7. Using a payoff matrix to determine the equilibrium outcome Suppose there are

Question

7. Using a payoff matrix to determine the equilibrium outcome Suppose there are only two firms that sell tablets: Padmania and Capturesque. The following payoff matrix shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its tablets Capturesque Pricing High High 11, 11 Low 18, 2 Low 2, 18 10, 10 Padmania Pricing For example, the lower-left cell shows that if Padmania prices low and Capturesque prices high, Padmania will earn a profit of $18 million, and Capturesque will earn a profit of $2 million. Assume this is a simultaneous game and that Padmania and Capturesque are both profit-maximizing firms price, and if If Padmania prices high, Capturesque will make more profit if it chooses a Padmania prices low, Capturesque will make more profit if it chooses a price If Capturesque prices high, Padmania will make more profit if it chooses a Capturesque prices low, Padmania will make more profit if it chooses a price, and if price. a dominant strategy for both Considering all of the information given, pricing high Padmania and Capturesque If the firms do not collude, what strategies will they end up choosing? Both Padmania and Capturesque will choose a high price Padmania will choose a high price, and Capturesque will choose a low price. Both Padmania and Capturesque will choose a low price Padmania will choose a low price, and Capturesque will choose a high price True or False: The game between Padmania and Capturesque is an example of the prisoners' dilemma. True False

Explanation / Answer

(a)

If Padmania prices high, Capturesque will make more profit if it chooses a Low price [Since payoff is higher: $18 million > $11 million], and if Padmania prices low, Capturesque will make more profit if it chooses a Low price [Since payoff is higher: $10 million > $2 million].

(b)

If Capturesque prices high, Padmania will make more profit if it chooses a Low price Since payoff is higher: $18 million > $11 million], and if Capturesque prices low, Padmania will make more profit if it chooses a Low price Since payoff is higher: $10 million > $2 million].

(c)

Pricing High Is Not a dominant strategy for both.

(Since both firms will choose Low price, not considering the which price the other firm chooses)

(d)

If firms do not collude,

- Both will choose a Low price.

(e) TRUE

If both firms do not collude, they will both choose Low price, therefore each will earn payoff of $10 million each (For (Low, Low)). But if they collude, each firm will be able to gain higher payoff of $11 million each (For (High, High)), maximizing joint profit. Therefore this is a Prisoners' Dilemma.

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