# Study-Discussion Questions on Game Theory

Study Questions:

1. What precisely defines a strategic situation? Why is rational choice more complicated in strategic situations?

2. What is a Nash equilibrium? Are Nash equilibria necessarily Pareto optimal? Why or why not?

3. What does one need to know in order to define a "game"?

Discussion questions:

1. Suppose that the social benefits of some outcome are the sum of individual benefits (and thus that individual benefits can be measured and added). In that case is the following principle P true?

P: If each individual chooses what maximizes his or her own benefits (given the choices of others) then the outcome will maximize the social benefits.

In his "invisible hand" argument does Smith assume that P is true?

2. Are the choices of traders on competitive markets strategic or non-strategic choices?

3. Since the best strategy to play in a prisoner's dilemma does not depend on what strategy the other player chooses, is a prisoner's dilemma really a strategic interaction?

4. What can players facing a prisoner's dilemma situation do to avoid the sub-optimal mutual defection outcome?

5. Consider the following game, which is a variant of the so-called "ultimatum game," concerning which a great deal of experimentation has been done. The first player can propose to divide \$10 evenly between himself/herself and the other player -- with each getting \$5, or the first player can propose a division whereby he or she takes \$9 and the other player gets \$1. The second player then gets to accept or reject the proposed division of the \$10. If the second player accepts the division, then the parties get what the first player proposed. If the second player rejects the division, then the two parties get nothing.

a. Draw the extensive form of this game (which is pretty easy)

b. What would game theorists predict will happen? What do you think actually happens? Why?

c. If you want a challenge, draw the normal form of this game and identify all the pure-strategy Nash equilibria.

6. Suppose two individuals are playing the following game: at each round they face an interaction which, if it were a one-shot game, would be a prisoner's dilemma. But at the end of each round a die is rolled and if it comes up with any number other than one, the two players play again. If it comes up with a one showing, then the game is over. Is the best strategy in this game the same as the best strategy in the one-shot prisoner's dilemma?