Suppose there are 4 agents i e (1, 2, 3, 4} and 4 objects je {a, b, c, d}. Below is a matrix of probability shares. Show how to represent it as a lottery over deterministic object allocations. Agent Good a bcd10.5 0.5002 0.125 0 0.875 0 3 0.125 0.5 0.125 0.25 4 0.25 00 0.75
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- . Ayça and Barış are playing a game and following payoff matrix is for the payoffs of Ayça. Answer the questions according to the following payoff matrix. a) What is the probability that the value of the game is 10?To go from Location 1 to Location 2, you can either take a car or take transit. Your utility function is: U= -1Xminutes -5Xdollars +0.13Xcar (i.e. 0.13 is the car constant) Car= 15 minutes and $8 Transit= 40 minutes and $4 What is your probability of taking transit given the conditions above? What is your probability of taking transit if the number of buses on the route were doubled, meaning the headways are halved? Remember to include units.Consider “Providing a Public Good under Incomplete Information". (refer to pages 70-74, lecture notes.) If c and cz have the following distribution. 2. 0.5 1.2 C2 0.5 1.2 Prob 1/2 1/2 Prob 1/3 2/3 Find all Bayesian Nash Equilibria of this game. Select all cOTrect amswers. Don't copy Chegg give new answer ASAP
- Charles is participating in an experiment. His payoff in the experiment is tied to his effort e doing a mundane task. There is also some risk involved by design-there is a chance p that Charles is going to get a fixed payment L regardless of his effort. Charles' payoff is thus: with probability p w.e with probability 1- p Charles has to pay a cost C, which increases with his effort. First, let us assume that Charles' utility is the expected payoff net of this cost: U(e) = pL + (1 – p)we – c(e) Derive the first order condition with respect to e. b. How doesp affect Charles' effort e? c. How does L affect e?Two friends, Khalid and Mahmood, are going to a watch a world cup football match. They play a simple game in which they hold out one or two fingers to decide who will pay for the other's ticket. Khalid wins if the fingers held out add up to an even number; Mahmood wins if the fingers held out add up to an odd number. The price of the ticket is 25 OMR. Construct a payoff matrix for the game. Is there a unique Nash equilibrium in this game? Which strategy should a player use to maximize her chances of winning the game?Imagine that a zealous prosecutor (P) has accused a defendant (D) of committing a crime. Suppose that the trial involves evidence production by bothparties and that by producing evidence, a litigant increases the probabilityof winning the trial. Specifically, suppose that the probability that the defendant wins is given by eD>(eD + eP), where eD is the expenditure on evidenceproduction by the defendant and eP is the expenditure on evidence production by the prosecutor. Assume that eD and eP are greater than or equal to0. The defendant must pay 8 if he is found guilty, whereas he pays 0 if heis found innocent. The prosecutor receives 8 if she wins and 0 if she losesthe case. (a) Represent this game in normal form.(b) Write the first-order condition and derive the best-response function foreach player.(c) Find the Nash equilibrium of this game. What is the probability that thedefendant wins in equilibrium.(d) Is this outcome efficient? Why?
- Suppose the payoff matrix was modified such that: Confess Lie About Lie About Confess to Peter / MJ About Knowing Liking Peter Liking Peter Knowing Admit Being 2,2 3,1 8,12 3,14 Spidey Lie About 1,1 4,2 9,8 1,7 Spidey Lie About 4,5 8,6 14,18 4,14 Liking MJ Confess to 5,2 7,1 12,14 5,16 Liking MJN=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…3. Find the saddle point, if it exists, for the following game. (b) Solve the following game by using the principle of dominance and find the probabilities of strategies for each player and the value of the game. Player B Player A II III IV V 3 4 4 II 2 4 III 4 4 IV 4 4 20 2420 8760