Suppose that two companies – AlphaTech and BetaLabs – are competing for market share and must simultaneously decide whether to develop a new product. Both companies are reluctant to make a decision as it is only economical for one company to develop a new product. Each company earns nothing if they decide not to develop a new product. One company can earn $50 million by developing a new product only if their competitor does not. If both companies decide to develop a new product, they each lose $10 million. Complete the payoff matrix to represent this game. Based on your solution in part (a), determine the maximin solution.

Synergy and Dynaco are the only two firms in a specific high-tech industry. They face the following payoff matrix as they decide upon the size of their research budget: Dynaco's Decision Synergy's Decision Large Budget Large Budget $30 million, $20 million Small Budget $0, $30 million If Synergy believes Dynaco will go with a large budget, it will choose a budget. If Synergy believes Dynaco will go with a small budget, it will choose a budget. Therefore, Synergy a dominant strategy. O True Small Budget $70 million, $0 $50 million, $40 million If Dynaco believes Synergy will go with a large budget, it will choose a budget. If Dynaco believes Synergy will go with a small budget, it will choose a budget. Therefore, Dynaco a dominant strategy. O False True or False: There is a Nash equilibrium for this scenario. (Hint: Look closely at the definition of Nash equilibrium.)

two timber companies, Alpha and Beta, have to decide whether to harvest timber from the North Hill or the South Hill and then sell the timbers in the same market. If both harvest from North Hill, each company can harvest 100 tons of timber. If both companies harvest from South Hill, each company can harvest 150 tons of timber. If one company harvests from North Hill and the other harvests from South Hill, the company at North Hill can harvest 150 tons of timber while the company at South Hill can harvest 250 tons of timber. The price of timber is dependent on the total supply of timber in the market. The price will be $180 per ton if the total supply is 200 tons, $150 per ton if the total supply is 300 tons and $100 per ton if the total supply is 400 tons. To both companies, the cost of harvesting in North Hill is $5,000 and the cost of harvesting in South Hill is $10,000. (a) If Alpha and Beta were to make a decision simultaneously, construct the payoff matrix in terms of profit for…

There are two oil producers, Saudi Arabia and Iran (these are countries which we are treating as players in this example).  The market price will be $60/barrel if the total volume of sales is 9 million barrels daily, $50 if the total volume of sales is 11 million barrels daily, and $35 if the total volume of sales is 13 million barrels daily.  Saudi Arabia has two strategies; either produce 8 million barrels daily or 6 million.  Iran has two strategies; either produce 3 million barrels daily or 5 million.  Assume for simplicity that marginal cost of production is zero for both countries. Here is the normal form representation of this game (where Saudi Arabia and Iran are players, they can choose strategies over what quantity to produce and they face payoffs in terms of profits).  Note that the following paragraph is simply an explanation of this representation of the game.  If you are already comfortable with the structure, feel free to skip to the questions below the horizontal line…

solve i and ii please.

Consider a strategic interaction between firms 1 and 2. In Stage 1, firm 1 chooses the level of advertising a > 0. In stage 2, firm 2 learns about firm 1's amount of advertising a. Subsequently, firms 1 and 2 compete in a Cournot fashion. That is, firms 1 and 2 simultaneously and independently choose their outputs: q1 and q2, where qi denotes the output of firm i = 1,2. The price that the consumers are willing to pay for the product produced by the two firms, or the inverse aggregate demand function, is given by 6a - q1 - q2. Firm 1's advertising cost is a3. Both firms have zero production costs. Both firms maximize their individual profits (equal to the total revenue minus total cost). In the unique subgame perfect equilibrium of the game, the two firms will choose the following strategies: a. Firm 1 will choose strategy (a = 3, q1 = a/3) while firm 2 will choose strategy q2 = a/3 b. Firm 1 will choose strategy (a = 1, q1 = 16/3 ) while firm 2 will choose strategy q2 = 16/3 c. Firm 1…