$11.$ Using a payoff matrix to determine the equilibrium outcome

Suppose that Slow Flow and Stew Star are the only two firms in a hypothetical market that produce and sell slow cookers. The following payoff matrix gives profit scenarios for each company $($in millions of dollars$),$ depending on whether it chooses to set a high or low price for slow cookers.

Stew Star PricingHighLowSlow Flow PricingHigh$14,145,21$Low$21,513,13$

For example, the lower$-$left cell shows that if Slow Flow prices low and Stew Star prices high, Slow Flow will earn a profit of $$21$ million, and Stew Star will earn a profit of $$5$ million. Assume this is a simultaneous game and that Slow Flow and Stew Star are both profit$-$maximizing firms.

If Slow Flow prices high, Stew Star will make more profit if it chooses a$$price$,$ and if Slow Flow prices low, Stew Star will make more profit if it chooses a$$price$.$

If Stew Star prices high, Slow Flow will make more profit if it chooses a$$price$,$ and if Stew Star prices low, Slow Flow will make more profit if it chooses a$$price$.$

Considering all of the information given, pricing high$$a dominant strategy for both Slow Flow and Stew Star.

If the firms do not collude, what strategies will they end up choosing?

Both Slow Flow and Stew Star will choose a low price.

Slow Flow will choose a low price, and Stew Star will choose a high price.

Both Slow Flow and Stew Star will choose a high price.

Slow Flow will choose a high price, and Stew Star will choose a low price.

True or False: The game between Slow Flow and Stew Star is not$$an example of the prisoners$$ dilemma.

True

False