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Actual authority is the authoritya partner appears to have to third parties external to the
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- 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:…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?True or false: Discuss if False Homoscedasticity means that E (e^2).
- ** 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.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.)Suppose that the University of Alabama and Clemson are making spending decisions for theupcoming year. Assume that Alabama is currently spending $15 million on their recruiting andfacilities, and Clemson is spending $10 million. Each team has an additional $5 million to spendor keep as profits. If they both choose to not spend the additional $5 million then Alabama hasa 60% chance of getting the highest quality quarterback recruit to commit to them (getting thecommitment of the player is the goal). However, if they both choose to spend the additional $5million then there is a 57% chance that Alabama gets the high quality quarterback to commit. IfAlabama spends the additional $5 million but Clemson doesn’t then there is a 67% chanceAlabama gets the recruit. However, if Alabama does NOT spend the additional $5million butClemson does then there is a 50% change either team gets the recruit’s commitment. Setup thepayoff matrix and label the players, their strategies, and their payoffs, and…
- a) What is the pure strategy Nash equilibrium outcome if there is one? (solved)b) Is this a socially optimal outcome? If not, which outcome is preferred? (solved)c) Do all three solution approaches for simultaneous games work independently (not together)? If not, which do not? (solved) d) Draw the game as a game tree (extensive form). (to be solved)e) Switch the payoffs in cells (A, A) and (D, D). What is the pure strategy Nash equilibrium outcome if there is one? (to be solved)You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…[Adverse Selection] Each of the two players receives an envelope, in which there is anamount of money that is equally distributed from $0, $1, $2, ..., $100. The amounts in twoenvelopes are independent. After receiving the envelope, each individual can check exactlyhow much money is put in his/her own envelope. Then each player has the option to exchangehis/her envelope for the other individual's prize. The decisions are made simultaneously. Ifboth individuals agree to exchange, then the envelopes are exchanged; otherwise, if at leastone player chooses not to exchange, each individual keeps his/her own envelope and receivesits attached sum of money.a. Model this game as a static Bayesian game (write the normal formrepresentation) and find the Bayesian Nash equilibrium.b. Consider a new game where the probability distribution of money in eachenvelope is changed. The amount is equal to $100 with probability 90%, and is equalto each number in $0, $1, $2, ... ,$99 with probability 0.1%.…
- 1) What are the Nash equilibria? Which one is unreasonable/non-credible threat? 2) What are the subgame perfect Nash equilibria? Does SPNE concept eliminate the unreasonable Nash equilibrium?Karen goes to the casino with 1000$ and plays the following strategy: In her first game, she putsin 1$. If she wins, she finishes playing and takes her profit home. If she looses a game, she willplay another game and put in twice as much money as she did in the previous game. If she wins,she will finish playing and take her profits home. She will keep going with that strategy, untilshe either wins a game or runs out of money.(a) Create a table for n = 1, 2, ..., 10 which lists: (a) The amount of money she puts in in game n;(b) the sum of the amount of money she has put in in all games up to this game n; and (c)her overall profit if the game n is the first game she wins.(b) What is the likelihood of her loosing 8 games in a row?(c) How many games can she loose in a row before she cannot afford to continue with herstrategy of doubling her bet?(d) Given the low likelihood of loosing, is this a smart strategy for Karen to pursue?* 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
