Asked by Kaianah Sweeting on Jun 13, 2024
Verified
In the game matrix below, the first payoff in each pair goes to player A who chooses the row, and the second payoff goes to player B, who chooses the column.Let a, b, c, and d be positive constants. 
If player A chooses Bottom and player B chooses Right in a Nash equilibrium, then we know that
A) b 1 and d 1.
B) c 1 and b 1.
C) b 1 and c d
Nash Equilibrium
A concept in game theory where each player's strategy is optimal, given the strategies of other players, and no player has an incentive to deviate unilaterally.
Positive Constants
Fixed values greater than zero used in mathematical equations or expressions.
Payoffs
The returns or outcomes received from a particular action or investment.
- Comprehend the principle of Nash equilibrium and its application in different strategic scenarios.
- Identify the distinctions between pure and mixed strategy equilibria within games.
Verified Answer
TF
Tammy FournierJun 19, 2024
Final Answer :
C
Explanation :
If player A chooses Bottom and player B chooses Right in a Nash equilibrium, it means that both players are making their best possible decisions given the other player's decision.
For player A:
- If player B chooses Top, player A gets a payoff of b
- If player B chooses Bottom, player A gets a payoff of d
Since player A is choosing Bottom, they would prefer player B to choose Bottom so they can get a payoff of d, which is higher than the payoff of b. Therefore, player B choosing Bottom is the best choice for player A.
For player B:
- If player A chooses Top, player B gets a payoff of c
- If player A chooses Bottom, player B gets a payoff of a
Since player B is choosing Right, they would prefer player A to choose Top so they can get a payoff of c, which is higher than the payoff of a. Therefore, player A choosing Top is the best choice for player B.
So, b 1 and c d are both true, which means the answer is C.
For player A:
- If player B chooses Top, player A gets a payoff of b
- If player B chooses Bottom, player A gets a payoff of d
Since player A is choosing Bottom, they would prefer player B to choose Bottom so they can get a payoff of d, which is higher than the payoff of b. Therefore, player B choosing Bottom is the best choice for player A.
For player B:
- If player A chooses Top, player B gets a payoff of c
- If player A chooses Bottom, player B gets a payoff of a
Since player B is choosing Right, they would prefer player A to choose Top so they can get a payoff of c, which is higher than the payoff of a. Therefore, player A choosing Top is the best choice for player B.
So, b 1 and c d are both true, which means the answer is C.
Learning Objectives
- Comprehend the principle of Nash equilibrium and its application in different strategic scenarios.
- Identify the distinctions between pure and mixed strategy equilibria within games.