7.6 CHAPTER 750%. Unlike Mars, Hershey knows the value of b. Draw the tree for this new game anddetermine its equilibrium.■7.6. HERNAN CORTÉZ. In a message to the king of Spain upon arriving in Mexico, Span-ish navigator and explorer Hernan Cortéz reports that, "under the pretext that [our] shipswere not navigable, I had them sunk; thus all hope of leaving was lost and I could actmore securely." Discuss the strategic value of this action knowing the Spanish colonistswere faced with potential resistance from the Mexican natives.■7.7.HDTV STANDARDS. Consider the following game depicting the process of standardsetting in high-definition television (HDTV). The US and Japan must simultaneouslydecide whether to invest a high or a low value into HDTV research. If both countrieschoose a low effort than payoffs are (4,3) for US and Japan, respectively; if the USchooses a low level and Japan a high level

Game theory is the mathematical study of decision making in situations where multiple individuals or…

7.6. HERNAN CORTÉZ. In a message to the king of Spain upon arriving in Mexico, Span- ish navigator and explorer Hernan Cortéz reports that, "under the pretext that [our] ships were not navigable, I had them sunk; thus all hope of leaving was lost and more securely." Discuss the strategic value of this action knowing were faced with potential resistance from the Mexican natives. I could act colonists the Spanish

7.6. HERNAN CORTÉZ. In a message to the king of Spain upon arriving in Mexico, Span- ish navigator and explorer Hernan Cortéz reports that, "under the pretext that [our] ships were not navigable, I had them sunk; thus all hope of leaving was lost and more securely." Discuss the strategic value of this action knowing were faced with potential resistance from the Mexican natives. I could act colonists the Spanish

Principles of Microeconomics (MindTap Course List)

8th Edition

ISBN:9781305971493

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter17: Oligopoly

Section: Chapter Questions

Problem 9PA

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6)Game Theory: The Prisoners’ Dilemma: Assume that the Wilson and Spalding athletic equipment companies are in a one-shot game for market share and profits, but that they have the option of choosing only one of two possible price strategies for basketballs: $20 or $80. Obviously if they choose different strategies, the firm with the lower price will win the entire market. The firms face the following payoff matrix (See Chap. 10). Wilson\ \Spalding Wilson $ 20 Price Wilson $ 80 Price Spalding $ 20 Price $ 400, $ 400 $ 1500, $ 0 Spalding $ 80 Price $ 0, $ 1500 $ 1000, $ 1000 What strategy will each firm choose? Why? Which strategy is dominant? Which strategy is preferred by each firm? What will be the outcome of the one-shot game? Where is the Nash equilibrium? Which outcome would be best for the two firms? What will happen if the game is repeated an infinite number of times?
Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land. Farmer 2 Farmer1 1 cow 2+ cows 1 cow 8,8 2,10 2+cows 10,2 4,4 What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off) The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…
What is Ann's maximin strategy? Game Bob L RAnn U 10,-1 4, 4 D 4, 1 8, -1 Select one: a.none of the other answers b.4/7 U + 3/7 D c.2/5 U+ 3/5 D d.2/7 U + 5/7 D e.3/5 U + 2/5 D
. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that
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6 Two people will select a policy that affects both of them by applying a "veto" in a sequential and alternate manner, that is: person 1 begins to veto a policy and then person 2 exercises his "veto" with the remaining policies; the process repeats until only one policy remains. Assume that there are 3 policies: X,Y,Z, and that person 1 prefers X to Y to Z and person 2 prefers Z to Y to X. a. Represents the game extensively b. Give the number of subgames C. Indicate the total strategies of the players d. find all subgame perfect nash equilibria e. Find all Nash Equilibriums.
Define the prisoner’s dilemma game. The prisoner’s dilemma game is a: two-person noncooperative sequential game that demonstrates the difficulty of cooperative behavior in certain circumstances. two-person cooperative simultaneous game that demonstrates the difficulty of cooperative behavior in certain circumstances. two-person noncooperative simultaneous game that demonstrates the difficulty of cooperative behavior in certain circumstances. two-person cooperative sequential game that demonstrates the difficulty of cooperative behavior in certain circumstances. a. What assumptions lead to the dilemma? If the prisoners 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 confess. If the prisoners do not confess, each would get a…
1. Ten commuters must decide simultaneously in the morning to use route A or route B to go from home (same place for all) to work (ditto). If a of them use route A, each of them will travel for 10a + 40 minutes; if b of them use route B, each of them will travel for 10b minutes. Everyone wishes to minimize his/her commuting time. a) Describe the pure Nash equilibrium (or Nash equilibria) of this ten-person game. Compute the corresponding profile of commuting times. Explicitly list all equilibrium conditions that are satisfied.
4. Boeing and Airbus, change in profits ($m) from the development of a super jumbo jet.AirbusDevelop Do not developBoeing Develop -50, -50 -30, 80Do not develop 80, -30 0, 0a) Identify the key assumption of Game theoryb) What important lesson does game theory reveal about coordination inan oligopoly market?c) In the game above, what is the Nash equilibrium?
Game Theory. 1. Yuppie town has two food stores, LA Boulangerie, which sells bread, and La Fromagerie, whichsells cheese. It costs $1 to make a loaf of bread and $2 to make a pound of cheese. If LaBoulangerie's price is P 1 dollars per loaf of bread and La Fromagerie's price is P 2 dollars per pound ofcheese, their respective weekly sales, Q 1 thousand loaves of bread and Q 2 thousand pounds ofcheese, are given by the following equations: a) For each store, write its profits as a function of P 1 and P 2 , and find the Nash equilibriumprices in this game. b) Suppose that the two stores collude and set prices jointly to maximize the sum of theirprofits. Find the joint profit-maximizing prices for the stores.c) Provide an explanation for the differences between the Nash equilibrium prices and thosethat maximize joint profits.
Solve for the Nash equilibrium (or equilibria) in each of the following games. (a) The following two-by-two game is a little harder to solve since firm 2’spreferred strategy depends of what firm 1 does. But firm 1 has a dominantstrategy so this game has one Nash equilibrium. Firm 2 Launch Don’tFirm 1 Launch 60, -10 100, 0 Don’t 80, 30 120, 0 What is the Nash equilibrium of this simultaneous-move game? (b) What would the outcome of this game be if instead firm 1 moved first and then, after seeing what firm 1 chose, firm 2 chose it strategy? In this case firm 1 doesn’t necessarily need to choose a best response, but firm 2 must choose a best response since it moves second.
1 True or False : Every finite extensive - form game of imperfect information admits at least one pure - strategy Nash equilibrium . Justify if true or give a counter - example if not