My cousin is preparing his exam. He needs tea. He wants me to go down and make it in the middle of the night. He gains control over my biscuits in my absence and black mails me, nudging me towards a "win-win" situation whereby i make tea for him to get my biscuits back. For me, this is pure black mailing. I don't want to make tea for him. I'd love him to do so instead since I walked a lot to buy the biscuits. I'd like tea for myself though. Here are the strategies for both of us. I've little to decide which strategy would make me better off. My motive is not to allow him maximizing his utility while trying to maximize my own.
The Contract
My cousin made an offer which I accepted: "within 20 mins leave the room to make tea and I will give your biscuits back to you."
Choosing Best Strategy (or Strategies) for Me & Cousin
(Click to enlarge)
I chose strategy en-rectangled by the green one. Given the information (my guess actually), my cousin is desperate for tea. Missing tea or getting a really bad one would decrease his utility, in turn giving me the pleasure of victory over him, which i'd see as a compensation for the loss I incurred in making tea (time, effort, etc.). It really happened that he didn't take tea because it lacked sugar; i must be overjoyed! (Actually, i didn't like him not taking the tea on moral grounds.)
Discussion with Cousin: Flaw in the Preceding Diagram & the Winner is...?
When I discussed this game with my cousin after the game was complete. He revealed that he wasn't desperate for tea at all; in fact he didn't want it. He loves tea that lack sugar and is strong; just the kind of thing i tried to make. He didn't take tea, the kind of tea he claims he like most, because he didn't want it. His sole goal was to force me into taking trouble of making tea at an odd time. He wanted to see me disrupt my studies.
Removing the wall of information asymmetry, we come to know that the game matrix shown above was flawed because it failed to anticipate all possible moves with all intentions of all players. It failed to take into account what my cousin was really wanting to do, i.e., he never wanted tea, he wanted me to take the pain of making tea in the middle of night!
Finding the Equilibrium Strategy
Was the move that I execute lead all players towards equilibrium - an action that no one regrets? This depends on what our perceived benefits or costs were associated with each action, as I will show.
Situation 1: Equilibrium not reached with original strategy: Cousin wins
Dominant strategy for my cousin. I worse off. Hence, i'd been better off by not making tea, because it would've saved my time.
Situation 2: Equilibrium reached with my original strategy
On the other hand, if at the moment i associated greater utility to a cup of tea with biscuits, i did the right thing. Hence, my original strategy resulted in equilibrium.
