Dominant Strategy in parts a) and b) complete the following
i. Set up the payoff matrix for the game
ii. Determine if either player has a dominant strategy
iii. Find the Nash Equilibrium and determine if it is efficient or not
a. Suppose two firms, Coke and Pepsi, are deciding whether or not to advertise towards a specific target audience. When Coke (player 1) does not advertise, Pepsi (player 2) will receive a payoff of 500 if it doesn’t advertise and a payoff of 750 if it does. When Coke advertises, Pepsi will receive a payoff of 200 if it does not advertise and a payoff of 300 if it does. When Pepsi does not advertise, Coke will receive a payoff of 400 if it does not advertise and a payoff of 300 if it does. When Pepsi does advertise, Coke will receive a payoff of 100 if it does not advertise and a payoff of 200 if it does.
b. Suppose another two firms, Samsung and Apple, are deciding whether to invest in a high level of research and technology or low level. Apple’s high level of technology is only useful if it is in conjunction with Samsung’s high level of technology. Specifically, when Samsung (player 1) invests in a high level, Apple (player 2) will receive a payoff of 200 if it invests in a high level of technology and a payoff of 60 if it invests in a low level. When Samsung invests in a low level, Apple receives a payoff of 0 if it invests in a high level of technology and a payoff of if it 40 if it invests in a low level. When Apple invests in a high level, Samsung will receive a payoff of 40 if it invests in a high level of technology and a payoff of 30 if it invests in a low level. When Apple invests in a low level of technology, Samsung will receive a payoff of 100 if it invests in a high level of technology and a payoff of 80 if it invests in a low level.