Games people play : 1

I was talking to to my friend's daughter, Roshni, or BM as I fondly call her, over the phone and somehow the topic of Games Theory came up in the context. My efforts to explain that over the phone turned out to be futile and hence this post.

Let's first start with a puzzle. Ram and Shyam are two thieves and got caught by the police. The police is separately interrogating them. They have the options to confess their crime and implicate the other thief. If none of them confesses, without having a solid evidence of their theft, will charge them falsely for carrying illegal weapons, and each one of them will be behind bars for two years each. However, if Ram confesses and implicate Shyam, Ram would be freed and Shyam would go to jail for 10 years and same option is available with Shyam. If both of them confesses, then both of them would go to jail for 5 years. Diagrammatically, we can show it like this:

		Shyam
		confesses	doesn't confess
Ram	confesses	Ram: 5 years Shyam: 5 years	Ram: 0 years Shyam: 10 years
	doesn't confess	Ram: 10 years Shyam: 0 years	Ram: 2 years Shyam: 2 years

The question is whether to confess or not so as to minimize the pay-off. If we consider both Ram and Shyam to be rational enough in logical thinking, they might think in the following line: "If I confess, then I would go scot-free and he would go to jail for 10 years. Good for me - hence I will confess." Fair enough. However, if both confess thinking in the same rational manner, both of them would go to the jail each serving 5 years. What if they take the irrational approach - that neither of them confesses. Despite the risk of other confessing, if both them actually end up NOT confessing, that gives them the best pay-off - only two years in prison for each!

This is really amusing and remarkable. Individual rational strategies in the above situation actually resulted the individuals to be in a worse situation! In the parlance of The Games Theory, the dominant strategy is to confess to achieve the most beneficial result to all the people concerned.

The whole idea is to develop a strategy to play a game so as to decide the pay-off. The game, in this context, may not necessarily be a game. The Game Theory applies to economics, social sciences etc. Let me give you one for example:

Two players play this game in a round circular board. There are smaller round pegs and each player takes a turn to place the pegs on the board. The pegs cannot overlap and a player cannot give pass. The last player to place the peg (after which there is no more space left to place a peg) wins the game. All the pegs are of same size.

The question is - can we develop a strategy to win this game? Yes - there is one simple strategy. Player 1 places her peg in the centre. After that for each peg placed by Player 2, Player 1 places is peg a diametrically opposite position. Think a while and you will know that Player 1 always wins in this strategy. Extending it further, we may conclude that (provided both the players are smart enough to devise the strategy), whoever plays first always wins!The following series of images show the first three moves.

Player 1 places her peg at the centre.

Player 2 places at her desired location

Player 1 places her peg at the diametrically opposite position

And this way, the Player 1 wins.
Enough to initiate you with some ideas of Games Theory. There's a lot more to it - which I will continue in some other post.