Analysis of a payoff matrix for a dominant strategy
The Candle Corporation and the Wick Company are the only producers of a very sophisticated type of flammable material. They each can engage in either a high or low level of advertising in trade journals. The payoff matrix is as follows:
Wick Company
Low Level High Level
Candle
Corp. Low Level Wick - $13 million Wick - $12 million
Candle - $12 million Candle - $11 million
High Level Wick - $12 million Wick - $11 million
Candle - $13 million Candle - $12 million
a. Will Candle engage in a high or a low level of advertising in trade journals?
b. Will Wick engage in a high or a low level of advertising in trade journals?
c. Is there a dominant strategy for each firm?
© BrainMass Inc. brainmass.com December 24, 2021, 7:41 pm ad1c9bdddfhttps://brainmass.com/economics/game-theory/analysis-payoff-matrix-dominant-strategy-210559
SOLUTION This solution is FREE courtesy of BrainMass!
To solve through this type of question you begin by seeing if each player has a dominant strategy.
First, suppose Wick chooses Low...it follows that Candle Corps Best response is to choose High
since $13 is a better payoff than $12
now, suppose Wick chooses High...it follows that Candle Corps Best response it to choose High
since $12 is a better payoff than $11
SO CANDLE CORP HAS A DOMINANT STRATEGY OF "HIGH LEVEL"
Next, suppose Candle Corp chooses Low...it follows that Wick's Best response is to choose Low
since $13 is a better payoff than $12
now, suppose Candle Corp chooses High...it follows that Wick's Best response it to choose Low
since $12 is a better payoff than $11
SO CANDLE CORP HAS A DOMINANT STRATEGY OF "LOW LEVEL"
© BrainMass Inc. brainmass.com December 24, 2021, 7:41 pm ad1c9bdddf>https://brainmass.com/economics/game-theory/analysis-payoff-matrix-dominant-strategy-210559