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- Q3. Explain the concept of mixed strategy and how to calculate the value of game. Also provide a suitable example for mixed strategy. Determine which of the following two-person zero-sum games are strictly determinable and fair. Give the optimum strategies for each player in the case of it being strictly determinable. I. I. a- Player A Player B B1 B2 B3 A1 8 4 A2 5 -1 b. I II II IV V I 4 -2 -2 3 1 A II 1 -1 III -6 -5 -2 -4 4 IV 3 1 -8Typed plzzz and Asap ThanksQ. 1
- In the following simultaneous-move game, what is player 1's maximin strategy? Player 2 OL OR OU OD Player 1 L R U 50, 50 0, -10 D -10, 0 0,04. Consider a two player game with Fred and Barney, who tal turns removing matchsticks from a pile. They start with 33 matchsticks, and Fred goes first. On each turn, ecach player may remove either one, two, three, four, or five matchsticks. The player to remove the last matchstick wins the game. What are the optimal strategies for each player? Who will win? b. Suppose now that they can remove up to six matchsticks, how will the optimal strategies change for- each player? a.Consider the Battle of the Sexes game illustrated here. Find all ESS’s.
- Define the term d two-person, zero-sum games?7. Which of the following is not true of the “Battle of the Sexes" Game? a. The predicted outcome demonstrates how independent and rational play by players can quickly reach an agreement or a convergence of expectations concerning which strategy will be played by each player in equilibrium. b. The Battle of the Sexes Game can be used to depict a variety of situations where the players' interests do not precisely coincide, except for the fact that they both want to avoid the outcomes that would result from choosing different actions from one another. c. Players do not have a dominant strategy but playing “Boxing" say, is a best response to the other playing "Boxing" even if it doesn't give the player the payoff associated with his or her preferred alternative. d. Played only once, the outcome where each goes to their preferred venue cannot be Nash Equilibrium.Q3. Find all SPNE in the following game. рз DNO о х р 2 а WN р 1 у т P3 0 2 Ь 3 2 P2 ४ у мом 3 P3 Ч 2 эра эрг → P3
- Use the following game table to answer the question: Player 2 Y 6, 3 1, 3 A 10, 5 0,0 Player 1 B 2,6 0,0 3,5 3, 4 3, 3 Is the Nash equilibrium of this game for Player 1 to choose A and Player 2 to choose X? Why or why not? O It is; if Player 2 chose B or C they would get less than 10, and if Player 1 chose Y or Z they would get less than 5. It is not; Player 2 could get 6, instead of 5, if they chose B. O It is; if Player 1 chose B or C they would get less than 10, and if Player 2 chose Y or Z they would get less than 5. It is; if Player 2 chose B or C they would get less than 5, and if Player 1 chose Y or Z they would get less than 10. It is not; Player 1 could get 6, instead of 5, if they chose B.1. Define Dominant Strategy and Dominant equilibrium in Game theory? 2. Do we depict the equilibrium of a game in pay-offs or strategies in Game theory?A 201.