Matt and Lin are both math tutors. They know that if they collude and set a high price, both will earn a profit of 100; whereas if they both set a low price, both will earn a profit of 50. If one person sets a high price and the other person sets a low price, the person who sets a low price price gets a profit of 125 and the one with a high price gets a profit of 0. Fill in the payoffs in the normal-form game below where Lin is player 1 (represented by rows) and Matt is player 2 (represented by columns). Matt High Low Lin High Low
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- Frank and Nancy met at a sorority sock hop. They agreed to meet for a date at a local bar the next week. Regrettably, they were so fraught with passion that they forgot to agree on which bar would be the site of their rendezvous. Luckily, the town has only two bars, Rizotti's and the Oasis. Having discussed their tastes in bars at the sock hop, both are aware that Frank prefers Rizotti's to the Oasis and Nancy prefer the Oasis to Rizotti's. In fact, the payoffs are as follows. If both go to the Oasis, Nancy's utility is 3 and Frank's utility is 2. If both go to Rizotti's, Frank's utility is 3 and Nancy's utility is 2. If they don't both go to the same bar, both have a utility of 0. There are two Nash equilibrium in pure strategies and a Nash equilibrium in mixed strategies where the probability that Frank and Nancy go to the same bar is 12/25. This game has two Nash equilibria in pure strategies and a Nash equilibrium in mixed strategies where each person has a probability of 1/2 of…Q3. Two ice cream trucks operate on a beach and play a simultaneous pricing game. If one of them prices low and the other high it gets all the customers and a pay off of 12 while the other gets zero. If both price high each gets 6, and if both price low each get 5. The best strategy is for both to price high. True/False/Uncertain. Explain.Suppose that two clothing manufacturers, Lands’ End and L.L. Bean, are deciding what price to charge for very similar field coats. The cost of producing these coats is $100. The coats are very close substitutes, so customers flock to the seller that offers the lowest price. If both firms offer identical prices, each receives half the customers. For simplicity, assume that the two firms have the choice of pricing at prices of $103, $102, or $101. The profit each firm would earn at various prices (Lands’ Ends Profit, LL Bean’s Profit) is attached in the payoff matrix below: a.) What is the Nash equilibrium and expected profits to LL Bean and Lands’ End of this game? b.) Suppose this is a mixed strategy game in which LL Bean has a 25% percent chance of choosing a priceof $101, a 25% chance of choosing price of $102, and a 50% chance of choosing $103, while Lands End has a1/3 chance of choosing each strategy. What’s the expected payoff to LL Bean? c.) Suppose that in hopes of raising…
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- Andy and Cathy are in the sporting good industry. Andy has developed a new lightweight soccer goal and is trying to decide whether to sell it at a high price or a low price. Selling the good at a higher price will provide higher profits but might entice Cathy to develop and sell a competing lightweight soccer goal. A lower price could deter entry from Cathy. After Andy sets his price, Cathy must decide to enter the market for the new lightweight soccer goal or not. Assume that both Andy and Cathy must make at least $5,000 to make the investment worthwhile. Which price will Andy charge? O high price ● low price What will Cathy do as a result of Andy's choice? O Cathy will enter the market. O Cathy will not enter the market. Indicate each person's final profit. Andy's profit: $ 7000 Cathy's profit: $ 7000 Andy: charges high or low price Andy charges the high price Andy charges the low price Cathy: enter or do not enter Cathy: enter or do not enter Cathy enters Cathy does not enter Cathy…Two gas stations in a rural town can engage in collusion over pricing. Because drivers often just stop at the first station they see as they go through town, price competition is not that severe in the first place. Assume either station can price gas at $0.30 above average total cost or $0.50 above average total cost. If they have equal prices, they split the market. If they have unequal prices, the lower price station gets 75% of the market (assume for simplicity no change in the size of the market; price elasticity of demand is very low for short term changes in the price of oil).a. Draw the normal form representation of this game. Identify the key aspects of the game.b. Identify the dominant strategy, if any, for each player.c. Identify any Nash equilibria.Brian and Matt own the only two bicycle repair shops in town. Each must choose between a low price for repair work and a high price. The yearly economic profits from each strategy are indicated in Figure bellow. The upper right side of each rectangle shows Brian's profits; the lower left side shows Matt's profits. Matt's Actions Low Price High Price Low Price Brian's Actions $1,500 $1,500 $200 $3,000 High Price $5,000 $200 $4,000 $4,000 Which of the following statements is correct for a one-trial game? The market equilibrium price is the low price. A market equilibrium price cannot be established unless Brian and Matt collude. A market equilibrium price cannot be established unless Brian or Matt engages in tit-for-tat strategy. A market equilibrium price cannot be established without repeated trials. The market equilibrium price is the high price.
- Microsoft and a smaller rival often have to select from one of two competing technologies, A and B. The rival always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. If the two companies select different technologies, Microsoft's payoff is 6 units of utility, while the small rival suffers a loss of utility of 2. If the two companies select the same technology, Microsoft suffers a loss of utility of 2 while the rival gains 2 units of utility. Using the given information, fill in the payoffs for each cell in the matrix, assuming that each company chooses its technology simultaneously. Microsoft Technology A Technology B Rival Technology A Rival: , Microsoft Rival: , Microsoft Technology B Rival: , Microsoft Rival: , Microsoft True or False: There is no equilibrium in pure strategies. True False Note:- Do not provide handwritten…Consider the following three-stage duopoly game. There are two firms in the market: Firm 1 and Firm 2. In the first stage, a first-price auction is conducted to determine the order of moves. The firm with the highest bid (first mover) pays a cost equivalent to its bid and chooses its action in the second stage. After observing this action, the other firm (second mover) chooses its action in the third stage. When there is a tie in the first stage (both firms submit the same bid), a coin is tossed to determine the winner, and only the winner pays its bid. Each firm has the following three possible actions: small (expansion), medium (expansion) and large (expansion), and the payoffs they obtain in the market (not the final payoffs yet) are shown below: The second mover Small Medium Large 16, 12 Medium 18, 8 19, 7 13, 10 14, 11 Small 9, 9 10, 13 12, 10 The first mover Large 14, 12 The final payoff is equivalent to the payoff obtained in the market minus the cost (if any) paid in auction.…John and Paul are walking in the woods one day when suddenly an angry bear emerges from the underbrush. They each can do one of two things: run away or stand and fight. If one of them runs away and the other fights, then the one who ran will get away unharmed (payoff of 0) while the one who fights will be killed (payoff -200). If they both run, then the bear will chase down one of them and eat them to death but the other one will get away unharmed. Assuming they don't know which one will escape we will call this a payoff of -100 for both. If they BOTH fight, then they will successfully drive off the bear but they may be injured in the process (payoff -20). Construct a payoff matrix for this game and identify the pure strategy Nash equilibrium. (Indicate it with words not with a circle!)