Two gas stations, A and B, are locked in a price war. Each player has the option of raising its price (R) or continuing to charge the low price (C). They will choose strategies simultaneously. If both choose C, they will both suffer a loss of $100. If one chooses R and the other chooses C, (i) the one that chooses R loses many of its customers and earns $0, and (ii) the one that chooses C wins many new customers and earns $1000. If they both choose R, the price war ends and they each earn $500. 1. Draw the payoff matrix for this game. B B R C A R (500,500) (0,1000) A C (1,000,0) (-100,-100) 2. What is the optimal strategy? R for A and R for B 3. Does player A have a dominant strategy? Explain. No player A doesn't have a dominant strategy. If player B chooses R, A's best response is to settle on C. If B chooses C, A's best response is to choose C. Since there is no single best response, A does not have a dominant strategy. 4. Does player B have a dominant strategy? Explain. 5. How many Nash equilibria does this game have? 6. What course of action will players A & B choose?
Two gas stations, A and B, are locked in a price war. Each player has the option of raising its price (R) or continuing to charge the low price (C). They will choose strategies simultaneously. If both choose C, they will both suffer a loss of $100. If one chooses R and the other chooses C, (i) the one that chooses R loses many of its customers and earns $0, and (ii) the one that chooses C wins many new customers and earns $1000. If they both choose R, the price war ends and they each earn $500.
1. Draw the payoff matrix for this game.
| B | B | |||
| R | C | |||
| A | R | (500,500) | (0,1000) | |
| A | C | (1,000,0) | (-100,-100) |
2. What is the optimal strategy?
R for A and R for B
3. Does player A have a dominant strategy? Explain.
No player A doesn't have a dominant strategy. If player B chooses R, A's best response is to settle on C. If B chooses C, A's best response is to choose C. Since there is no single best response, A does not have a dominant strategy.
4. Does player B have a dominant strategy? Explain.
5. How many Nash equilibria does this game have?
6. What course of action will players A & B choose?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 1 images
