Nash equilibrium

January 31, 2009

In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy (i.e., by changing unilaterally). If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium. In other words, to be in a Nash equilibrium, each player must respond negatively to the question: “Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?”

(From Wikipedia)

There are a lot of assumptions to this model but I have to say that it alarms me slightly that I frame a lot of problems this way.  Hmmm.

(Also just gave someone love life advice with the phrase “Nash equilibrium” in it.  It is official.  I am a geek.)


We need to invest

January 23, 2009

He traced an imaginary declining stock market chart with his finger, letting it trail to a plateau.  He pointed at the dip.  We need to invest, he said.  It was just another way of saying that we haven’t caught up in a while and should soon.  I smiled at the economic metaphor.  Some people might scorn the seemingly transactional economic metaphor used on something like friendship but it made complete sense to me. 

It is said that the metaphors you use say a lot about the way you view something.  Some people view love (platonic or otherwise) as fresh air.  There is something pure and free about that metaphor but I am not one of those people.  The love/fresh air metaphor makes me think about public goods.  And market failures, free-rider problems and the tendency to under-invest.  (And the fact that I am analysing the love/fresh air metaphor in economic terms is probably very telling.)

I much prefer the economic metaphor.  Relationships are things to invest in.  And the currency of investment is finite (time).  At least it is this side of heaven.  The flipside of the metaphor is some expectation of return on investment and the unsentimentality of selling a low-yield bond.  But in the case of a high-yield bond, it seems to imply continued intentional investment and a rather happy, mutually beneficial situation.  There is a part of me that likes the predictability.  It is straight-forward and I know how to troubleshoot it.  Output = f(input)  I can understand a relationship framed in this way. 

The Christian in me wonders where is the role of grace and mercy  in all of this because for the most part, the call to godly behaviour completely defies normal human logic.  (I once hear a sermon about what it means to love mercy and it was explained as “knowing that you could get seriously screwed over and still doing it anyway”.)  But the cynic in me laughs and says, Grow up, child.  (Notice how he didn’t call me “kid”.)

This is the kind of thing that economists circulate.  (From Science Daily):

“The research uses game theory to analyse how males and females behave strategically towards each other in the mating game. The mathematical model considers a male and a female in a courtship encounter of unspecified duration, with the game ending when one or other party quits or the female accepts the male as a mate. The model assumes that the male is either a ‘‘good’’ or a ‘‘bad’’ type from the female’s point of view, according to his condition or willingness to care for the young after mating. The female gets a positive payoff from mating if the male is a ‘‘good’’ male but a negative payoff if he is ‘‘bad’’, so it is in her interest to gain information about the male’s type with the aim of avoiding mating with a “bad” male. In contrast, a male gets a positive payoff from mating with any female, though his payoff is higher if he is “good” than if he is “bad”.

The study looks for evolutionarily stable equilibrium behaviours, in which females are doing as well as they can against male behaviour and males are doing as well as they can against female behaviour. It shows that extended courtship can take place, with a good male being willing to court for longer than a bad male and the female delaying mating. In this way the duration of a male’s courtship effort carries information about his type. By delaying mating, the female is able to make some use of this information to achieve a degree of screening. Because bad males have a greater tendency to quit the courtship game early, as time goes on and the male has not quit it becomes increasingly probable that he is a “good” male.”

Random application of economic theory amuses me greatly.  Especially when applied to relationships which I’m sure says a number of horrible things about the transactional way I’m starting to view human interaction.

So here’s my question:  Where does the quality of the female come in?  Presumably it is a variable that affects both her behaviour/strategy as well as the payoff to the guy.  Some women are assets.  Some are liabilities.  (The same can be said for men.) It was also pointed out to me that the fundamental assumption was that the female assesses that being stuck with a bad male is a negative payoff when we know that is probably not true.  There are a lot of people in bad relationships.  I suppose loss aversion kicks in at some point.  You’ve already invested so much time/energy into the relationship.  My economist brain says that this is not rational.  Decisions should always be made with future payoff (not past payoff) in mind.

Constraint optimisation

January 13, 2009

Excuse me while I muse aloud about my exercise regime.  Char Kuay Teow is evil.

Here are my constraints:  I’m supposed to do a PT session once a week.  It takes me a couple of days for my arms to recover from a PT session so more gym during that time is unrealistic.  But ideally should be at the gym at least 1 other time.  Classes are fun but I’m limited by the schedule.  Then, I’m supposed to do cardio (the equivalent of a 6km or so run) twice a week.  Cardio should preferably be whole body since I have no upper body strength to speak of.  I am a sucky swimmer.

So now I’m thinking about constraint optimisation and efficiency.  What’s the best way to get my workouts in without spending too much time on them/disrupting my life?  This is what I’ve come up with…

M – (interchangeable with Wednesday) Run home from work – I figure that would be the most efficient way (time wise) to incorporate running into my schedule. Pilates class at the gym is an option on Mondays.

T – PT session

W – Rest

Th – Rest.  Or a really sissy Gym class called Flex + some sort of workout

F – Rest.  If I’ve missed a workout, I could conceivably do it early and then have late dinner/drinks (which would be common for Fridays anyway).

Sa – (interchangeable with Sunday) Long run or a swim

Su – Gym

I wondered if this would work.  Then I realised that Chinese New Year kinda fucks up my exercise plans!  Oh dear.

A sub-optimal outcome

December 17, 2008


A funny email that was circulating around at work.  We economists are rather geeky.  Another reason why I’m convinced there is a matching problem.  My next question is whether better data leads to better decisions and changes in behaviour.  Ha.

From The Washington Post:

“I have never met a Japanese man who did not want me to be his mommy.”

That is the reason, Takako Katayama says, that she has not married. At 37, she has carved out a comfortable life here in Tokyo, with her own apartment, a good job at a cable television network, and a network of family and friends.

She has not closed the door on marriage and children. When she meets girlfriends for dinner, they ask each other, “Where are the good guys?” But she refuses to settle for a man who works long hours, declines to share in child-rearing and sees marriage mainly as a way to acquire lifetime live-in help.

“I want a mature, equal-partner kind of marriage,” she said. “Anyway, there are complete lives without a baby.”

Therein lies a dismal prognosis for Japan and for many of the other prosperous nations of East Asia. In numbers that alarm their governments, Asian women are delaying marriage and postponing childbirth.

In Japan, the percentage of women who remain single into their 30s has more than doubled since 1980. The trend is similar in Taiwan, Singapore, South Korea, and the booming Chinese cities of Shanghai and Beijing.

Equally annoying, according to Katayama, is the rarely stated but almost universal expectation of Japanese men to be fed, clothed and picked up after. “I am willing to take care of and give comfort to a man whom I care about, but that does not mean I want to be his mother,” she said.

So my thought when reading this article was that like Katayama, I’m only happy to “look after / take care” of a guy who doesn’t actually need the looking after.  Then I realised that this value proposition doesn’t  actually make any logical sense –  Only willing to supply where there is no demand?  Somehow.

Sell immediately

July 16, 2008

If it wasn’t already obvious, I increasingly see relationships (romantic and otherwise) in economic terms. I surprise myself at how callous I can be. There was once a time when I’d be much much more generous with my time and affection. But now when the relationship value proposition and the returns are consistently one-sided over a period of time, I’m increasingly willing (and able) to walk away. I wonder what that says about the person I’m becoming.

I was also wondering about what that means for me as a Christian but then for QT yesterday, I read this verse – Matthew 13:58 ” Now He did not do many mighty works there because of their unbelief.” And decided that I wasn’t going to guilt-trip myself anymore. I’m a pretty stand up friend by most counts. Past a point, even Jesus didn’t bother.

I suppose that love analysed in economic terms is methodical and almost clinical but I still loved this article in the NYTimes. This passage in particular totally cracked me up.

“In love, the data is even clearer. Stay with high-quality human beings. And once you find you that are in a junk relationship, sell immediately. Junk situations can look appealing and seductive, but junk is junk. Be wary of it unless you control the market. (Or, as I like to tell college students, the absolutely surest way to ruin your life is to have a relationship with someone with many serious problems, and to think that you can change this person.)”

Ha! Tell it like it is. Friends, lovers… Junk is junk. Don’t waste time. “It feels different this time” and other similarly ridiculous statements trigger my reflex eye-roll. There have been situations where I’ve been too sentimental. If I had to do it again, I would have sold much quicker. Much much quicker. Also, am I the only person who thinks it is absurd that people expect me to continue to be charming to them after they’ve been bastards to me? Bizarre.

Anyway, before I get all self-righteous and indignant, I should probably also point out that the inherent assumption underlying the entire article is that just as you are screening for “high-quality bonds”, so is the other person and the value-proposition should probably work both ways.