Consumers are located uniformly across thestreet, with their location ranging between 0and 1. There are two apple sellers in themarket (Seller 1 and Seller 2) who must decidewhere to locate their shops. Consumersprefers to travel a shorter distance to a seller:(i.e. if Seller 1 is located at 0.3 and Seller 2 islocated at 0.8, a consumer located at 0.5 willbuy ice cream from Seller 1). If both sellers arein the same location, they split the market. (a)Set-up a matrix for a game in which sellershave one of three options: (i) locating at 0, (ii)locating at 1/2, or (iii) locating at 1; and writedown the associated payoffs.

1.Location at 0: only the customers who are settled at 0 or .5 will make purchase.2. Location at .5:…

buy ice cream from Seller 1). If both sellers are in the same location, they split the market. (a) Set-up a matrix for a game in which sellers have one of three options: (i) locating at 0, (ii) locating at 1/2, or (iii) locating at 1; and write down the associated payoffs.

buy ice cream from Seller 1). If both sellers are in the same location, they split the market. (a) Set-up a matrix for a game in which sellers have one of three options: (i) locating at 0, (ii) locating at 1/2, or (iii) locating at 1; and write down the associated payoffs.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter13: best-practice Tactics: Game Theory

Section: Chapter Questions

Problem 5E

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** Please be advsed that this is practice only from previous yeasr *** Answers: (a) There are no Nash equilibria.(b) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and no mixed strategy Nash equilibria.(c) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 1/2.(d) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 1/2 and q = 3/4.(e) There are two pure strategy Nash equilibra, one with (H,H) and another with (L,L), and one mixed strategy Nash equilibria with p = 3/4 and q = 1/2.
Suppose that there are two ice cream vendors on a beach which isrepresented by the 0-1 interval. Customers are uniformly distributedalong that interval. The vendors simultaneously select a position. Cus-tomers go to the closest vendor and split themselves evenly if the ven-dors choose an identical position. Each vendors want to maximize itsnumber of customers. Which location should the vendors choose in the0-1 interval, why?
8. Two states, A and B, have signed an arms-control agreement. This agreementcommits them to refrain from building certain types of weapons. The agreement is supposed tohold for an indefinite length of time. However, A and B remain potential enemies who wouldprefer to be able to cheat and build more weapons than the other. The payoff table for A (player1, the row player) and B (player 2, the column player) in each period after signing thisagreement is below. a) First assume that each state uses Tit-for-Tat (TFT) as a strategy in this repeated game.The rate of return is r. For what values of r would it be worth it for player A to cheat bybuilding additional weapons just once against TFT? b) For what values of r would it be worth deviating from the agreement forever to buildweapons? c) Convert both values you found in parts a and b to the equivalent discount factor dusing the formula given in lecture and section. d) Use the answers you find to discuss the relationship between d and r:…
A game is played as follows: First Player 1 decides (Y or N) whether or not to play.If she chooses N, the game ends. If she chooses Y, then Player 2 decides (Y or N) whetheror not to play. If he chooses N the game ends. If he chooses Y, then they go ahead and playanother game with the payoffs shown below. A player who opts out by choosing N gets 2 andthe other player gets 0. Draw the tree of this game and then find the two subgame-perfect Nashequilibria.
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. If you examine the decision tree in Figure 9.12 (orany other decision trees from PrecisionTree), you willsee two numbers (in blue font) to the right of each endnode. The bottom number is the combined monetaryvalue from following the corresponding path throughthe tree. The top number is the probability that thispath will be followed, given that the best strategy isused. With this in mind, explain (1) how the positiveprobabilities following the end nodes are calculated,(2) why some of the probabilities following the endnodes are 0, and (3) why the sum of the probabilitiesfollowing the end nodes is necessarily 1.
Consider a setting in which player 1 moves first by choosing among threeactions: a, b, and c. After observing the choice of player 1, player 2 choosesamong two actions: x and y. Consider the following three variants as towhat player 3 can do and what she knows when she moves:a. If player 1 chose a, then player 3 selects among two actions: high andlow. Player 3 knows player 2’s choice when she moves. Write down theextensive form of this setting. (You can ignore payoffs.)b. If player 1 chose a, then player 3 selects among two actions: high andlow. Player 3 does not know player 2’s choice when she moves. Writedown the extensive form of this setting. (You can ignore payoffs.)c. If player 1 chose either a or b, then player 3 selects among two actions: high and low. Player 3 observes the choice of player 2, but not that of player 1. Write down the extensive form of this setting.(You can ignore payoffs.)
You and your friend will divide $4. You have agreed to use the following procedure.Each of you will name a number of dollars, either $0, $1, $2, $3, or $4. You will chooseyour numbers simultaneously. If the sum of the amounts is less than or equal to $4, theneach of you receives the amount you named and the rest of the money is thrown away.If the sum of the amounts is greater than $4 and the amounts named are different, thenthe person who named the smaller amount receives that amount and the other personreceives the remaining money. If the sum of the amounts is greater than $4 and theamounts named are the same, then each receives $2. (a)Draw the payoff matrix of this game. Let “you” be the row player and “yourfriend” be the column player.(b) Derive the best reply functions of all players.(c) Find the Nash equilibrium (or all of the equilibria) of this game using thebest reply functions you found in part (a).
A clothing store and a jeweler are located side by side in a shopping mall. If the clothing store spend C dollars on advertising and the jeweler spends J dollars on advertising, then the profits of the clothing store will be (36 + J )C - 2C 2 and the profits of the jeweler will be (30 + C )J - 2J 2. The clothing store gets to choose its amount of advertising first, knowing that the jeweler will find out how much the clothing store advertised before deciding how much to spend. The amount spent by the clothing store will be Group of answer choices $17. $34. $51. $8.50. $25.50.
1.4. Suppose you are against one of two alternatives but 90% of theelectorate disagrees with your position and favors that option. Is there avoting method that is anonymous, neutral, and monotone that preventsthat option from being selected as the winning alternative?
There are N>=2 collectors who engage in the auction of an antique. The collectorshave a common valuation of the antique, denoted by v, which is known to all. Thecollectors make a simultaneous bid. Let pn denote the bid by collector n = 1,....,N. The one with the highest bid wins the antique. The winner receives payoff v-pi.The other(s) receive zero payoff. If more than one collectors make the same highestbid, then they have an equal chance of winning the item. Prove that: A) It is not a Nash Equilibrium (NE) if the highest bid is v and onlyone collector bids this price.(b) It is not a NE if the highest bid is less than v.(c) It is a NE that the highest bid is v and more than one collector bidsthis price
* Please be advised this is for practice preperation only ** i just really need help on this - I dont undertsand X is an arbitrary number Suppose the stage game was played for 3 rounds. Consider the following strategy: Round 1: play C. Round 2: play C if both players played C in round 1. Otherwise, play E. Round 3: play D if both players played C in rounds 1 and 2. Otherwise, play E.Ignore discounting (that is, δ = 1). Suppose that both players pick the strategy above. What condition on x is needed to make this strategy profile a SPNE? Hint: remember to check for possible deviations separately for rounds 1 and 2.(a) 5 ≥ x(b) 7 ≥ x(c) 9 ≥ x(d) 11 ≥ x(e) 13 ≥ x