# payoff matrix

Joe is the owner of the Texaco Mini Mart, Sam is the owner of the Exxon Mini Mart and together they are the only gas stations in town. At the current price of $1 per gallon both receive total revenues of $1,000. Joe is considering cutting his price to 90 cents, which would increase his total revenue to $1,350 if Sam continues to charge $1. If Sam's price remains $1 after Joe cuts his price, Sam will collect $500 in revenues. If Sam cuts his price to 90 cents, his total revenues would also rise to $1,350 if Joe continues to charge $1. Joe will collect $500 in revenues if he keeps his price at $1 while Sam lowers his to 90 cents. Joe and Sam will receive $900 each in total revenue if they both lower their price to 90 cents.

a. Fill in the payoff matrix below based on the information provided above.

Joe

Cut

Price Keep Old

Price

Sam

Cut

Price

Keep Old

Price

b. Locate, if there are any, dominated and dominant strategies in the pay-off table.

c. Locate the likely outcome of this pricing game.

d. Is the likely outcome a Nash equilibrium? Explain.

g. Is the likely outcome strategically stable? Explain.

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#### Solution Preview

Please refer to the attachment.

Joe is the owner of the Texaco Mini Mart, Sam is the owner of the Exxon Mini Mart and together they are the only gas stations in town. At the current price of $1 per gallon both receive total revenues of $1,000. Joe is considering cutting his price to 90 cents, which would increase his total revenue to $1,350 if Sam continues to charge $1. If Sam's price remains $1 after Joe cuts his price, Sam will collect $500 in revenues. If Sam cuts his price to 90 cents, his total revenues would also rise to $1,350 if Joe ...

#### Solution Summary

The expert formulates a payoff matrix. The outcome of the Nash equilibrium is determined.