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 $1,000. If they both choose R the price war ends and they each earn $500.
a. Draw the payoff matrix for this game.
b. Does either player have a dominant strategy? Explain.
c. How many Nash equilibria does this game have? Defend your answer carefully.