How many total pure and mixed-strategy equilibria does the game below have? Player 2 y a 3, 3 4, 2 Player 1 6, 3 2, 6 5,3 3, 2 Numerical answer b.
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- 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?What is the secure strategy for player B in the game presented in TableBrown’s TV Production is considering producing a pilot for a comedy series for a major network. While the network may reject the pilot and series, it may also purchase the program for 1 or 2 years. Brown may produce the pilot or transfer the rights for the series to a competitor for $100,000. Brown’s profits are summarized in the following payoff table (profits in thousands). sate of nature reject 1 year 2 years produce pilot -100 50 150 sell to competitor 100 100 100 If the probability estimates for the states of nature are, P(reject)=0.20, P(1 year)=0.30, and P(2 years)=0.5, what is the maximum Brown should be willing to pay for inside information on what the network will do?
- Suppose that Alex and Bob complete the project sequentially. Assume that Alex decides his effort level and starts the project first, and then Bob decides his effort level and finishes the project. Present the extensive-form representation of the game (i.e., draw a decision tree which is also referred as the game tree). What is your prediction regarding the outcome of the game? Explain your prediction.Determine all of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following game:Amy must decide whether or not to make an investment that costs 1. The investment pays a return of 5, but is risky to Amy because Bill must be given charge of the asset if it is to be productive. If Amy invests, then Bill must decide whether to keep the entire return for himself, or to split the return, giving 3 to Amy and keeping 2 for himself. (Amy pays the cost 1 even if Bill does not pay her back.) If Amy does not invest, then both players get 0. This is called a trust game because Amy wants to invest only if she trusts Bill to pay her back. (a) Model this as an extensive-form game (b) What is the strategic-form corresponding to your extensive-form? (c) Find all of the Nash equilibria. Which are the subgame-perfect?
- Normal-Form GameFind all Nash equilibria of the following two-player game. Provide necessary computation.Consider the following game 1\2 Y Z A 10,3 3,9 B 8,5 6,1 Suppose Player 2 holds the following belief about Player 1: θ1 (A,B) = (9/10,1/10) What is the expected payoff from playing ‘Y’ ? What is the expected payoff from playing ‘Z’ ? Based on these beliefs, player 2 should respond by playing _____Suppose the following game is played infinite times in the future. Time discount is 0.90. What should be the value of x so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (x, x) (2, 14) Defect (14, 2) (5, 5)
- 5,3 4,4 3,6 7,6 Find the pure strategy nash equilibriaDetermine 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 4Q23. At what time is the game expected to stop? 1 2 3 4 5 6 after time 6 (when there are no more moves)