Question

Dan Murphys (DM) and BWS are the only two liquor chains in Australia that hold the rights to sell a popular new beer named Victoria Sweeter (VS).

Both Dan Murphys and BWS are contemplating between charging a high price ($60 per case) or a low price ($40 per case).

The payoff matrix below shows all possible scenarios and outcomes for the two firms.

		BWS
		Charge $60 per case	Charge $40 per case
Dan Murphys (DM)	Charge $60 per case	DM: $30,000 profit BWS: $25,000 profit	DM: $13,000 profit BWS: $38,000 profit
	Charge $40 per case	DM: $45,000 profit BWS: $12,000 profit	DM: $19,000 profit BWS: $20,000 profit

* Profits reported in the above table are monthly figures on the Victoria Sweeter (VS) beer only.

Required:

(a) Identify the dominant strategy for Dan Murphys in this game. Clearly explain why this is the dominant strategy. (0.5 + 0.5 = 1 mark).

(b) Identify the non-cooperative* Nash equilibrium for this game. Clearly explain why this is the Nash equilibrium. (1 + 1 = 2 mark).
(* Non-cooperative means that each firm makes their decision independently and does NOT cooperate)

(c) Notice that Dan Murphys and BWS can both earn good profits by both charging $60 per case. Clearly explain why this is NOT the non-cooperative Nash equilibrium. (0.5 + 0.5 = 1 mark).

(d) For Dan Murphys and BWS to both charge $60 per case and earn high profits ($30,000 and $25,000 respectively); a certain form of collusion is needed. While explicit collusion is prohibited and subject to hefty penalties in Australia, what strategy can both firms employ to achieve an implicit, tacit form of collusion? Clearly explain how (1 mark)

Answer 1

(a). The dominant strategy for both firm is to charge a price of $40. This is because both maximize their total payoffs while charging $40, regardless of the other's actions as can be seen below:

For DM, At $60, total payoff is $43,000 and at $40, total payoff is $64,000

For BWS, At $60, the total payoff is $37,000 and at $40, the total payoff is $58,000

(b). Non-cooperative Nash Equilibrium for this game is also ($40,$40). This is because every dominant strategy is a Nash equilibrium.

(c). ($60,$60) is not the non-cooperative Nash Equilibrium because;

If DM chooses price=$60, then best option for BWS is to charge price = $40,

If DM chooses price=$40, then best option for BWS is to charge price = $40,

If BWS chooses price=$60, then best option for DM is to charge price = $40,

If BWS chooses price=$40, then best option for DM is to charge price = $40,

Therefore, choosing $40 is the best option for each of them given the action taken by the other.

(d). For tacit collusion, both firms can employ either of the 2 strategies given below:

(i). conscious parallel actions : When both firms know that setting price at $60 will be beneficial for both of them, then both will raise the price.

(ii). price leadership : Knowing the fact that $60 is beneficial for both of them, either of the two can take an initiative of raising the price and earn more profits. The other will follow the suit, in order to increase its profits.