I have been reading a bit on game theory and I find the subject fascinating. Thought I could share some interesting ideas.
A game is essentially the following - there are a set of agents and each of them follows a particular strategy. A game could be zero sum - i.e. only one of them win or it could be co-operative where the agents need to co-operate to get something done. I think game theory quantifies one of the biggest dilemnas of mankind - for self or common good? Meaning, if you are to do something, do you do it to maximize personal benefit or maximize joint benefit. Consider the famous Prisoner's Dilemna - there are 2 prisonors in different rooms. They have the choice of ratting or keeping quiet. If, both don't rat, both go free. If one rats, the other goes to jail for 10 years. However, if both rat on each other, then each goes to jail for 5 years. So, what is best for each prisoner to do?
If he assumes that the other prisinor is purely concerned only about himself, and is going to rat to maximize his personal benefit, it is in his best interest to rat as well. If he didn't he would go to jail for 10 years as opposed to 5. But, not ratting works if he has a strong reason to believe that the other person is not going to rat. If both people share this belief, both go free.
This brings up the famous Nash Equillibria. A system is supposed to be in Nash Equillibria if each party is following the best strategy for itself given the strategy that others are following. Everyone is doing the best for himself under the set of conditions. So, no one has reason to change strategy. Hence, it's in equillibrium. If, a set of people are nice to each other, then it's best to be nice, assuming that others are going to be nice. This can go on forever. It's stable.
But, what if suddenly someone is not nice. Even though it's not to his best interest, assume he is like that. What happens? A evolutionary stable strategy is one in which members are not affected by a new entrant with a different strategy. Meaning, a player who suddenly changes his strategy cannot harm others. A strategy which assumes no trust. It is robust. This is not necessarily the best for everyone. But, it's safe for everyone. It avoids losses, but it also minimizes gains. All strategies that animals follow are evolutionarily stable.
So, being good as a strategy works if everyone else is being good. Everyone does well. It's a Nash Equillibria. But, it's not evolutionarily stable. Even, if one of the players decide to cheat, all players need to take a more defensive strategy to prevent losses. What this means is that interest in the common good works as long as its shared across players. Even if one takes up a selfish strategy it forces others to take up a similar strategy.
A great example of this phenomena is the building up of global arsenals. It's a huge waste to do so, but it's the safest strategy. You don't gain anything, but you make sure that you lose nothing. It's evolutionarily stable, as it doesn't matter if another country likes you or not. But, if you assume that all countries like you, and all countries do that then it makes more sense to not have any arsenal. The basis for all this waste is a simple lack of trust.
The India-Pakistan conflict (or any conflict for that matter!) is another excellent example. Each side takes up more and more paranoid strategies, which make sure it doesn't lose, but it makes it more and more difficult to resolve as none can let down on it's strategy - it leads to immediate loss!
This kind of logic also extends to personal relationships, signing a pre-nuptial agreement is against the spirit of blindly trusting your partner. This probably reduces the happiness that you get out of your married life, but it makes it a lot safer for you if things go awry. Trust. Short on letters and long on benefits :D! That was quite a philosophical end to a very practical subject.
PS: More here. It's in any kind of system which has competition. Politics. Auctions. Markets. Biological systems.
A game is essentially the following - there are a set of agents and each of them follows a particular strategy. A game could be zero sum - i.e. only one of them win or it could be co-operative where the agents need to co-operate to get something done. I think game theory quantifies one of the biggest dilemnas of mankind - for self or common good? Meaning, if you are to do something, do you do it to maximize personal benefit or maximize joint benefit. Consider the famous Prisoner's Dilemna - there are 2 prisonors in different rooms. They have the choice of ratting or keeping quiet. If, both don't rat, both go free. If one rats, the other goes to jail for 10 years. However, if both rat on each other, then each goes to jail for 5 years. So, what is best for each prisoner to do?
If he assumes that the other prisinor is purely concerned only about himself, and is going to rat to maximize his personal benefit, it is in his best interest to rat as well. If he didn't he would go to jail for 10 years as opposed to 5. But, not ratting works if he has a strong reason to believe that the other person is not going to rat. If both people share this belief, both go free.
This brings up the famous Nash Equillibria. A system is supposed to be in Nash Equillibria if each party is following the best strategy for itself given the strategy that others are following. Everyone is doing the best for himself under the set of conditions. So, no one has reason to change strategy. Hence, it's in equillibrium. If, a set of people are nice to each other, then it's best to be nice, assuming that others are going to be nice. This can go on forever. It's stable.
But, what if suddenly someone is not nice. Even though it's not to his best interest, assume he is like that. What happens? A evolutionary stable strategy is one in which members are not affected by a new entrant with a different strategy. Meaning, a player who suddenly changes his strategy cannot harm others. A strategy which assumes no trust. It is robust. This is not necessarily the best for everyone. But, it's safe for everyone. It avoids losses, but it also minimizes gains. All strategies that animals follow are evolutionarily stable.
So, being good as a strategy works if everyone else is being good. Everyone does well. It's a Nash Equillibria. But, it's not evolutionarily stable. Even, if one of the players decide to cheat, all players need to take a more defensive strategy to prevent losses. What this means is that interest in the common good works as long as its shared across players. Even if one takes up a selfish strategy it forces others to take up a similar strategy.
A great example of this phenomena is the building up of global arsenals. It's a huge waste to do so, but it's the safest strategy. You don't gain anything, but you make sure that you lose nothing. It's evolutionarily stable, as it doesn't matter if another country likes you or not. But, if you assume that all countries like you, and all countries do that then it makes more sense to not have any arsenal. The basis for all this waste is a simple lack of trust.
The India-Pakistan conflict (or any conflict for that matter!) is another excellent example. Each side takes up more and more paranoid strategies, which make sure it doesn't lose, but it makes it more and more difficult to resolve as none can let down on it's strategy - it leads to immediate loss!
This kind of logic also extends to personal relationships, signing a pre-nuptial agreement is against the spirit of blindly trusting your partner. This probably reduces the happiness that you get out of your married life, but it makes it a lot safer for you if things go awry. Trust. Short on letters and long on benefits :D! That was quite a philosophical end to a very practical subject.
PS: More here. It's in any kind of system which has competition. Politics. Auctions. Markets. Biological systems.
12 comments:
In the social context, everyone I guess tries to minimize the maximum loss they could make
Whoa!!! Originating from Applied Mathematics, Game Theory has widespead application in economics... to determine optimum choice under conflicting situations ...
As a continuation of my post in Prashanth's Blog, of dragging any topic to movies, here's more .... Remember "A Beautiful Mind" ... where Prof. Nash uses Game Theory to determine his friends should date brunettes and blonde !!!!
Well "Nash Equilibrium" revolutionized economics; for which he won Nobel Prize ... But Game Theory originated in the field of Mathematics....
... and anyone got any explanation for why is there NO Nobel Prize for Mathematics ( when every other branch of science has a prize.. Physics, Chemistry, Medicine ) ?????
I've come across some intriguing pointers; like Alfred Nobel hated the most celebrated mathematician of his time, who he didnt want to win the prize ... to scandalous ones ... like his mistress had affair with a mathematician ..
There is a site " The Nobel Prize Internet Archive" which has this topic... " Why is there no Nobel Prize in Mathematics?"
Yes, game theory is very intuitive and of course one that has had profound impacts on economics, biology, etc. BUT, there are some deep assumptions in game theory whose implications may not be all that obvious -- to do with rationality, to do with what each player knows (i.e. partial vs full information), and the properties of the payoffs (numbers that can be summed). If you read the original [Von Neumann and Morgenstern] book, as well as the early works of [Luce and Raiffa], [Axelrod]'s "evolution of cooperation", [Ken Arrow] and [Amartya Sen], you will see that these assumptions make its real-world interpretation a very complicated and unituitive beast. :) All the signs of a useful theory, I guess.
Who is Intern? I want to know her.
I thought it was Alf Nobel's wife who had an affair with a mathematician...
Game theory is actually a favourite topic of mine, being at the intersection of Artificial Intelligence as well as Multiple Human Opponent Strategy Gaming, which interest me immensely.
Apart from simple things like Tic-Tac-Toe, Chess is the purest application of game theory in the world of strategy games; you try to counter your enemy's strategy that will be aimed at inflicting the maximum losses on you. Games like bridge involve a combination of estimating odds as well as opponents' strategy; that makes it even more interesting! But of course, the most interesting are the myriad multiplayer computer strategy games; balancing defense vs offence is walking on a razor's edge, and is absolutely exhilarating.
Prashanth,
you made The Game Theory, a real "game" theory
.. chess, bridge ..and ... tic-tac-toe!!!
Kidding!!!
Who is this Anon; who wanna know me?
As I said earlier...
I am a real nowhere girl,
Sitting in her nowhere world,
Making all my nowhere plans, for nobody..
*Intern
And I'm a idle little kid
Idling away his idle time
In this idle world of ours
Making idle plans for the idle days
That fill up my idle existence...
[anon] It is interesting why there is still no Nobel Prize in Maths. I think the quivalent to the Nobel prize is the fields medal. But, it's given only to mathematicians under 40. So, you should have done breathtaking work pretty early in your career so that it gets recognized before you are 40. I think it's even tougher to get a Fields Medal because 4 are awarded it every 4 years.
Actually, peace, economics were incorporated only later on by the Nobel Committee. It's weird why you would give one for peace. Maybe it's for leadership or something like that.
[linearizer] Yes, I agree with you. In real life decisions are hardly rational. They are based on a lot of other factors. Example, the perception by the media of a decision largely reflects if it is made or not. Though in some times it is good, it leaves a lot of space for jingoistic behaviour.
make its real-world interpretation a very complicated and unituitive beast. :) All the signs of a useful theory, I guess.
Loved that line. All great theories tend to be highly non-intuitive atleast to the naive bystander. Quantum Mechanics, Relativity. Most great theories find little acceptance when they come out. If they did, it wouldn'
t be great, as someone would have thought through that already.
[prashanth] I think a game like poker or bridge is interesting as it is not purely rational. It's a combination of optimal play combining some non-tangible factors about your opponent. Personality, previous history etc etc.
I miss playing computer games. Don't know if it's because I have overgrown them or I feel I am too old for them. Or not supposed to be playing them!
[prashanth and intern]
Beatles. Nowhere man.
He’s a real nowhere man,
Sitting in his nowhere land,
Making all his nowhere plans
For nobody.
Doesn’t kave a point of view,
Knows not where he’s going to,
Isn’t he a bit like you and me?
Nowhere man, please listen,
You don’t know what you’re missing,
Nowhere man, the world is at your command.
Most interesting! :)
*off to read more*
Can't provide as much insight as the rest... but i agree... enthralling it was.
Ramani,
I think Nobel's Will provided for prizes in 5 fields: Physics, Chemistry, Medicine, Literature n Peace. So it was only Economics (not economics and peace) which was added later. (Not sure - plz confirm) Interestingly though all other awards are decided by Swedish Academy, but Peace prize is by Norwegians! Thanks for information on Fields Medal.
[ditty] good good have fun
[karuna] thanks for dropping by
[anon] hmm..i woulndn't think he had the peace prize..but considering the fact that he was the biggest manufacturer of dynamite and the Nobel Prize was a way for him to give back to the world..it makes sense...
Peace by the Norwegians..whats the reason for that..interesting..
I find all these Scandinavian people very nice..structurued, disciplined..
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