In the game theory class last week, the lecturer played a game with all of us. The rules are as follows: Every student should write down an integer between 0 and 100 (both ends included). The TA will collect all the numbers and calculate the average, then multiply the average by 0.7. The final number is the target number. Whoever writes a number closest to the target one will win 20 dollars.

After careful consideration, I wrote 1. Game is about maximizing my own payoff under some certain belief about others’ behavior. I belief every one of my classmates will be rational enough to choose an integer between 0 and 70. And therefore I will choose 70*0.7=49. Knowing that others will choose 49 as well, I will choose 0.7*49=34 instead, so on so forth. The number will finally be within 0 and 1. So 1 is rational.

But the point is: is everyone rational? The rationality assumption states that every player aims at maximizing his or her own payoff. But in this casual game, many students might have been playing around. In other words, they might have written down some random number regardless of rational expectation of people’s behavior. Therefore the final answer became hard to predict.

These days, our house always undergoes cleaning problems in the kitchen. I always see dishes piled up, left unwashed in the sink, when I want to prepare food. The only choice for me is to clean it up. This is an example of positive externality. The players do not have an incentive to clean the sink, because:

1) If they just leave the dishes unwashed, no one will blame them explicitly;

2) If they let others wash the dishes, they will be better off because they will enjoy the tidy cooking environment.

In this game, if everyone is rational, they will just leave the dishes. But is this reasonable? Of course not! If it were the case, no one would have been able to use the kitchen. The possible reasons for this are:

1) The players meet often, therefore it’s better to cooperate and be friendly to each other. This might have changed their payoff in that cleaning yields higher payoff.

2) Some players in this game value a clean environment more than others, and they end up cleaning all the dishes. If cleaning the sink is always a best strategy for a certain player but not for others, she will surely bear most of the cleaning work. Eileen and I are both of this kind.

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