Week 3

Question 1

What are the assumptions of a game in game theory in normal form?

Answer 1

1. All players understand how actions lead to outcomes and how outcomes determine theirs and others’ utilities.
2. The players that populate the normal form are assumed to have the same model of their situation (i.e. they all have common knowledge about the game).
3. For finite sets of action profiles A, we may replace all utility functions by their complete and transitive preference relations. Note that all decisions are made independently and that they are decentralized.
4. We can depict simultaneous interdependent choice as a black box, the rules, the players and outcomes are outside it, the utility functions are in it.
5. The a_i is the decision variable of player i, A_i is the set of feasible solutions.

Question 2

When is a’ a Pareto improvement?

Answer 2

a’ in A is a Pareto improvement with respect to a in A if u_i(a’) ≥ u_i(a) for all i in N and there is a player j in N for whom u_j(a’) > u_j(a).

Question 3

What is the definition of a best response?

Answer 3

If there is no u_i(a_i^*, a_-i) ≥ u_i(a_i, a_-i)

Question 4

What is an unilaterial deviation?

Answer 4

Individual deviations

Question 5

What is the definition of a pure Nash equilibrium?

Answer 5

for all i in N, for all a_i in A_i: u_i(a_i^*, a^*_-i) ≥ u_i(a_i, a_-i^*)

Question 6

How to calculate the Nash equilibria? (this question needs to be updated, but it will be okey)

Answer 6

1. State each player’s utility function
2. For each player calculate the partial derivative of this players utility function with respect to this player’s own action
3. Set all partial derivatives equal to 0 and solve the system
4. Verify whether the sufficient second-order conditions for a maximum. hold for each layers utility function with respect.

Question 7

What are the assumptions of the Nash Equilibrium?

Answer 7

1. Consistent predictions
2. Self-fulfilling predictions
3. Coordinations of Nash equilibrium predictions
4. Flawless choices of best responses
5. Self-oriented preferences

Question 8

What is the tragidy of the commons?

Answer 8

When resources that are free and open to use for everyone, often let individuals exploit those resoucres.

Question 9

Voeg nog vragen toe tijdens het maken