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Homework answers / question archive / Consider the payoff matrix below, which shows the pricing strategies of two competing firms
Consider the payoff matrix below, which shows the pricing strategies of two competing firms. Firm B Price high Price low $150 $100 $100 -$50 Price high Firma Price low -$50 $0 $150 $0 The dominant strategy for Firm A is to(Click to select) The dominant strategy for Firm B is to (Click to select) If both firms play their dominant strategies, the outcome (Click to select a Nash equilibrium. A Nash equilibrium occurs when: O both firms earn the highest profit O every player wants to change strategy, given the actions of other players. Ono player wants to change strategy, given the actions of other players. O both firms earn the lowest profit
Use the figure below to determine the dominant strategy for each player, if a dominant strategy exists. Player B Strategy 1 2 Strategy 2 Strategy 1 10 Player A Strategy 2 11 3 What is the dominant strategy for Player A? (Click to select) What is the dominant strategy for Player B? Click to select)
Answers to Diagram 1.
Ans. 1. The dominant strategy for Firm A is to 'price low' ($150 or $0), because whatever is the action of Firm B, Firm A is better off compare to selecting option 'Price high'($100 or -$50).
i.e. in both case he is better off ($150>$100, & $0 > -$50)
Ans. 2. The dominant strategy for Firm B is also to select Price Low($150 or $0) because whatever is the action of Firm A, Firm B is always better off compared to his other option price high($100 or -$50).
i. e. in both case he is better off ($150 > $100 & $0 > -$50)
Ans. 3. If both the player play their dominant strategy, then The nash equilibrium in this game is (Price low, Price low) For both the firm with outcome ($0, $0).
Because it is their best response given other Firms action.
Ans. 4. Statement first.
A Nash equilibrium is where both player earn the highest profit by selecting best outcome from the given option irrespective of other Firms Action plan, i.e. bigger is the better.
Second statement will not form nash equilibrium because here we take best possible move, irrespective of others move.
Third statement does not form nash equilibrium because if we know others action, he is going to take, then we will also take suitable move, however it will not be pure nash equilibrium.
Fourth statement is false, as each firm always tries to maximize his profit.
Answers to diagram 2.
Ans. 1. Dominant strategy for player A is Strategy-2,
Because, he his better off in both the cases,
(i.e. 11>11 & 3>1)
Ans. 2
player 2 does not have any best dominant strategy,
Because he will go for strategy 1, when player A selects strategy -2.
He will select strategy 2 if player A selects strategy-1 as per his profit.
