# 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?

Â© 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"

Â© BrainMass Inc. brainmass.com December 24, 2021, 7:41 pm ad1c9bdddf>https://brainmass.com/economics/game-theory/analysis-payoff-matrix-dominant-strategy-210559