Question
Got 5 already, just need help with 6!
Thank you!
5. Consider the following game played between two microwave meal producers, Wanson (W) and Stuffer (S). Each firm can choose either to charge a low price (1) or high price (h) The following table shows the payoff matrix for the two firms in terms of their profits in million dollars represented by (T1 ,T ) In each cell Stuffer low price (1) high price (h) low price () (1,1) Wanson high price (h) (0, 3) (2,2) (a) Find the Nash equilibrium strategy(ies) (b) Is this an example of a prisoners dilemma game? wanson chooses to charge a low price then Stuffer charges a low price too and If if Wanson charges a higher price Stuffer still charges low price. So irrespective of what Wanson charges Stuffer always prefers to charge a low price as his payoff from charging low price is greater than that from high price. On the other hand, if Stuffer chooses to charge a low price then Wanson charges a low price too and if Stuffer charges a higher price Wanson still charges low price. So irrespective of what Stuffer charges Wanson always prefers to charge a low price as his payoff from charging low price is greater than that from high price. Hense the naslh equilibrium strategy in this case is that both charge a low price and receive (1,1) as This is an prisoner dilemma's game since both Wanson and Stuffer could have charged high price and received a higher payoff of (2,2) however, they settle for lovw price and receive payoff less than what they could have from charging high price 6. Suppose that we repeat the game in question 5 an indefinite number of times (a) Explain how repeating the game can allow for the best outcome for the two firms to be an equilibrium. (b) Describe one factor that could make the best outcome not be an equilibrium.
Explanation / Answer
(a) If the game is repeated an indefinite number of times, both the firms will choose to go for high price and hence earn the maximum output (2,2). Even though this is not the Nash Equilibrium, it is in mutual interests of the firm to collaborate and earn the maximum profit. The firms do not have an incentive to deviate from this, since any deviation will be consequently punished by the other firm in the next round.
For instance, if both the firms have prices it High earning (2, 2) and suddenly Wanson greedily reduces its prices, earning 3. Stuffer will now reduce the prices and keep the prices low for the entirety of the game, and Wanson's overall profits will reduce. Hence, it is in mutual interests of both the firms to keep the prices high and earn the maximum profit.
(b) Incomplete information may cause the best outcome not be an equilibrium. If either of the firm is not aware of the extra profits to be made by colluding, then they might price their product differently and lose out on this.
Greed of the firm may also result in lower profits, as described above.
