Question about Game Theory 3 (a) Explain the concept of a dominated strategy, di

Question

Question about Game Theory

3 (a) Explain the concept of a dominated strategy, differentiating between a strictly dominated and a weakly dominated strategy [20 marks] (b) Consider the following two-player game composed of two stages. In the first stage, one of the two following matrices is chosen by a coin toss (with each matrix chosen with probability ½). In the second stage, the two players play the strategic-form game whose payoff matrix is given by the matrix that has been chosen. Player 2 Player 2 Player 1 T 0,01,10 Player 1 T1,2,-11 B 2,-23,-12 B 1,1/21,10

Explanation / Answer

A strategy is termed as dominant is irrespective of what other play is adopting the strategy, the selected strategy earns a greater pay off to the player in comparison to other. Thus the strategy is said to be dominant if it provides the better pay off all the time in comparison to any other strategy irrespective of the actions of the other player.

In the basis of the definition of “better” as weak or strict inequalities, a strategy can be defined either as weakly dominant or strictly dominant. If one strategy is dominant then it will dominate rest of the strategies.

A strategy is termed as strictly dominant if irrespective of the moves of the other players, the player selects the only one strategy which yields him the greater pay off all the time. Thus a strategy is termed to be strictly dominant is it always better in comparison to any other strategy.

On the other hand, the strategy is termed as weakly dominant if irrespective of what the other player selects, the selected strategy by the player provides him the payoff at least as high as any other strategy and the strategy provides a strictly higher payoff for some strategy of other players.

Answer:-

Player 2

L

R

Player 1

T

0,0

-1,10

B

-2,-2

-3,-12

In the above matrix, Player 1 has the dominant strategy as T, while Player 2 has the dominant strategy as R. The Nash equilibrium is obtained at the cell with pay off (-1,10)

Player 2

L

R

Player 1

T

-1,1

-2,-11

B

1, 1/2

-1, 10

In the above matrix, Player 1 has the dominant strategy as B, while Player 2 has no dominant strategy . The Nash equilibrium is obtained at the cell with pay off (-1,10)

Player 2

L

R

Player 1

T

0,0

-1,10

B

-2,-2

-3,-12

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.