1. Find the optimum strategies of player A and player B and the value of the game? Player B 1 2 3 4 I 2 3 11 8 II 7 2 7 III 6. 4 -4 9 Player A
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- Determine the optimum strategies and the value of the game with the followingpayoff matrix of player A where A1, A2 are the strategies for player A and B1, B2 are for player B.B1 B2A1 5 1A2 3 4Which of the following gambles is “unfair”? a. A game that promises to pay you $1 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. b. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. c. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with an entry fee of $4.50 for the right to play. d. All of the above.32. What aspects of a game are specified by "the rules of the game"? A) timing of players' movesB) payoffsC) information available to each playerD) All of the above
- 5 WHILE USING GAME THEORY METHOD EXPLAİN CLİMATE CHANGE STRATEGIES PLAYERS PAYOFFS AND OUTCOMES IN 200 WORDS33. When neither player has a dominant strategy, A) game theory will not provide information.B) no Nash-Equilibrium exists.C) at least one Nash-Equilibrium exists.D) the game cannot be analyzed.1. What is the expected value of playing this game ? a. The player repeatedly rolls a six - side d die until it comes up 6. b. When the die comes up 6 , the player receives a payoff, and the game ends. The player get s precise ly one payof f. c. The initial payoff is $6, and it increases by 20%. The f irst roll payoff is $6 ; the second roll payoff is $7.20 (1.2*$6) ; the third roll payoff is $8.64 (1.2*$7.20), and so on. What is the expected value of playing this game?
- Game theory: Consider a collective action game with thirty individuals (N = 30). When the number of participants in the joint project is n, each individual, including shirkers, receives a benefit of B(n) = 18n and each participant incurs a cost of C(n) = 32 − 2n. 1. Find all of the Nash equilibria, both stable and unstable ones. 2. Find the socially optimal outcome. 3. Check if any of the Nash equilibria is socially optimal. Explain your answer.Questions:1. What kind of game (according to outcome and sequence) is Crandall proposing to Putnam?2. If Putnam agreed with Crandall’s proposal, how will this decision affect the buyers?Solve Both Questions!2. Do we depict the equilibrium of a game in pay-offs or strategies in Game theory? 3- 3. What is meant by the phrase, "Best Response of a player"? in Game Theory?
- Question 1 Consider a first-price sealed bid auction of a single object with two biddersj = 1,2 and no reservation price. Bidder 1′s valuation is v1 = 2, and bidder 2′s valuation isv1 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts.In the event of a tie, the object is awarded by a flip of a fair coin.(a) Find an equilibrium of this game.(b) Is the allocation of your answer to (a) efficient?Problem1 A)Provide an example of the extended form of a sequential game with perfect information. B) Provide an example of a repeated game with complete but imperfect information.5.Each of Player 1 and Player 2 chooses an integer from the set {1, 2, ..., K}. If they choose the same integer, P1 gets +1 and P2 gets -1; if they choose different integers, P1 gets -1 and P2 gets +1. (a) Show that it is a NE for each player to choose every integer in {1, 2, ..., K} with equal probability, K1 . (b) Show that there are no NE besides the one you found in (a).