# Lecture 021

Issue

• many (inconsistent) goal people have

• ranking subjective feelings are inconsistent

Dominant strategy: Best strategy indifferent of other agents Equilibrium: a set of strategies composed of the best strategy for each player Prisoner's dilemma: - assume cannot talk to one another

Observation:

• the ordering of choice does not matter

• everything is included in utility function

Weak dominant strategy: sometimes better but never worse Zero Sum Game: no equilibrium Nash equilibrium: no player can do better by unilaterally changing strategies

## Homework

1. school lists

a. The question is unanswerable because it doesn't specify the utility associated with not getting into any college. This issue is visible in the following example: suppose inability to get into any college will give you a "simple ordinal utility" of 0.999, and your chance of getting into schools (from 5 to 1) is as the following set {A=96%, B=97%, C=98%, D=99%, E=100%}, then a rational agent would not consider applying school E since the utility of getting into E is essentially equivalent as not getting into any of the schools. However, suppose inability to get into any college will give you a "simple ordinal utility" of negative infinity (you have to get into at least one school or else the universe will blow up), a rational agent will choose to apply school E. If the missing piece of the question is specified, a rational agent will calculate the expected gain as the utility for each possible action (assuming the agent only care about the expected value and is indifferent to the standard deviation). If the overall utility function that takes the probability into account is known to the agent, then the question becomes trivial as selecting the maximum action associated with the utility.

b. Yes. With the problem specified and clear, there exists a rational decision. College application is a major decision in my lifetime. Before I apply schools, I actually wrote a python script to simulate the best strategy to apply schools among my school lists in order to reduce my chance of not getting into any school below 1% while getting into better schools. However, such calculation, even reduced to a relatively simple form as above, require advanced statistical skill. I can expect people who don't know how to write programs to aid their calculation could have a hard time convince themselves that they have made rational choice. In reality, the problem above can be more complex. Even with the aid, I failed to prove that I made a rational decision because the chance of getting into a school is subjective and getting into colleges are not independent events (they are at least correlate to the GPA). Therefore, in reality, it is possible for me to act "rational" according to the information and prediction that I have. However, since individuals can't know the complete set of actions and result of the actions, one cannot choose the best series of actions.

1. prisoner's dilemma a "description" or how people "should" act. It sometimes is a description. (There are people out there who is very rational - like room selection) It also provide a baseline of how people should act.

2. prisoner's dilemma is a thought experiment

3. to some extend, it is never a one round game. there for it is not applicable in almost all cases

4. Judge whether this is actually a prisoner dilemma. Other utility?

5. not applicable with one-round

6. only the last round is prisoner's dilemma

7. It is only a thought experiment that perhaps will lead to greater insight with RCT

8. Nash equilibrium is, knowing the player's current decision, changing one's strategy would be worse for every player. Nash equilibrium is good for policy maker to make cost-efficient policy. (eg. traffic light)

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