Alice and Bob are playing a repeated game in which a certain stage game is played twice in succession. All behaviour in the first period is observed by both players before the second period commences. In the stage game, Alice has 3 pure strategies and Bob has 2 pure strategies. How m
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FINITE REPETITION
Alice and Bob are playing a repeated game in which a certain stage game is played twice in succession. All behaviour in the first period is observed by both players before the second period commences. In the stage game, Alice has 3 pure strategies and Bob has 2 pure strategies.
How many pure strategies does Bob have in the repeated game? (If necessary, use a calculator to compute this number.)
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- FINITE REPETITION Alice and Bob are playing a repeated game in which a certain stage game is played twice in succession. All behaviour in the first period is observed by both players before the second period commences. In the stage game, Alice has 2 pure strategies and Bob has 3 pure strategies. How many pure strategies does Bob have in the repeated game? (If necessary, use a calculator to compute this number.) 6. 36 216 128 64 3 729 2187A route in the city has trains that depart from station every 20 minutes. It takes a train 40 minutes to make a trip from the station to its destination. For commuters, shorter trips are considered better. Suppose that one such train with 200 commuters on it is about to depart when an additional commuter (who is running slightly late) blocks the doors in order to get on the train, which delays the train by 15 seconds. If this commuter had chosen not to block the train doors, they would have to catch the next train after this one. Question: (Please show the detailed calculation process) What is the private marginal gain of the commuter who barges on the train? What is the marginal spillover effect to all the commuters on the train in terms of travel time? What is the change in the total travel time to all the commuters on the train?FINITE REPETITION Alice and Bob are playing a repeated game in which a certain stage game is played twice in succession. All behaviour in the first period is observed by both players before the second period commences. In the stage game, Alice has 3 pure strategies and Bob has 2 pure strategies. How many pure strategies does Bob have in the repeated game? (If necessary, use a calculator to compute this number.) 2 6 2187 3 36 64 7 729 128 216 Please do fast ASAP fast
- 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?Two players bargain over 1 unit of a divisible object. Bargaining starts with an offer of player 1, which player 2 either accepts or rejects. If player 2 rejects, then player 1 makes another offer; if player 2 rejects once more, then player 2 makes an offer. If player 1 rejects the offer of player 2, then once more it is the turn of player 1 where he makes two consecutive offers. As long as an agreement has not been reached this procedure continues. For example, suppose that agreement is reached at period 5, it follows that player 1 makes offers in period 1,2 then player 2 makes an o er in period 3, then player 1 makes offers in 4,5. Negotiations can continue indefinitely, agreement in period 't' with a division (x, 1- x) leads to payoffs ( , (1-x)).(The difference from Rubinstein's alternating offer bargaining is that player one makes two consecutive offers, whereas player 2 makes a single offer in her turn.) a. Show that there is a subgame perfect equilibrium in which player 2's…Find the perfect Bayesian equilibria in the following two-person game: B. Chance 1/4 U 3/4 2 L \R (:) (?) (3) (6) () (:) (:) (*) 8
- If Firm 1 chooses to release the console in October with probability of 0.692 or December with a probability of 0.308, then Firm 2 is indifferent between choosing a release date. If Firm 2 released the console in October with probability of 0.50 or December with a probability of 0.50, then Firm 1 is indifferent between choosing a release date Suppose now that instead of choosing the release date at the same time, the firms choose sequentially (but still in advance). Firm A chooses its release date first, then firm B observes that date and chooses its own date. Thepayoffs are otherwise the same as above. Represent the game tree corresponding to this dynamic game.Tonight at 7pm a professional basketball game featuring the Golden State Warriors and the Washington Wizards will be played at the Chase Center, an indoor arena in the Mission Bay neighborhood of San Francisco, California. Our teaching assistants Yang and Guangchu are making fair bets on the game. During office hours you learn that Yang thinks the Warriors will win and believes he is making a fair bet, assigning a probability of 5/6 or 83 % to the Warriors winning. Guangchu is betting on the Wizards and also believes he is making a fair bet, assigning a probability of 7/12 or 58% to the Wizards winning. You seek to bet a total of $N with Yang and Guangchu and capture a guaranteed, risk-free arbitrage profit. Now assume that N = $240. Let x be the number of dollars bet with Yang. What is the exact range of x that guarantees that your profit is greater than or equal to zero, no matter who wins the game? O 40 < ¤ < 140 O 40 < ¤ < 24O O0 < x< 140 O0Suppose Don's wants to invest to build a condominium tower in Moscow. If he can get his friend Vlad to buy one of the units, he figures the investment will be a success (because all Vlad's rich friends will want to buy one too) and his income will be $1,000,000 this year. However, there is a 60% chance that Vlad will not be interested. In that case, the investment will fail and Don's income will be only $100,000. Don's utility function is U=In(income) The British insurance company Lloyds of London will insure the investment and they will charge him a premium of $600,000. Graph the risk situation described above. Note the expected utility. What would be the actuarially fair premium for a policy that would pay Don $900,000 in the event the investment fails? а. b С. What is Don's Risk Premium? d. Will Don buy the policy from Lloyd's of London? Explain why or why not?Suppose a group of chess players gather and decide to rank themselves in "popularity". The popularity score of a player in the gathering is the number of other players in the gathering that player has previously played a game against. Prove that there will be ties in this score among the players in the gathering.Suppose Var(X) = 36, Var(Y) = 42, and X and Y are independent. What is Var(.25X + .75Y)? Suppose Var(X) = 63, Var(Y) = 87, and X and Y are independent. What is Var(.79X + .21Y)? Suppose that Var(X) = 907.96, Var(X) = 10219.44, and Cov(X,Y) = 2694.59. What is Var(.33X + .67Y)?Suppose you are running a construction company and are in the process of signing a new contract with a lumber supplier. Getting lumber to a work site on time is critical and based on two things. First is the effort exerted by the lumber supplier and second how fast the shipper of the lumber will get the lumber to the construction site which involves some randomness. The lumber supplier can exert a high or low level of effort. If they exert a high level of effort they will produce the lumber quickly and there is then a 75% chance the shipper can get it to the construction site on time, and only a 25% chance that the shipper will be slow, and the lumber will arrive late. If the lumber supplier exerts a low level of effort, they will take a long time to produce the lumber and there is no chance that it will ship on time. If the lumber supplier exerts low effort it costs them zero dollars, but if high effort is exerted then it costs six thousand dollars in extra resources. The lumber…SEE MORE QUESTIONS