Sunday, July 22, 2007

An Intriguing Game

Unfortunately the world works just like this game. Sometimes we imagine, if everyone obeys traffic rules, the traffic congestion would be dramatically reduced. But people break the rules. If every country in the world destroys their nuclear weapons, this will be a much safer world. But we will never live to see a day with a nuclear-free world. If everyone unites and strive for the greater good, this will be a much better world. But human won't unite. The reason? The same as in this game. As long as there are competitions, there will be "good" and "bad" people who assume their own niches in the equilibrium of the complex net of interactions. Game theory dictates it.
Game theory is fascinating. Since I first learnt about it some years ago, I have been absolutely enchanted by how it seems to apply to everything in this world - including, but not restricted to animal behaviours (including human's), evolution, cultural revolution, economics, politics, nuclear warfare, global warming treaties etc. The implications of game theory just seem to pop up everywhere.

What is game theory?

Game theory is just what it says - the theory of games. Examples of theory of games could range from anything as simple as how to tackle tic-tac-toe, to what happens when two players play checkers perfectly (which was solved just recently). However, in its modern word usage, game theory is not about winning and losing in a table-top game (which is in the field of combinatorial game theory) - it's more about everything that involves competition, everything that involves different parties aspiring to maximize their own return (among others). Basically this covers almost every organic interaction. Games, in the context of game theory, are played between countries and populations.

Consider this interesting game:

An investment game is played in a group of 4. In each round of the game, each player will make a choice of investing 10 dollars or investing nothing. At the end of each round, the sum of the investment by the four players is pooled together, and each player (regardless of the amount he has invested) will get 40% of the sum in the pool. For example, if everyone invests 10 dollars, then there will be 40 dollars in the pool, and therefore everyone will get 16 dollars at the end which means a 6-dollar profit.

By doing some analysis, the outcomes of the game can be described as follows:
4 x 10 dollars: Everyone earns 6 dollars - a total profit of 24 dollars.
3 x 10 dollars: 3 player who invested will earn 2 dollars, the person who didn't invest earns 12 dollars. A total profit of -6 dollars.
2 x 10 dollars: The 2 investing players LOSE 2 dollars, the 2 non-investing players earn 8 dollars each. A total profit of 12 dollars.
1 x 10 dollars: The investing player LOSES 6 dollars, the 3 non-investing players earn 4 dollars each. Total profit of 12 dollars.
0 x 10 dollars: Nobody invests, nobody earns or loses anything. Total profit is zero.

At the first glance of the game, it seems that it would be ideal if everyone just keeps on investing in every round - that would be the best outcome, everyone earns and the total profit is the highest. However, a few rounds into the game, someone might realize - hey wait, if the other three players continue to invest and I stop, I will earn 12 dollars, more than the previous scenario! And hence some people will stop investing. Then some other player may stop investing as well, and now the two non-investors get 8 dollars, at the expense of the investors' loss! In some rounds everyone might get selfish, and it ends up as the 0 x 10 dollar case - at this point some people realize that someone has got to invest to keep it going. So in the end the game will bounce somewhere between all the scenarios, but it will not stay at the 4 x 10 dollars, the supposedly best option for everyone.

Unfortunately the world works just like this game. Sometimes we imagine, if everyone obeys traffic rules, the traffic congestion would be dramatically reduced. But people break the rules. If every country in the world destroys their nuclear weapons, this will be a much safer world. But we will never live to see a day with a nuclear-free world. If everyone unites and strive for the greater good, this will be a much better world. But human won't unite. The reason? The same as in this game. In this page, you can see how the theory behind this game applies to real-life scenarios, ranging from political science, economics to athletic competitions.

As long as there are competitions, there will be "good" and "bad" people who assume their own niches in the equilibrium of the complex net of interactions. Game theory dictates it.

p/s: Yes, this game is a variation of the
prisoner's dilemma.

4 comments:

Ai Ling said...

I played this game before in a research study organised by the econs dept UniMelb. Got so angry when I invested so much money in the first few rounds but the others didn't and I ended up getting so little in the end till I decided to play the 'bad girl' too. Aihs, if everyone cooperated, all of us would have money together and we would also get the same amount by the econs dept. Life is life. People are selfish.

Eric Fu said...

I agree that game theory is fascinating. When I first learn about the prisoner's dilemma and Nash equilibrium two years ago, I was pretty surprised at the result. I mean, while it makes total sense, it's still something with a tinge of surprise. And it's mathematics!

crushedguava said...

fascinating indeed.

you should watch Liar Game, a Japanese drama (I have all the episodes). the acting is terrible, but the concepts are fantastic. go google and find out.

my first encounter with game theory was when i read an old book i found at home which was talking about tic tac toe, and i never lost a single game after that!

youngyew said...

ai ling: Yeah agreed, that's the whole point of my post... Unless you have authority or control over other's behaviour, you will always end up with such non-optimum outcomes. :(

Anyway I learnt about this game because Xuan Ni went for the same experiment. :)

eric fu: Yeah maths rocks! :)

crushedguava: Haha how come you went and watch the show if the acting was terrible? :P