Chapter $18$ Homework

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Attempts $$

$3$

Keep the Highest $\frac{3}{5}$

$5.$ Using a payoff matrix to determine the equilibrium outcome

Suppose that Vitablend and Blend Magic are the only two firms in a hypothetical market that produce and sell personal blenders. 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 blenders.

$\backslash$table$[[$Vitablend Pricing,,Blend Magic Pricing$],[,$High,Low$],[$High$,13,13,7,15],[$Low$,15,7,12,12]]$

For example, the lower$-$left cell shows that if Vitablend prices low and Blend Magic prices high, Vitablend will earn a profit of $$15$ million, and Blend Magic will earn a profit of $$7$ million. Assume this is a simultaneous game and that Vitablend and Blend Magic are both profit$-$maximizing firms.

If Vitablend prices high, Blend Magic will make more profit if it chooses a $q,$ price, and if Vitablend prices low, Blend Magic will make more profit if it chooses a $q,$ price.

If Blend Magic prices high, Vitablend will make more profit if it chooses a $q,$ price, and if Blend Magic prices low, Vitablend will make more profit if it chooses a $q,$ price.

Considering all of the information given, pricing low $$ a dominant strategy for both Vitablend and Blend Magic.

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