The Negotiation Game: Believe me, I'm crazy !

Can being crazy be helpful to anybody? Not if he’s really the only crazy person in a world full of rational* people. Being rational may be a boon for an individual but being perceived as a rational may land him into trouble. And at times it is very harmful for societies or groups if all of its members are rational.* The society may be better off if all the members behave somewhat irrationally. Confused? Welcome to the game-theory land.

Let’s play a simple game. Suppose I have a ticket for a movie I don’t want to watch. The ticket is worth Rs.100. Now suppose you are the only person I know who wants to watch that movie. You can purchase the ticket from the counter for Rs.100; or else you can buy it from me if I offer a discount. I will, obviously, have to sell the ticket at a price less than Rs.100. At what price do you think would the deal settle? Should I sell it at half the price – Rs.50 – and incur a loss of Rs.50? No. That is not the solution. The solution depends on the negotiation which goes on between you and me.

Simply put, the ticket is worth nothing to me, and worth Rs.100 to you. We both know this quite well. I have only one buyer (you) and you have only one seller ready to offer a discount (me). Suppose I have a reputation of being rational and intelligent. I think only of myself. In every deal, the only thing I care about is to maximize my profits. I never get carried away by sentiments or principles and may not keep promises. You know that. Now suppose you offer me Rs.40 for that ticket. Since I know that the ticket is worth Rs.100 to you, I may insist on a higher price. I would demand Rs.90 because I know any price below Rs.100 would be beneficial to you. You decline. You say you won’t pay more than Rs.40. Then suppose I say I would settle on Rs.85, but no less. Take it or leave it. I say I wouldn’t lower the price further.

Should you believe me? You know that if I move out of the deal I don’t have any other buyer for my ticket. I would not gain anything at all by moving out of the deal. I would be in a better position if I accept rupees 40 from you. (And, for that matter, even a single rupee!). I have a reputation of being rational. So you know I won’t move out. Suppose I perceive you as a person who makes arbitrary decisions not totally based on personal profit, I must then fear that you would rather buy a ticket from the counter for Rs.100 than paying me Rs.85. (because maybe you don’t like my face L). Hence I must accept whatever price you propose. Since you know all this and also know that I am rational, you would offer even lower price. Maybe Rs.10. Since I know you’re crazy and won’t even mind a loss of 90 bucks, I would accept Rs.10 from you – because I have no other option!

So I finally end up selling to you Rs.100 ticket for Rs.10. What a pity! But what went wrong? Did my being a rational man go against me? Absolutely not. The fact that I am rational can never go against me. It is always beneficial for me if I am rational. What went against me was my being perceived as a rational being. Since you believe that I am rational, you won’t let the bargain go in my favour. And just because I believe that you are crazy, you end up as a winner in the game.

Again, welcome to the game-theory land !

*[A rational person is one who can guess and interpret all the moves in the game. He is greedy and selfish. His only motive is to make the highest possible profit (or the lowest possible loss) for himself. He is extremely intelligent. About rational members beng harmful to groups, I will write in another post soon.]