Question

Coke and Pepsi dominate the global market for cola soft drinks. For the sake of simplicity, say they are the only two brands that produce cola, that they share the global market for cola equally, and produce nothing else. Suppose that Coke and Pepsi can each adopt one of two pricing strategies: ‘price low’ or ‘price high’. If they both price high, then they each make profits of $200 million, or ‘2’ for short. If they both price low then they both make zero profits. If one company prices high while the other prices low, then the company that prices low makes a profit of $400 million , or ‘4’ for short, while the company that prices high makes a loss of $200 million, or ‘-2’ for short. Summarise these payoffs in a payoff matrix for this game?

Answer 1

If Pepsi and Cola price low, they both earn $0 as profit. If one of them charge high price and othet low price, firm charging high price will loss by $200 and firm charging low price gain $400. If both of them charge high price, they will gain $200 each.

			Cola
			Price low	Price high
Pepsi	Price low		($0, $0)	($400, -$200)
Price high		(-$200, $400)	($200, $200)

If Pepsi price low, Cola will charge low price as it gives profit of $0 in against loss of $200.

If Pepsi price high, Cola will charge low price as it gives profit of $400 in against profit of $200.

Thus, Cola have a dominant strategy by choosing low price no matter what Pepsi choose.

If Cola price low, Pepsi will charge low price as it gives profit of $0 in against loss of $200.

If Cola price high, Pepsi will charge low price as it gives profit of $400 in against profit of $200.

Thus, Pepsi have a dominant strategy by choosing low price no matter what Cola choose.

As both firm tends to choose low price, Nash equilibrium is to choose low price.