Topic 7

Question 1

Define mixed strategy

Answer 1

When player i has N pure strategies to choose from, a mixed strategy is defined as a probability distribution over these N pure strategies, a mixed strategy is then represented by a probability vector (p1,p2,…,pn) satisfying the two conditions
Pn >/= 0, for all n=1,…,N
£pn=1

Question 2

From the definition of mixed strategies we can state that a pure strategy is also a ….

Answer 2

(Degenerate) mixed strategy.

It assigns probability to one action and zero to all remaining.

Question 3

When players use mixed strategies how are their payoffs calculated?

Answer 3

As expected payoffs

Question 4

What are expected payoffs

Answer 4

The weighted sum of pure strategies’ payoffs where the weight is the other players choice of the probability that the pure strategy will be played

Question 5

When there are 2 players and player 2 has N possible pure strategies available, each one of them denoted as Xn, player i’s expected payoff of choosing strategy A is:

Answer 5

Ei[U(A)]= p1ui(A1X1) + p2ui(A1X2) + … pnui(A1Xn)
Where:
ui(Xn) is player i’s utility when choosing A, given that player 2 has played Xn
pn is the probability of playing Xn chosen by player 2

Question 6

It would not make sense that a player randomizes between two actions if -

Answer 6

Given the strategy of the other players, one of the actions does better than the other

Question 7

What is the difference between a strictly dominant strategy and a strictly dominated strategy

Answer 7

Strictly dominant - dominates every other strategy

Strictly dominated strategy- ‘V is dominated by Y’

Question 8

What are the conditions for a NASH equilibrium?

Answer 8

No player has incentive to defect given all other players remain constant