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.