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

Question

6. 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.

For example, the lower-left cell shows that if Padmania prices low and Capturesque prices high, Padmania will earn a profit of $15 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.

If Padmania prices high, Capturesque will make more profit if it chooses a ______ (choose one: high or low) price, and if Padmania prices low, Capturesque will make more profit if it chooses a _____ (choose one: high or low)  price.

If Capturesque prices high, Padmania will make more profit if it chooses a _____ (choose one: high or low) price, and if Capturesque prices low, Padmania will make more profit if it chooses a _______ (choose one: high or low) price.

Considering all of the information given, pricing low ______ (choose one: is or is not) a dominant strategy for both Padmania and Capturesque.

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

Padmania will choose a high price, and Capturesque will choose a low price.

Padmania will choose a low price, and Capturesque will choose a high price.

Both Padmania and Capturesque will choose a high price.

Both Padmania and Capturesque will choose a low price.

True or False: The game between Padmania and Capturesque is not an example of the prisoners’ dilemma.

True

False

Explanation / Answer

(1)

If Padmania prices high, Capturesque will make more profit if it chooses a Low price [Since profit is higher: $15 million > $11 million], and if Padmania prices low, Capturesque will make more profit if it chooses a Low price [Since profit is higher: $8 million > $2 million].

(2)

If Capturesque prices high, Padmania will make more profit if it chooses a Low price [Since profit is higher: $15 million > $11 million], and if Capturesque prices low, Padmania will make more profit if it chooses a Low price [Since profit is higher: $8 million > $2 million].

(c)

Pricing Low Is 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) FALSE

If both firms do not collude, they will both choose Low price, therefore each will earn profit of $8 million each (For (Low, Low)). But if they collude, each firm will be able to gain higher profit of $11 million each (For (High, High)), maximizing joint profit. Therefore this is a Prisoners' Dilemma.

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