You own a miniature golf course on the boardwalk in Ocean City, New Jersey. Right next to you on the boardwalk is another miniature golf course. Your golf course has a dinosaur theme. Your competitor’s course is newer and has several impressive waterfalls and original hole designs that are attractive to your avid miniature golf fan. From past experience you have determined that the own-price elasticity of demand for your golf course is -1.5. You also know that the cross-price elasticity of demand for your course with respect to your competitor’s price is +0.8. You suspect that your competitor’s own-price elasticity of demand is -1.5 as well, but that the cross-price elasticity of demand for his course relative to your prices is only +0.4 due to the more modern design features. Currently you charge $5.00 for a round of miniature golf and have 2,000 customers in a typical week. Your competitor charges $7.50 for a round of golf and currently has 3,000 customers in a typical week. You are considering lowering your price from $5.00 to $4.00. Your fear is that if you lower your price, your competitor will also lower their price by $1.00 and charge $6.50. Your competitor is also considering lowering their price by $1.00, but is concerned that you will match their price cut. Assume that your costs and your competitor’s costs will not change as a result of this decision. Required:
a. Construct the payoff matrix for this game.
b. Do you or your competitor have a dominant strategy? If so, what is it?
c. Does this game have a Nash equilibrium? If so, what is it?