1.For the situation, identify the two players and their possible choices, and construct a payoff matrix for their conflict.

Andersonville has two gas stations, Ralph's Qwik-Serv and Charlie's Gas-n-Go. Both Ralph and Charlie are considering raising prices by 1, staying with their current prices, or lowering prices by 1. If they both make the same choice, there will be no change in their market shares, but if they make different choices, the one with the lower price will gain9%of the market for each penny difference in their prices.

Charlie

RSL

R____________% __________% ___________%

Ralph S____________% __________% ___________%

L____________% __________% ___________%

What doesRrepresent?

• Rrepresents raising the price by 1.
• Rrepresents keeping the price the same.
• Rrepresents lowering the price by 1.

What doesSrepresent?

• Srepresents lowering the price by 1.
• Srepresents raising the price by 1.
• Srepresents keeping the price the same.

What doesLrepresent?

• Lrepresents keeping the price the same.
• Lrepresents lowering the price by 1.
• Lrepresents raising the price by 1.

2.For the game, identify the saddle point and determine the corresponding optimal strategy for each player.

3 7

2 6

The saddle point is the___________________in row______________and column______________.

The optimal strategy is forRto always choose row_______and forCto always choose column________________.

3.For the game, identify the saddle point and determine the corresponding optimal strategy for each player.

31 1

534

The saddle point is the_________in row ________and column________.

The optimal strategy is forRto always choose row________and forCto always choose column____________.

4.For the game, identify the saddle point and determine the corresponding optimal strategy for each player.

2 1 5

6 4 6

4 2 3

The saddle point is thein row ____________and column___________.

The optimal strategy is forRto always choose row__________and forCto always choose column___________.

5.For the game, identify the saddle point and determine the corresponding optimal strategy for each player.

25 6 5 2

21 16 17 26

13 14 20 10

The saddle point is thein row ____________and column___________.

The optimal strategy is forRto always choose row__________and forCto always choose column___________.

6.Determine the optimal strategy for the situation by representing it as a game and finding the saddle point. State your final answer in the terms of the original question.

A Republican and a Democratic candidate are running for office in a heavily Republican county. A recent newspaper poll comparing their views on taxes and welfare reform showed that when compared on taxes or on welfare reform, the Republican leads by25%. When comparing the Democrat on welfare reform to the Republican on taxes, the Republican leads by40%. But when comparing the Democrat on taxes to the Republican on welfare reform, the Republican leads by only20%. Use this information to decide what each candidate should discuss at their next debate. (LetTrepresent taxes andWrepresent welfare reform.)

Democrat

TW

T___________% _____________%

Republican W___________% _____________%

The saddle point is the______________in row_____________and column____________

What should each discuss at their next debate?

• They both should discuss taxes at their next debate.
• The democratic candidate should discuss welfare reform, while the republican candidate discusses taxes.
• They both should discuss welfare reform at their next debate.
• The democratic candidate should discuss taxes, while the republican candidate discusses welfare reform.