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- 5pls solve this ques within 10-20 minutes in clear handwriting I'll give you multiple upvotes.rock paper scissors гock 0. -3 1 рарer 1. -1 scissors -1 3 0. (a) Show that xT= ( ) and yT= (3) together are not a Nash equilibrium 3 3 313 for this modified game. (b) Formulate a linear program that can be used to calculate a mixed strategy x € A(R) that maximises Rosemary's security level for this modified game. (c) Solve your linear program using the 2-phase simplex algorithm. You should use the format given in lectures. Give a mixed strategy x E A(R) that has an optimal security level for Rosemary and a mixed strategy y E A(C) that has an optimal security level for Colin.
- Problem 10-03 (algo) Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. с 9, 8 23, 13 a. What is player 1's optimal strategy? Strategy A B Player 1 O Strategy A O Player 1 does not have an optimal strategy. O Strategy B b. Determine player 1's equilibrium payoff. Player 2 D 14, 14 10, 18 E 18, 25 14, 26 F 12, 19 19, 213.Students A and B decide whether to clean the dormitory. Regardless of whether the other party participates, the cleaning cost for each student to clean the dormitory is $ 8; and the benefit for each student from cleaning is $5 times the number of participants. (hint: if both of them clean the dormitory together, A and B benefit. If one cleans while the other does not, A and B benefit too) (a) Please use a game theory to briefly describe the above scenario, (that is to calculate the revenue for different strategies) (b) Draw the payoff matrix, find the Nash equilibrium.Typed plz and asap thanks
- 1. For the following game Player B Player A Left 7,17 10,5 4,4 Middle Right 14,11 4,3 10,25 21,21 Тop Middle 14,4 Bottom 7,3 a) Determine the Nash equilibrium is any? b) Represent the game sequentially starting with player 1 and determine the sub-game perfect equilibrium c) Represent the game sequentially starting with player 2 and determine the sub-game perfect equilibrium d) Find the mixed strategy Nash equilibrium of the following game e) Firm 1 Firm 2 High price Low price High price 4,3 2,4 Low price 2,4 3,3Only typed Answer5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let X2 denote B’s gain (or loss) in a game where A has written down 2.(a) Find the pmf of X1 and X2(b) Find B’s expected gain for these two cases, E[X1] and E[X2].(c) What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…
- Game Theory Question A non-profit firm is on a local community online donation platform for a community event it wants to hold (only community members can donate via the website). The event will be held only if the non-profit firm collects $20,000 total from members of the community. Each member values the event at $500. Suppose that there are 100 community members. Community members can only donate by purchasing a lottery ticket from the firm. Each ticket costs $200 and only one ticket can be purchased per member. The proceeds will be collected by the firm. The lottery winner gets a premier meal at a local restaurant that's worth $100. Remember, the firm keeps all the donated money. If the amount of donations is less than $20,000, then the firm returns the donated money to the community members (since there'll be no event held but the lottery winner still gets to eat that fancy meal). If the donations sum up to $20,000, the community event will take place. What are the Nash…Typed plzzz and asapQUESTION 9 D 2 C D D, D OD, C C, D C II C (2,2) (4,0) (0,4) (3,3) In the dynamic game represented by the graph above, the numbers inside paranthesis show the payoffs of Player 1 and Player 2, respectively. The Nash equilibrium of this game is for Player 1 to choose O C, C and Player 2 to choose