(Table 12.6) Payoffs represent profits in thousands. Fruit of the Loom T-Shirt Price $8 $6 Hanes T- $8 20, 20 15, 22 Shirt Price $6 22,15 17, 17 $4 19, 10 15, 16 What is the Nash equilibrium? O (14, 14) O (19, 10) or (10, 19) O (17,17) O (20,20) $4 10, 19 16, 15 14, 14 D
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- Q, Please sold the Unique baysian Nash equilibrium and the mixed strategy nash equilibrium p1/p2 u n a 8,8 8,2 b 0,8 10,10 c 8,8 9,2Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays up. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that
- Thank you! Would you be able to answer the final part? Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animals is greater than the mixed strategy equilibrium proportion you calculated, which strategy does better, Hawks or Doves?Consider a modified Traveler’s Dilemma. In terms of strategy options that the players have and the dollars they earn, it is like the standard Traveler’s Dilemma, but the players do not have endless appetite for money. Up to 100 dollars, each dollar feels like a dollar. But any moneybeyond 100 is psychologically like 100 dollars. Assuming that players are maximizers of ‘psychological’ dollars instead of real dollars, describe all the Nash equilibria of this modified Traveler’s Dilemma.Jacob wants to rent out car from James. Jacob has a big passion for cars and enjoys speeding, so much that he often gets fined. Jacob receives £400 in utility from being able to speed on the road whereas James would like to avoid getting fined. If Jacob spreads don the road, it will cost James £700. Thus, James is considering charging Jacob a fine deposit of £700. a) Draw the extensive form of this principal-agent problem and use backward induction to solve for the Nash Equilibrium. b) Explain why this situation could be considered a principal-agent problem
- q60c- Is the Nash equilibrium the best outcome for this problem? Explain1. Find all subgame perfect nash equilibrium 2. Find a nash equilibrium that is not SPNE, and explain why it is not an SPNE.Refer to the Ultimatum Game in Figure 17.7. Recall that the payoffs are monetary payoffs. a. Suppose that players only care about monetary payoffs, with $1 = 1 util. Find the subgame– perfect equilibrium. b. Suppose that players are imperfectly altruistic. They receive 1 util for each dollar they earn but = util for each dollar the other player earns.Write down the extensive form reflecting the new payoffs. Find the subgame–perfect equilibrium. c. Suppose that players are perfectly altruistic, receiving 1 util for each dollar in the sum of their earnings. Write down the extensive form reflecting the new payoffs. Find the subgame– perfect equilibrium. d. Suppose that players are perfectly selfless, getting 1 util for each dollar the other player earns but no utility for their own earnings. Write down the extensive form reflecting the newpayoffs. Find the subgame–perfect equilibrium. Does player 1 end up choosing the outcome that player 2 prefers?…
- Please no written by hand Two players bargain over how to split $10. Each player i ∈ {1, 2} choose a number si ∈ [0, 10] (which does not need to be an integer). Each player’s payoff is the money he receives. We consider two allocation rules. In each case, if s1 + s2 ≤ 10, each player gets his chosen amount si and the rest is destroyed. 1. In the first case, if s1 + s2 > 10, both players get zero. What are the (pure strategy) Nash equilibria? 2. In the second case, if s1 + s2 > 10 and s1 6= s2, the player who chose the smallest amount receives this amount and the other gets the rest. If s1 + s2 > 10 and s1 = s2, they both get $5. What are the (pure strategy) Nash equilibria? 3. Now suppose that s1 and s2 must be integers. Does this change the (pure strategy) Nash equilibria in either case?At a company, 20 employees are making contributions for a retirement gift.Each person is choosing how many dollars to contribute from the interval[0,10]. The payoff to person i is bi X xi - xi, where bi > 0 is the “warm glow”he receives from each dollar he contributes, and he incurs a personal cost of 1.a. Assume bi < 1 for all i. Find all Nash equilibria. How much is collected?b. Assume bi > 1 for all i. Find all Nash equilibria. How much is collected?c. Assume bi = 1 for all i. Find all Nash equilibria. How much is collected?Now suppose the manager of these 20 employees has announced that shewill contribute d > 0 dollars for each dollar that an employee contributes.The warm glow effect to employee i from contributing a dollar is now bi X(1 + d) because each dollar contributed actually results in a total contribution of 1 + d. Assume bi = 0.1 for i = 1, . . . , 5; bi = 0.2 for i = 6, . . . , 10; bi = 0.25 for i = 11, . . . , 15; and bi = 0.5 for i = 16, . . . , 20.d. What…QUESTION: What is the Nash equilibrium usineg the payoff matrix below? Profit Payoff Matrix Frontier High Price Frontier Low Price United High Price United 50 Frontier 12 United 40 Frontier 15 United Low Price United 30 Frontier 0 United 25 Frontier 10 A. UNITED: HIGH FRONTIER: HIGH B. UNITED: HIGH FRONTIER: LOW C. UNITED: LOW FRONTIER: HIGH D. UNITED: LOW FRONTIER: LOW E. THERE IS NO NASH EQUILIBRIUM.
