ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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- Ma4. Please give only typed answer.arrow_forward(a) In the extensive form below, player 1 moves first, and player 3 moves last. (3) Note the two information sets including the nodes where player 3 moves: P1 L R P2 P2 A B P3 P3 d 2,3.2 2,1,1 3,0,4 3.4,0 3,1,1 Ennio Stacchetti December 17, 2021 (a) Find all subgame perfect equilibria in pure strategies. (b) Find a Nash equilibrium that is not a subgame perfect equilibrium.arrow_forwardN=2 video broadcasting websites, You and Twi, must decide the number of minutes of ads to be displayed for every video that the user elects to watch. Let tY be the number of ad-minutes per video set by You, and tT the number of ad-minutes per video set by Twi. Streaming one video costs You cY=0.02, while it costs Twi cT=0.03. There are 100 million potential users, and each watches videos according to the following demand curves: qY((tY,tT) =10-2tY+tT=10-2tT+tY a- What is the cross-price elasticity between You and Twi? b- Suppose, for now, that You and Twi enter an (illegal) agreement by which they set tY=tT=t Derive the total number of users in the market as a function of t. Derive the profits for each website as a function of t. c- Now let the two platforms compete by each setting their number of ad-minutes: i. What is the best reply of You? What is the best reply of Twi? ii. Find the Nash Equilibrium of the game. iii. How many total users choose You and how many total users choose…arrow_forward
- In a small business, there are two players: the boss and the employee. The employee has to choose whether to undergo training or not. The training costs Php1000. Now, the boss has to decide whether to pay a fixed wage of Php10000 to the employee or share the total profit of the small business exactly half to the employee. The total profit depends on the training and profit sharing. With no training and fixed wage, the total profit is Php20000. If either training or profit sharing is implemented, the total profit rises to Php22000. If both training and profit sharing are implemented, the total profit is Php25000. Let the employee be the row player and the boss be the column player. If the employee does not undergo training and the boss decides on fixed wage, what is the payoff ordered pair for this scenario? O (9000,12000) O (11500,12500) O (11000,11000) O (10000,10000)arrow_forwardSuppose there are five people, Adem, Damla , Hakan, Sema, Birsen to rank projects, Hospital (H), University (U), Cinema (C ), Shopping center (S) as follows: a) Sketch the preferences (LIST PREFERENCES AS H-C-U-S). b) Will any project be chosen by a majority vote rule? If so, which one? If not, explain why.arrow_forwardIn this version of the ultimatum game experiment, one participant is given £100, and is told to offer to split that amount with another participant. The second player can either refuse to accept the division, in which case the participant receiving the £100 has to give it back, or can accept the division, in which case, the player receiving the money splits the £100 as proposed. For the participant who has to accept or reject the offer A) The best strategy is to accept any offer which meets the social norm for fairness. B) The best strategy is to threaten to turn down any transfer of less than £100 to ensure that the person receiving the money makes a fair offer. C) There is a dominant strategy to accept any offer because gaining some money is better than gaining no money D) There is a dominant strategy to turn down any offer other than £50 because an unequal split would be unfair.arrow_forward
- One type of systematic error arises because people tend to think of benefits in percentage terms rather than in absolute dollar amounts. As an example, Samir is willing to drive 20 minutes out of his way to save $4 on a grocery item that costs $10 at a local market. But he is unwilling to drive 20 minutes out of his way to save $10 on a laptop that costs $400 at a local store. In percentage terms, how big is the savings on the grocery item? On the laptop? In absolute terms, how big is the savings on the grocery item? On the laptop? If Samir is willing to sacrifice 20 minutes of his time to save $4 in one case, shouldn't he also be willing to sacrifice 20 minutes of his time to save $10?arrow_forwardA crime is witnessed by 3 citizens. Every citizen would like the police to be informed about the crime, but prefers that someone else reports it (filing a report is a hassle). Each of the three citizens chooses simultaneously (and independently) whether to call the police or not. When no one makes a call, every citizen receives payoff 0. If at least one citizen calls the police, citizens who call get payoff 5, and those who don't call get payoff 9. (a) Find all Nash equilibria in pure strategies. (b) Compute a symmetric Nash equilibrium in mixed strategies (i.e., an equilibrium in which every citizen calls with the same probability p E (0, 1)). (c) Does the game have a Nash equilibrium in pure or mixed strategies different from those you identified in (a) and (b)? If yes, construct one. If not, argue why not.arrow_forwardLet us see the example of Juan and María given but modify their preferences. It is still the case that they are competitive and are deciding whether to show up at their mom’s house at 8:00 A.M., 9:00 A.M., 10:00 A.M., or 11:00 A.M. But now they don’t mind waking up early. Assume that the payoff is 1 if he or she shows up before the other sibling, it is 0 if he or she shows up after the other sibling, and it is 1 if they show up at the same time. The time of the morning does not matter. Find all Nash equilibria.arrow_forward
- Context : The London Metro Bus is crowded for travel during peak hours. During such travel hours two daily passengers ‘James’ and ‘Robert’ enter the Metro. Luckily, two adjacent seats are free in the bus. Each of them must decide whether to sit or stand. For both, sitting alone is more comfortable than sitting next to the other person, which in turn is more comfortable than standing. Question : Assume that both ‘James’ and ‘Robert’ are altruistic, ranking outcomes according to the other person’s comfort and, out of politeness, prefer to stand than to sit if the other person stands. Model the situation as a strategic game and find any Nash equilibrium (equilibria) if it exists. Does a dominant strategy exist for either ‘James’ or ‘Robert’ with these preferences? show ALL steps and working in support to your answerarrow_forwardConsider the following game played by four individuals, players 1, 2, 3, and 4. Each individual has $10,000. Each player can donate between $0 and $10,000 to build a public park that costs $20,000. If they collect enough money, they construct the park, which is worth $9,000 to each of them. However, if they collect less than $20,000, they cannot build a park. Furthermore, regardless of whether the park is built or not, individuals lose any donations that they make. a) Describe the Nash equilibria for a simultaneous game. What makes them equilibria? Hint: There are many equilibria, so you may want to use a mathematical expression! b) Suppose that players 1, 2, and 3, each donate $4,000 for the park. How much will player 4 donate and why. What are the resulting payoffs for the players? c) Suppose instead that player 1 donated first, player 2 second, player 3 third, and player 4 last. Furthermore, players could only donate in intervals of 1,000 (0, $1,000, $2,000, etc.). How much will…arrow_forward4 In a gambling game, Player A and Player B both have a $5 and a $10 bill. Each player selects one of the bills without the other player knowing the bill selected. Simultaneously they both reveal the bills selected. If the bills do not match, Player A wins Player B's bill. If the bills match, Player B wins Player A's bill. (a) Develop the game theory table for this game. The values should be expressed as the gains (or losses) for Player A. Player B Player A $5 $10 $5 (b) Is there a pure strategy? Why or why not? ---Select--- . Since the maximum of the row minimums is --Select--- (c) Determine the optimal strategies and the value of this game. probability Player A selects $5 probability Player A selects $10 probability Player B selects $5 probability Player B selects $10 = = $10 = = Does the game favor one player over the other? Yes O No and the minimum of the column maximums is (d) Suppose Player B decides to deviate from the optimal strategy and begins playing each bill 50% of the…arrow_forward
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