Mitchell Electronics produces a home video game that has become very popular with children. Mitchell’s managers have reason to believe that Wright Televideo Company is considering entering the market with a competing product. Mitchell must decide whether to set a high price to accommodate entry or a low, entry deterring price. The payoff matrix below shows the profit outcome for each company under the alternative price and entry strategies. Mitchell’s profit is entered before the comma, and Wright’s is after the comma.
Wright Televideo
Mitchell Electronics
Enter Do not Enter
60, 25 85, 0
30, -20 60, 0
High Price
Low Price
a. Does Mitchell have a dominant strategy? Explain (5 points)
b. Does Wright have a dominant strategy? Explain (5 points)
c. Mitchell’s managers have suggested a willingness to lower price in order to deter entry. Is this threat credible in light of the payoff matrix above? Explain. (7 points)
d. If the threat is not credible, what changes in the game would be necessary to make the threat credible? What business strategies could Mitchell use so that the threat is credible?
To determine if Mitchell has a dominant strategy, we need to compare the payoffs of each strategy. A dominant strategy is one that will always yield a higher payoff regardless of the strategy chosen by the other player.
a. Looking at the payoff matrix, we can see that Mitchell's payoffs are 60, 30, 85, and 60 for high price/enter, high price/do not enter, low price/enter, and low price/do not enter, respectively. Mitchell's dominant strategy is the one that maximizes its own profit. Comparing the payoffs, we see that the high price strategy consistently yields higher payoffs than the low price strategy. Therefore, Mitchell's dominant strategy is to set a high price, regardless of Wright's strategy.
b. Similarly, we can determine if Wright has a dominant strategy by comparing the payoffs. Wright's payoffs are 25, 0, 0, and 0 for high price/enter, high price/do not enter, low price/enter, and low price/do not enter, respectively. As we compare the payoffs, we can see that Wright's highest payoff is 25, obtained when Mitchell enters the market with a high price. Therefore, Wright's dominant strategy is to enter the market when Mitchell sets a high price.
c. Mitchell’s managers suggest lowering the price to deter entry. However, looking at the payoff matrix, we see that if Mitchell lowers the price, Wright still has a positive payoff when entering the market. The threat of lowering the price to deter entry is not credible because Wright would still make a profit by entering with a low price. Mitchell's threat does not have a strong deterrent effect.
d. To make the threat credible, Mitchell would need to change the payoffs in the matrix so that entering the market with a low price is less profitable for Wright. Mitchell could achieve this by increasing its own profit when entering with a high price or reducing Wright's profit when entering with a low price. Mitchell could implement various business strategies such as enhancing the product's features, improving its marketing campaign, or forming exclusive partnerships to increase the perceived value of the game and make it harder for Wright to compete effectively. By making the market less attractive for Wright, Mitchell's threat to lower the price would become more credible.