Consider a repeated game with two players and two rounds. The stage game is shown below. Assume the players have a common discount factor & e (0, 1). Which of the following is NOT TRUE?
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Q2
There are two players : Player 1 & 2
Strategy set of both the players : { L , M , H }
Discount factor :
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- Normal Form: Which one of the following descriptions below is CORRECT according to this Normal Form shown? 1.) If Player 2 believes that Player 1 randomly choose H or L with same probability, then Player 2's expected for choosing HC is 2. 2.) If Player 1 has 20% chance to play H and 80% chance to play L, Player 2 has 40% chance to play HD and 60% chance to play LC; then Player 1's expected payoff is 2. 3.) If Player 2 randomly play one of its 4 strategies without any preference, then Player 1's expected payoff for playing L is 2.5. 4.) If Player 2 believes that Player 1 has no probability to play L, then Player 2 would prefer to choose HC or HD.The mixed stratergy nash equalibrium consists of : the probability of firm A selecting October is 0.692 and probability of firm A selecting December is 0.309. The probability of firm B selecting October is 0.5 and probability of firm selecting December is 0.5. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?The Federal Communications Commission (FCC) has hired you as a consultant to design an auction to sell wireless spectrum rights. The FCC indicates that its goal of using auctions to sell these spectrum rights is to generate revenue. Since most bidders are large telecommunications companies, you rationally surmise that all participants in the auction are risk neutral. Which auction type—first-price, second-price, English, or Dutch—would you recommend if all bidders value spectrum rights identically but have different estimates of the true underlying value of spectrum rights?
- The Federal Communications Commission (FCC) has hired you as a consultant to design an auction to sell wireless spectrum rights. The FCC indicates that its goal of using auctions to sell these spectrum rights is to generate revenue. Since most bidders are large telecommunications companies, you rationally surmise that all participants in the auction are risk neutral. Which auction type—first-price, second-price, English, or Dutch—would you recommend if all bidders value spectrum rights identically but have different estimates of the true underlying value of spectrum rights? Kindly give a brief one-page description as part of the assignment.Suppose Real Option Inc. has a product that generates the following cash flow. At t=1, the demand can be high or low. There is a probability of 0.6 that demand is high. If demand is high (low) the cash flow is CFH=400 (CFL=200). At t=2, the demand can also be high or low. If demand was high at t=1, then a high demand at t=2 arises with probability 0.7. If demand was low at t=1, then a high demand at t=2 arises with probability 0.2. If demand is high (low) at t=2 then CFH=400 (CFL=200). The interest rate for this project is 20%. (a) Draw the event and decision tree. (b) What is the market price (expected value) of Real Option Inc. at t=0? Now suppose Real Option Inc. can rent a platform to run a marketing campaign. For this purpose Real Option Inc. must sign a two year contract with the platform provider. The costs for using the platform are 180 per period. Marketing itself does not cost anything and has the following effect. In the high demand state, marketing doubles the demand. In…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.
- Q56 A Nash equilibrium is an outcome... a. Achieved by cooperation between players in the game. b. That is achieved by collusion where no party has an incentive to change their behaviour. c. Where each player's strategy depends on the behaviour of its opponents. d. That is achieved when players in the game have jointly maximized profits and divided those profits according to market share of each player. e. Where each player's best strategy is to maintain its present behaviour given the present behaviour of the other players.* 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** 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 the constant relative risk aversion utility of wealth function from Chapter 3 for an investor with gamma parameter equal to 0.25: U(W) = W^(0.25)/(0.25) = 4W^(0.25). Suppose this investor is faced with a 50-50 bet to receive nothing or to receive 1000 dollars. What's a fair price for this bet to the investor? I.e., what is the certainty equivalent wealth (CEW) associated with this bet, for this investorThere 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 priceYou are considering a $500,000 investment in the fast-food industry and have narrowed your choice to either a McDonald’s or a Penn Station East Coast Subs franchise. McDonald’s indicates that, based on the location where you are proposing to open a new restaurant, there is a 25 percent probability that aggregate 10-year profits (net of the initial investment) will be $16 million, a 50 percent probability that profits will be $8 million, and a 25 percent probability that profits will be −$1.6 million. The aggregate 10-year profit projections (net of the initial investment) for a Penn Station East Coast Subs franchise is $48 million with a 2.5 percent probability, $8 million with a 95 percent probability, and −$48 million with a 2.5 percent probability. Considering both the risk and expected profitability of these two investment opportunities, which is the better investment? Explain carefully.