game theory

Question 1

What are “Beliefs” in game theory

Answer 1

a player’s assessment about the strategies of the others in the game
a belief of player i is a probability distribution over the strategies oft he other players.

Question 2

what is Probability distribution:

Answer 2

How often do you expect the other player to use each action
p ∈(0,1) and 1 – p ∈(0,1)

Question 3

What is Pure strategy:

Answer 3

You will always play the same strategy, e.g. always
“catch” or always “drop” .

Question 4

Mixed strategy:

Answer 4

Sometimes you play one way, sometimes another.

Question 5

Strict dominance

Answer 5

For one strategy to dominate another it must deliver strictly more than the other. Not equal to or larger than!

Question 6

What is a general assumption of rational players related to what strategy they play?

Answer 6

Rational players do not play dominated strategies.

Question 7

Pareto efficiency

Answer 7

an outcome being “better in every possible way”. A change is called a Pareto improvement if it leaves at least one person in society better-off without leaving anyone else worse off than they were before.

Question 8

Rationalizability assumes: (3 things)

Answer 8

People form beliefs about other’s’ behavior
People play their best response based on these beliefs
These facts are common knowledge among players

Question 9

Nash equilibrium

Answer 9

A pair of strategies where one player’s choice is optimal given the other player’s
choice and vice versa. Neither has an incentive to change what they are doing.

Question 10

First strategic tension

Answer 10

There may be a clash between individual and group interests.
Doing what is in the interest of each individual player may lead to an outcome that is bad for the group as a whole.

Question 11

Second strategic tension

Answer 11

Strategic uncertainty

You are rarely certain that your beliefs about other’s behavior are correct.

Question 12

Third strategic tension

Answer 12

There may be inefficient coordination

Question 13

A mixed strategy Nash equilibrium

Answer 13

In a mixed strategy Nash equilibrium no player has an incentive to change how often
they play each strategy given how often the other player plays each strategy. These
are randomizes strategies but do need to be played a certain proportion of time to be
an equilibrium.

Question 14

ASYMMETRIC INFORMATION

Answer 14

Different players have different information.

The information that one player has but the other lacks is called private information.

This can be about the preferences or characteristics of the player, but also information about external events the other player does not have.

Question 15

Adverse selection

Answer 15

If high quality can not be distinguished from low quality, the high quality may be driven out of the market. The market may disappear as a whole.

Question 16

Principal-Agent problem

Answer 16

One party requires another party to act to achieve a goal they cannot achieve on their own. The principal determines the goal, the agent acts.

The problem arises when:
The agent has the information needed to achieve the goal and the principal does not.
The principal does not observe the agent’s ability or effort.
The attainment of the goal does not depend only on the ability and effort of the agent but also on random circumstances.
Principal and agent have different objectives.

Question 17

What is Bi

Answer 17

Bi is the set of strategies for player I that are best responses, over all of the possible beliefs of player i.

Question 18

What is UDi.

Answer 18

UDi is the set of strategies for player i that are not strictly dominated.