Answer it by game theory. Its very easy for any eco major. please don\'t answer
ID: 1130417 • Letter: A
Question
Answer it by game theory. Its very easy for any eco major. please don't answer if you are not sure, please answer correctly! I need the answer what should be their dominant price that one too!!!
2. Using the following game matrix, what price will Coke and Pepsi charge and what are each companies profits. The italics are for Pepsi, and the bold is for Coke. Is there a way to get to a different solution? Explain. Pepsi S1.89 $1.99 S2.09 S13000 S12000 S9000 S1.89 $22000 S18000 $14000 $16000 $15000 $13000 $1.99 $19000 $15000 $12000 S20000 S18000 S16000 $2.09 S16000 S13000 S10000 CokeExplanation / Answer
Consider this game theory problem here there are 2 players, “Coke” and “Pepsi”, both of the players have same sets of strategies, {$1.89, $1.99, $2.09}, now given the different strategy they will get different profits as a payoff.
Now, if “Coke” will choose to charge “$1.89” then the optimum price for “Pepsi” is “$1.89”, since $22,000 > $19,000, $16,000. If “Coke” will choose to charge “$1.99” then the optimum price for “Pepsi” is “$1.89”, since $18,000 > $15,000, $13,000. Similarly, if “Coke” will choose to charge “$2.09” then the optimum price for “Pepsi” is “$1.89”, since $14,000 > $12,000, $10,000. So, it is very easy to see “$1.89” be the dominant strategy for “Pepsi”, it does not matter what “Coke” will choose.
Similarly with the same explanation we can explain that “$1.89” is also the dominant strategy for “Pepsi”. So, {$1.89, $1.89) = ($13,000, $22,000) be the NE equilibrium here.
No, there do not have any different way to get different solution, if we want to apply, “iterated elimination of the strictly dominated strategy” then also we will end up with the same solution, because "$1.89" be the strictly dominant strategy for both the players.
If we follow the “mixed strategy solution” we will find that “Coke” will choose “$1.89” with probability “1” and will play {1.99, 20.9} with probability “0”,same goes for “Pepsi”. So, in all the other way we will end up with the same solution of the game.