Mixed Nash Equilibrium Player 2 A 5,1 1,3 В 2,6 4,2 PLAYER 1 a) calculate the probability In equilibrium Player 1 chooses A with probability a= [?] and player 2 chooses M with probability B = [ ?] b) calculate payoff for mixed strategy nash equilibrium Player 1 gets payoff of [?] Player 2 gets payoff of [?] c) Suppose the payoff for (B,C) would change to (0,8) Would probability a increase,decrease, stay the same? Would probability B increase,decrease, stay the same?
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- 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.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…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.
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- Consider the following 3×3 two player normal form game that is being repeated infinite number of times. The discounting factor for player 1 is δ1 and the discounting factor for player 2 is δ2. left center right up (10 ,40) (32 ,75) (65 ,58) middle (55 ,63) (21 ,45) (23 ,83) down (14 ,76) (16 ,65) (37 ,42) a. Find the total discounted utility for player 2 if player 1 decides to play middle all the time and player 2 decides to play left all the time. b. Now suppose both players are following the strategy of part (a) until player 1 decides to play up in the 6th stage. The the new NE after the 6th stage is (up,right). Find the total discounted utility for player 2 in this case. c. Using the grim trigger strategy, find the minimum value of δ2. Can you find any anomaly in your calculated value of δ2?Consider the game of Chicken in which each player has the option to “get out of the way” and “hang tough” with payoffs: Get out of the way Hang tough Get out of the way 2,2 1,3 Hang tough 3,1 00 a. Find all pure strategy Nash equilibria, if they exist b. Let k be the probability that player 1 chooses “hang tough” and u be the probability that player two chooses “hang tough.” Find the mixed stragety Nash equilibria, if they existollowing is the payoff table for the Pittsburgh Development Corporation (PDC) Condominium Project. Amounts are in millions of dollars. State of Nature Decision Alternative Strong Demand S1 Weak Demand S2 Small complex, d1 8 7 Medium complex, d2 14 5 Large complex, d3 20 -9 Suppose PDC is optimistic about the potential for the luxury high-rise condominium complex and that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong (S1) and a corresponding probability of 0.2 that demand will be weak (S2). Assume the decision alternative to build the large condominium complex was found to be optimal using the expected value approach. Also, a sensitivity analysis was conducted for the payoffs associated with this decision alternative. It was found that the large complex remained optimal as long as the payoff for the strong demand was greater than or equal to $17.5 million and as long as the payoff for…
- Compare and contrast the Winning Strategy Theorem and the Equilibrium Existence Theorem (in the forms that these two results were stated and discussed in ECN214). In your own words, describe the hypotheses and the conclusions of each theorem. Which result (if either) has more demanding hypotheses? Which (if either) has more powerful conclusions? Is one of these two theorems logically stronger than the other? Explain. What is the significance of each result, both for the application of game theory to real world problems and for the historical development of the subject? Give one or more original examples to show how these theorems can be used in practice.(Symmetric mixed strategy Nash equilibrium) A profile α∗ of mixed strategies in a strategic game with vNM preferences in which each player has the same set of actions is a symmetric mixed strategy Nash equilibrium if it is a mixed strategy Nash equilibrium and α∗ i is the same for every player i. Solve this problem: At a large round table sit n ≥ 2 players, each holding 3 cards: one white, one black, and one red. Each player must secretly choose one of their cards and then, when the bell rings, simultaneously reveal it publicly with all the others. If all players choose the white card, each of them receives 6 points. If player i chooses the white card, and at least one of the other players chooses a card of a different color, player i receives 1 point. If player i chooses the black card, they receive 3 points, regardless of the decisions of the other players. If player i chooses the red card, they receive 0 points, regardless of the decisions of the other players. Find all symmetric…Consider two bidders – Alice and Bob who are bidding for a second-hand car. Each of them knows the private value she/he assigns to the car, but does not know the exact value of others. It is common knowledge that the value of other bidders is randomly drawn from a uniform distribution between 0 and $10000. Assume that Alice values the car at $8500 and Bob values the car at $4500. a) If Alice and Bob participated in the second-price sealed bid auction, what would they bid and what would be the result of the auction? Explain your answer. b) If they participate instead in a first-price sealed bid auction, what would they bid and what would be the result of the auction? Explain your answer. c) Calculate and compare the revenue of the seller in the above situations. Which type of auction should the seller use? Explain your answer