Suppose that you and a friend play a matching pennies game in which each of you uncovers a penny. If both pennies show heads or both show tails, you keep both. If one shows heads and the other shows tails, your friend keeps them. Show the pay- off matrix. What, if any, is the pure-strategy Nash equilibrium to this game? Is there a mixed-strategy Nash equilibrium? If so, what is it?

Sam and Sarah are thinking about getting married. However if either of them cheats on the other, they would get a payoff of 10, while the other person gets zero. If neither cheat, they stay with each other and get a payoff of 7 each and if both cheat, the relationship falls apart and each get a payoff of 1. What is the Nash equilibrium of this game? a. Cheat, Cheat b. Not cheat, Not cheat Sam cheats, Sarah doesn't Sarah cheats, Sam doesn't

Consider a market with two firms, Hewlett-Packard (HP) and Dell, that sell printers. Both companies must choose whether to charge a high price ($500) or a low price ($350) for their printers. These price strategies with corresponding profits are depicted in the payoff matrix to the right. HP's profits are in red and Dell's are in blue. Suppose HP and Dell are initially at the game's Nash equilibrium. Then, HP and Dell advertise that they will match any lower price of their competitors. For example, if HP charges $350, then Dell will match that price and also charge $350. What effect will matching prices have on profits (relative to the Nash equilibrium without price matching)? (Enter either positive or negative numeric HP's profit will change by $ and Dell's profit will change by responses using integers.) Price = $500 Dell Price $350 HP Price = $500 Price = $350 $80 $100 $80 $15 $15 $50 $100 $50

4.2. Game theory (Prisoner's dilemma). Often, many sectors in an economy have two main rivals, battling it out in the marketplace. There can be rivalry such as between Apple and Samsung in Phones and Laptops. Suppose Apple plans to cut its price. Samsung will likely follow suit to retain its market share. This may end up with low profits for both companies. A price drop by either company may thus be construed as defecting since it breaks an implicit agreement to keep prices high and maximize profits. Thus, if Apple drops its price but Samsung continues to keep prices high, Apple is defecting, while Samsung is cooperating (by sticking to the spirit of the implicit agreement). In this scenario, Apple may win market share and earn incremental profits by selling more. Assume that the incremental profits that accrue to Apple and Samsung are as follows: If both keep prices high (Cooperate), profits for each company increase by AED200 million (because of normal growth in demand). If one drops…