Homework help, Chapter 20
Homework help, Chapter 20 Econ 121
Santa Ana College
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Date Created: 05/22/16
1. Define the prisoner’s dilemma game. The prisoner’s dilemma game is a twoperson noncooperative cooperative simultaneous game that demonstrates the difficulty of cooperative behavior in certain circumstances. a. What assumptions lead to the dilemma? If the prisoners do not confess, each would get a light sentence. But each prisoner is interrogated separately and is offered the chance to go free if he or she confesses to the crime and agrees to serve as a witness against the other prisoner. This creates the incentive for both prisoners to confess. If the prisoners do not confess, each would get a light sentence. But each prisoner is interrogated separately and is offered the chance to go free if he or she confesses to the crime and agrees to serve as a witness against the other prisoner. This creates the incentive for both prisoners to confess. If the prisoners do not confess, each would get a light sentence. But each prisoner is interrogated separately and is offered the chance to go free if he or she confesses to the crime and agrees to serve as a witness against the other prisoner. This creates the incentive for both prisoners to not b. Cheap talk creates the possibility of escaping it. c. What does the standard model say about your answer to b? What does experimental economics say? Standard economics would say that the answer to b does matter. Experimental economics would say it does not matter. Standard economics would say that the answer to b does not matter. Experimental economics would say it does matter. Standard economics would say that the answer to b does not matter. Experimental economics would say it does not matter. Standard economics would say that the answer to b does matter. Experimental economics would say it does matter. 2. Is the solution to the prisoner’s dilemma game a Nash equilibrium? Why? The solution to the prisoner’s dilemma game is a Nash equilibrium because no player can improve his or her payoff by changing strategy unilaterally. The solution to the prisoner’s dilemma game is not a Nash equilibrium because both players can improve their payoffs by cooperating. The solution to the prisoner’s dilemma game is not a Nash equilibrium because players do not end up in the best combination for both. The solution to the prisoner’s dilemma game is a Nash equilibrium because it is a noncooperative game in which both players have to expect that the other is purely selfish. 3. If a player does not have a dominant strategy, can the game still have a Nash equilibrium? Yes. There is no reason that a dominant strategy must exist to have a Nash equilibrium. The outcome is a Nash equilibrium because each player has made his or her choice based on the best strategy of the other player. No. At least one player must have a dominant strategy for the outcome to be a Nash equilibrium. No. If there is no dominant strategy, there is no predictable outcome and therefore no Nash equilibrium. Yes. A Nash equilibrium is possible only if neither player has a dominant strategy. If a dominant strategy exists, it is no longer a Nash equilibrium. 4. Two firms have entered an agreement to set prices. The accompanying payoff matrix shows profit for each firm in a market depending upon whether the firm cheats on the agreement by reducing its prices. a. What is the dominant strategy for each firm, if any? Firm A: cheat Firm B: cheat b. What is the Nash equilibrium, if any? Both cheat 5. Two people are arrested and charged with the same crime. Each is given the opportunity to accuse the other of the crime. The payoff matrix shows how much time each will serve depending on who rats out whom. a. What is the dominant strategy for each, if any? Prisoner A: there is no dominant strategy Prisoner B: there is no dominant strategy b. What is the Nash equilibrium, if any? Both remain silent. Both accuse the other prisoner. Prisoner A remains silent and Prisoner B accuses. Prisoner A accuses and Prisoner B remains silent. There is no Nash equilibrium. 6. Would the results of the prisoner’s dilemma game be different if it were a sequential rather than a simultaneous game? It would no longer be a dilemma because one player’s choice would be revealed. The first player would reveal his or her choice and then the second player would choose the best strategy, potentially making both better off. It would no longer be a dilemma because the second player has all the power. There would no longer be a Nash equilibrium because the second player essentially determines the outcome. It would still result in a dilemma because the second player would have more power than the first player. This would lead to a different Nash equilibrium, but it doesn't change the fact that the first player doesn't know what the second player will do. It would be unchanged because both players still have to make choices without fully knowing what the other player is thinking. The Nash equilibrium would remain the same. 7. State whether each of the following situations is a simultaneous or sequential game. Explain your answer. a. A congressional vote by roll call. Sequential because people choose one after the other. Sequential because roll call is done privately. Simultaneous because roll call is done all at once. Simultaneous because the question is framed by the person calling the roll. b. The ultimatum game. Simultaneous because the two people must write down their highest offer and lowest acceptance at the same time. Sequential because the two people must write down their highest offer and lowest acceptance at the same time. Simultaneous because the question is framed by the person making the offer. Sequential because an offer is made and then the next person decides whether to accept. c. The Civil War. Simultaneous because neither side had time to respond to the tactics of the other. Each had to decide before the Civil War began on its strategy and then engage. Sequential because the Civil War had many sequential battles. Neither sequential nor simultaneous. Wars cannot be characterized within the game theory framework. Both sequential and simultaneous. Sequential because battles are initiated one after the other, allowing each side to respond to the other in sequence. Simultaneous in that the battles are fought where each side determines a strategy and engages at the same time. d. The segregation game (requires reading the box “The Segregation Game and Agent Based Modeling” on page 447). Sequential because players respond to the choices others have made before. Simultaneous because players do not know the decisions of the other players ahead of time. Simultaneous because players have to choose where to live in the neighborhood at the same time and stick with their decisions. Sequential because players make choices after the game has been set up. 8. Can a player have a rollback strategy in a simultaneous move game? Yes. Rollback strategies exist for both simultaneous and sequential games. In a simultaneous game, a rollback strategy is based on the expected choices of other players. No. Rollback strategies only exist for sequential games. This is because a player can begin with a desired outcome and then determine the decisions that will lead her to that outcome. Yes. In fact, rollback strategies exist only for simultaneous games. The rollback strategy is based on the expected choices of other players. No. Rollback strategies do not exist for either simultaneous or sequential games because it is impossible to predict the choices of other players. 9. True or false? If a game has a Nash equilibrium, that equilibrium will be the equilibrium that we expect to observe in the real world. False. People don’t always act in the way that a Nash equilibrium requires. People don’t always make the necessary calculations and they take into account the outcome of others. True. As long as people are rational and have their own selfinterest at heart, reallife games will result in the Nash equilibrium. False. A Nash equilibrium is based on very strict assumptions that rarely hold in the real world. No realworld situation leads to a Nash equilibrium. True. Nash’s theory of equilibrium outcomes was derived from realworld interactions. The theory holds true for almost all realworld scenarios. 10. Why might the multipleplay ultimatum game have a different result than the singleplay ultimatum game? The multipleplay ultimatum game allows for players to send signals. Therefore, the receiver can punish a player who doesn’t share enough. The multipleplay ultimatum game leads to a simpler equilibrium: the first player offers exactly half of the total sum to the second player. The multipleplay ultimatum game generally results in less cooperation because both players fall into a backandforth pattern of trying to punish the other player. In the multipleplay ultimatum game, the first player generally offers less money to the second player than in the singleplay ultimatum game. 11. Why do sellers generally prefer a Vickrey auction to a regular sealed bid if sellers don’t receive the highest bid in the Vickrey auction? The secondhighest bid is about the same in both auctions. Sellers prefer the final price is not revealed to all bidders. The secondhighest bid in a Vickrey auction is generally higher than the highest bid in a regular sealedbid auction. Sellers would never prefer Vickrey auctions. Sellers only have to sell their item if the bid is the highestprice bid. 12. Say that you are bidding in a sealedbid auction and that you really want the item being auctioned. Winning it would be worth $250 to you. Say you expect the nexthighest bidder to bid $100. a. In a standard “highestbid” auction, what bid would a rational person make? The rational choice is to bid a little bit more than $100 because that is the expected nexthighest bid. The rational choice is to bid $250 since that is what the item is worth to you. The rational choice is to bid just under $250 so that you have a higher chance of winning the auction and would still have a net benefit. The rational choice is to bid over $250 to guarantee that you win the item. b. In a Vickrey auction, what bid would he make? The rational choice is to bid $250. The rational choice is to bid slightly more than $100. The rational choice is to bid slightly more than $250. The rational choice is to bid slightly less than $250. 13. When consumers were given the opportunity to select a package of ground beef labeled “75% lean” or a package of ground beef labeled “25% fat,” most consumers chose “75% lean.” Why? What concept from the chapter does this illustrate? The reason is that consumers are loss averse. This is called a framing effect. The reason is that consumers infer the value of a product from positive advertising. This is called inference induction. The reason is that consumers respond better to higher numbers. They feel they are getting more because 75 is greater than 25. The concept is the endowment effect. The reason is that consumers are swayed by cheap talk. Cheap talk is the concept. 14. Why does it take just a few people to act rationally for the standard model to hold? If “money is left on the table,” the few people who act rationally will take advantage of the irrationality of others, and they will take that money off the table. Once people see that all other players are acting rationally (selfishly), they will also adopt a rational approach. A Nash equilibrium requires that only a small proportion of players act rationally. Those who act irrationally will always lose to the rational players. This leaves only rational players, so the standard model holds in the long run.
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