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# Mary and Lisa mow lawns Mary 15 20 Lisa 15 20 Mary and Lisa are both kids living in the same area. To earn money, they mow lawns in their...

Economics, Games, Prisons etc. Would appreciate math for very last example

Mary and Lisa mow lawns Lisa Mary 15 20 15 20 Mary and Lisa are both kids living in the same area. To earn money, they mow lawns in their neighborhood. Each can charge \$15 or \$20 per lawn. If they both charge \$15, each will get 10 lawns to mow. IF they both charge \$20 each will get 5 lawns to mow. If one charges \$15 and the other charges \$20, then the less expensive one will get 12 lawns to mow and the more expensive one will get only 3 lawns to mow. If Mary charges \$15 per lawn, she will earn a payoff of either ________( \$60 or 150, \$100 or 180, \$60 or 100, \$150 or 180, \$60 or 180, \$100 or 150) depending on what price Lisa charges. If Mary charges \$20 per lawn, she will earn a payoff of either_______________( \$60 or 150, \$100 or 180, \$60 or 100, \$150 or 180, \$60 or 180, \$100 or 150 depending upon what price Lisa charges. Does Mary have a dominant strategy? _______________ (Yes, charge \$15 per lawn, No, Yes, charge \$20 per lawn. ) Campaign Problem Dawn Robert Play Clean Attack Pay clean 6,6 1,8 Attack 8,1 3,3 Dawn and Robert candidates running for office are trying to raise funds. In their promotional attempts, each candidate can choose whether to attach the opponent or to refrain and keep the campaign clean. The table above shows the payoff matrix for the candidates in this fund-raising game. The payoffs represent the amount of \$ raise by each campaign in thousands of dollars each week the game is played. a. What is the Nash equilibrium of this game? b. In equilibrium, Dawn will raise _________for her campaign and Robert will raise _______for his. c. IS there a different choice either of the candidates can make that would make them both better off? ______( Options - Yes, Both attack, Yes, Dawn attacks and Robert plays clean, Yes, both play clean, Yes, Dawn plays clean and Robert attacks, No, there is no other payoff that leaves both better off, No, they are already playing such that payoffs are maximized) Suppose the fame is repeated once each week for five weeks until Election Day . What will each candidate choose for the first round of the game_____ (Options - There is not enough info, both will play clean, Dawn will stack and Robert will play clean, Dawn will play clean and Robert will attack, Both will attack). In 3 rd round _____________(Dawn will attack and Robert will play clean, Dawn will play clean and Robert will attack, Both will play clean, Both will attack, There is not enough info to determine) In fifth round of the game______(Both will attack, There is not enough info to determine the choices, Dawn will play clean and Robert will attack, Both will play clean, Dawn will attack and Robert will play clean). d. Now suppose that the candidates expect to play this game in future elections, not only this one. Namely the candidates expect to play for an unknown number of rounds. In hopes of gaining more funds, Dawn announces she will keep her campaign clean as long as her opponent Robert does that same and will attack only if Robert attacks. She is playing “tit-for-tat: strategy and will play clean for first round and subsequent rounds depend on opponent. Think of candidates as two parties that can rationally expect to have candidates run against each other in future elections. It’s safe to assume the political parties don’t know how long they will exist and therefore don’t know how many rounds of this game will be played or when the last run will be.
What will each candidate play for the first round?___________(Dawn will play clean and Robert will attack, Both will play clean, Both will attack, There is not enough info, Dawn will attack and Robert will play clean) For second round___________( Dawn will play clean and Robert will attack, Both will play clean, Both will attack, There is not enough info, Dawn will attack and Robert will play clean). So long as the assumptions above don’t change, what do you expect each candidates to play in all subsequent rounds ___________________( Dawn will play clean and Robert will attack, Both will play clean, Both will attack, There is not enough info, Dawn will attack and Robert will play clean). Campaign Problem Elementary Junior High Large Small Large Small Schools having a bake sale. Both plan to sell cupcakes at a concert at the park. Each must decide to sell large or small size. The schools net a profit of \$1 on large cupcakes and \$1.50 on small cupcakes sold. No matter what size the cupcakes, 240 people will purchase cupcakes at the concert. If both Engle and Granger make the same-size cupcakes, each school will sell 120 cupcakes. However if one school makes large cupcakes and the other school makes small cupcakes, all 240 people will buy the large cupcakes. Any excess cupcakes will be sold to school’s cafeteria at a price equal to average cost. (So no loss is incurred for unsold cupcakes). a. If Elementary bakes large cupcakes, Granger will earn a payoff of _________(\$80, \$0, \$40, \$100, \$60) b. If it makes small cupcakes or (\$180, \$200, \$240,\$120, \$300) if it bakes large. c. If Elementary bakes small, Granger will earn a payoff of (\$180, \$200, \$240,\$160, \$300) if it bakes small cupcakes or _______((\$260, \$220 \$240,\$160, \$200) if it bakes large cupcakes. d. Does Granger Have a dominant strategy? ____________(Yes, baking small, No, Yes, baking large). e. IS this payoff matrix an example of a prisoner’s dilemma?________(Yes, No). Medication Problem Digestible Medications Nelly Pharma Advertise Don’t Advertise Enter 4,12 8,10 Stay Out 0,14 0,20 Nelly Pharma is selling prescription ulcer meds. The patent on the meds is about to expire. Digestible’s a new phama company is considering entering the market but does not have the resources to advertise. Nelly Pharma must decide whether to advertise its product. If Digestibles enters the market, advertising will help differentiate the Nelly Pharma product from that of Digestibles, thereby increasing the number of doctors prescribing the Nelly Pharma medication and increasing its profits. However, if Digestibles doesn’t enter, money spent on advertising will be wasted because all doctors will prescribe the medication made by Nelly Pharma (because there is no other option).
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