late that one of the people I was supposed to meet, having waited for me for over an hour, went home. I didn’t notice. I also frequently lie about my location to make it easier for the other person to endure the wait. Of course, when it becomes apparent that I lied because it doesn’t take 2 hours to reach anywhere from Connaught Place, they get a bit annoyed, disregarding the fact that I did it for their own good. Nobody appreciates how considerate I really am.

I do, however, have very strict rules about waiting for others. I don’t like to do it, so I don’t. I make sure I’m adequately late so that I don’t need to do so. In addition to my natural gift for being appallingly late, this determination helps me time things to perfection. Of course, this means that I have no idea of how to reach a place on time, say, for an interview. I turn up freakishly early, try to while away time, lose track of it and end up being late anyway.

Recently, one of my friends turned this habit into a two-player waiting game and lied about her location as well as the time we were supposed to meet. Imagine her astonishment and my indignation when I was the first to reach. Obviously, this means that I will have to further delay my arrival in future to account for the possibility of her lying. The only optimum that exists is for everyone to tell the truth while I do as I please. Otherwise, as a cursory study of any cheap talk game will tell you, there will only exist a babbling equilibrium. 

Saturday, November 5, 2011

Game Theory Atheist emerges

Local man Pramod Thakur has strongly criticised game theorists for spending a lot of time agonising over what he calls “just semantics”. A well-known game theory atheist, Thakur is also believed to worship pagan gods like common sense.

“It’s just a case of poor problem phrasing. If we didn’t get into these ‘I know that you know that I know...’ cycles, and simply started with ‘we all know’, the solutions would be more intuitive and the reasoning less complex. It is rather unrealistic to assume that everyone knows how to solve a problem and will solve it exactly as we predict.”

He cites Prisoner’s Dilemma as a case in point. “Earlier, most people would have chosen to cooperate, but game theory came along and messed things up for criminals. We used to understand that we all have to work towards something mutually beneficial to expect a good outcome. If we deviate, the other guy will beat the crap out of us when he finds us. If there’s one thing I’ve learnt from gangster movies, it is that there will be revenge.”

“If it’s somebody else’s problem, leave it alone,” he sums up. 

Saturday, October 29, 2011

Game Theorist receives $2 for lost luggage

A top airline company reportedly compensated a top game theorist with $2 for his lost luggage based on the famous Traveller’s Dilemma formulated by Kaushik Basu.

“We just assumed that he would be rational so instead of going through the motions of telling him that another traveller has lost an identical item and that we would pay $2 extra to the passenger who claims a lower value, we just directly skipped to the Nash equilibrium outcome. Our corporate motto is to anticipate customer expectations and fulfil them and I think we have lived up to our reputation,” said an airline official on condition of anonymity.

The elated passenger commended the airline for its farsightedness and excellent grasp of rationality and game theory. “The ideal world is within reach now,” he declared.

Airlines are queuing up to offer exclusive services to game theorists and rational economic persons.