Question

3 part question

Consider the Normal Form game below between Pepsi and Coca-Cola and then answer the questions that follow: Pepsi Don't Supply (D) 250,200 Supply(S) 300,0 Don't Supply (D) Coke Supply(S) 200,100 350,200 a. What is the Nash equilibrium/equilibria strategy of the game? O a. {SS} b.{D,S} OC {D,D) O d. {S,D} QUESTION 12 Consider the Normal Form game from question 10: If Coca-Cola was to utilize a maximin strategy, what strategy will it choose? O a. Don't supply b. Supply

Answer 1

a. Let's calculate the nash equilibrium of this game.

Let's find out the best strategy for Pepsi first.

When coca cola chooses to play don't supply (D) the Pepsi can either choose to supply(S) or don't supply (D). If Pepsi chooses to supply it will get a payoff of 0 and if it chooses to don't supply then it will get a payoff of 200. Since 200 is better than getting 0, the best strategy for Pepsi is to choose don't supply when coca cola chooses to play don't supply.

When coca cola chooses to play supply again Pepsi can either choose to don't supply or supply. If it chooses to supply it will get a payoff of 200 and if it chooses to play don't supply it will get a payoff of 100. Since 200 is better than 100 the best strategy for Pepsi when coca cola chooses to play supply is to choose supply.

Now let's find the best strategy for coca cola.

When Pepsi chooses to play don't supply coca cola can either choose to play don't supply or supply. If it chooses to supply it will get a payoff of 200 and if it chooses to play don't supply then it will get a payoff of 250. Since 250 is better than 200 the best strategy for coca cola is choose to don't supply when Pepsi chooses to play don't supply.

When Pepsi chooses to play supply, again coca cola can either choose to play supply or don't supply. If it chooses to supply then it will get a payoff of 350 and if it chooses to play don't supply then it will get a payoff of 300. Since 350 is better than 300 the best strategy for coca cola is to play supply when Pepsi is choosing to play supply.

As you can see the best strategy for the players are symmetric that is to say when player choose to supply other will also choose to supply and if one player chooses to don't supply then other player will also choose to don't supply. So there are two nash equilibrium.

The two nash equilibrium are (D,D) and (S,S). Since the best strategies for the both players are symmetric we have two pure strategy nash equilibrium.

12. If coca cola want to utilize the maximum strategy then it should play supply since supply gives coca cola a payoff of 350 while don't play gives it a payoff of 300 which is less than 300. And we also know that there are two pure strategy Nash equilibrium (D,D) and (S,S) so we can sure that if coca cola chooses to play supply then Pepsi will also choose to play supply.

So if coca cola wants to utilize the maximum strategy then it should choose to play supply and get a payoff of 350.

13. As we have already seen that the maximum payoff that Pepsi can get is 200. And we already saw in last question that coca cola is going to play supply each time the game is played and we also know when coca cola chooses to play supply then Pepsi will also choose to play supply and it will get a payoff of 200. ​​​​​​

So if the game is played three times and all the players know the payoffs of each other, the Pepsi will get the payoff of 200.