Question

Merebut and Ichiban provide private-hire services. The strategic choices and payoffs for Merebut and Ichiban are as follows:

Payoffs: Merebut, Ichiban	Ichiban’s Strategy
Merebut’s Strategy	Cut Prices	Don’t Cut Prices
Cut Prices	-$200, -$200	$400, $500
Don’t Cut Prices	$300, $650	$500, $600

If Merebut and Ichiban choose simultaneously and with full knowledge of the payoff structure, what is the Nash Equilibrium/Equilibria, if any?

Explain your answer.

2. (ii) Consider the game given in Question 3(a)(i). Suppose Merebut chooses its strategy first, followed by Ichiban. Draw the extensive form, or game

   tree, of this sequential game.

3. (iii) Analyse and solve for the extensive form Nash Equilibrium in the

   sequential game where Merebut goes first.

(iv) Suppose that the right to move first is auctioned to the highest bidder. The highest bidder can move first; the lower bidder must move second.

Which firm would bid more in the auction, and what price would they be willing to bid up to? Why?

Note: If you are not confident of your earlier answers, describe the general principle determining the value of moving first, for partial mark.

(b) Is the private-hire market best modelled using the Bertrand (price) competition model, or the Cournot (quantity) competition model? What are the implications of the model you chose on prices and profits? Do not use Question 3(a) to answer this. You must provide a real-life argument to answer this question.

Answer 1

The Nash Equilibrium is a decision-making theorem within game theory that states a player can achieve the desired outcome by not deviating from their initial strategy. In the Nash equilibrium, each player's strategy is optimal when considering the decisions of other players. in another words, we can say that here wach player choses the best possible pay-off for them given the payoff for the other player. Every player wins because everyone gets the outcome they desire.

In the question above the Nash Equilibrium stand out to be Don't Cut Prices for both the players. This can be studied in the format below,

	Ichiban's Strategy
Merebut's Strategy		Cut Prices	Don't Cut Prices
Cut Prices	$200, $200	$400,$500
Don't cut prices	$300,$650	$500,$600

In the table above, lets check the dominant strategy that is the optimal move for an individual regardless of how other players act, for Merebut. He will choose the payoff $400 when he is willing to cut the prices and $500 when he doesn't want to cut the prices. Similarly, Ichiban will go with $650 and $600 for both the cases.

Thus we get the nash equilibruim to be $500,$600 i.e. "Don't cut prices" for both the players, and none of the player is willing to switch their payoff for other.

(ii)

The Squential game will take a form as shown in the picture, as Merebut has the right to go first and on that basis Ichiban makes his decision. below every strategy are the payoffs for the player respectively.

(iii) The nash equilibrium for the the sequential game cannot be determined, as Merebut will be willing to chose Don't cut price strategy whereas Ichiban's beneficial payoff is $650 ie cut prices, Thus there is no nash equilibrium in case of the Sequential game.

(iv) According to the strategy given, Ichiban is likely to bid the highest, in respect to his payoffs, and take the first mover advantage. he is likey to bid between $200-$600 and chose the best payoff and move first. Ichiban has the more weight in comparison to the Merebut's payoff also, his payoff is comparatively more even in the nash equilibrium, thus is likely to bid more and and secure is best payoff.

In case Ichiban moves first, he is likely to chose $650 i.e. Cut prices as his dominant strategy.