Consider a game with the following payoff table for player 1: Strategy Player 1 1 2 3 1 5 23 2 2 0 042 Player 2 3 330 4 1 2 4 (a) Follow the approach described in Sec 15.5 to formulate the problem of finding optimal mixed strategies according to the minimax criterion as a linear programming problem. Please give the linear programming problem for each player.
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![7. Consider a game with the following payoff table for player 1:
Strategy
1
Player 1 2
3
1
523
2
042
Player 2
3
3
ww
3
124
2
(a) Follow the approach described in Sec 15.5 to formulate the problem of finding optimal mixed strategies
according to the minimax criterion as a linear programming problem. Please give the linear
programming problem for each player.
(b) Use Excel Solver (the simplex method) to find the optimal mixed strategies for each player. Also find
the value of the game. Is this a fair game? If not, is this game in favor of player 1 or 2?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2f2c4bd-bf4c-4a3b-a0a2-6333c3306a45%2F5fb7dc4a-3278-4338-8933-f85bae2f8300%2Fv61h6jv_processed.png&w=3840&q=75)
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- 5. Consider a game with the following payoff table for player 1: Strategy Player 1 1 2 3 1 3 -4 1 Player 2 2 -3 -2 3 3 -2 -1 2 (a) Use the graphical procedure to determine the value of the game and the optimal mixed strategy for each player. (b) Without eliminating any dominated strategies, follow the approach described in Sec 15.5 to formulate the problem of finding optimal mixed strategies according to the minimax criterion as a linear programming problem. Please give the linear programming problem for each player. (c) Use Excel Solver (the simplex method) to find the optimal mixed strategy for each player.Prove that in the variation on the centipede game given in figure 14.5(b) the unique sequential equilibrium described is, in fact, the unique Nash equilibrium. (Hint: Take some presumed Nash equilibrium and suppose information set 2n+ 1 [for player 2] is the first unreached information set. Derive an immediate contradiction. Then suppose that node (2n) t is the first unreached information set and derive a contradiction that is one degree removed from immediate.)1. One-Shot, Pricing Game. You are a pricing manager at Argyle Inc.-a medium-sized firm that recently introduced a new product into the market. Argyle's only competitor is Baker Company, which is significantly smaller than Argyle. The management of Argyle has decided to pursue a short-term strategy of maximizing this quarter's revenues, and you are in-charge of formulating a strategy that will permit the firm to do so. After talking with an employee who was recently hired from the Baker Company, you are confident that a) Baker is constrained to charge $10 or $20 for its product, b) Baker's goal is to maximize this quarter's profit, and c) Baker's relevant unit costs are identical to yours. You have been authorized to price the product at two possible levels ($5 or $10) and know that your relevant costs are $2 per unit. The marketing department has provided the following information about the expected number of units sold (in millions) this quarter at various prices to help you…
- P1| P2 Left Middle Right Left 1,1 5,0 0,0 Middle 0,5 4,4 0,0 Right 0,0 0,0 3,3 Consider the simultaneous move game represented in normal form by this payoff matrix. Suppose that the game is repeated for two periods and the players know that the game will end at the end of two periods. They observe the first period outcome before they move to the second period. Assume that there is no discounting, i.e. 2nd period payoffs are not discounted. Which of the following outcomes could occur in some subgame perfect equilibrium (SPE) of this repeated game? Choose True if you think the outcome can be a SPE, otherwise choose False. a. (Middle, Middle) is played in the first period, followed by (Right, Right) b. (Left, Left) is played in both periods. c. (Right, Right) is played in both periods.2. Consider the odds and evens game and whose payoff table is shown as below. Player 2 (odd player) 2 (fingers) Strategy Player 1 (even player) 1 (finger) 2 (fingers) 1 (finger) 3 -4 −4 3 (a) Use the graphical procedure described in Sec. 15.4 from the viewpoint of player 1(the evens player) to, first find the maximin point, then determine the optimal mixed strategy for player 1 (the even player) according to the minimax criterion. (Do not need to find the optimal mixed strategy for player 2.) (b) Use the Oddments Method directly to find the optimal mixed strategies for both player 1 and player 2. (c) What is the corresponding value of the game?Betty and Sue both have accounting practices that specialize in income tax preparation. If they both advertise their services each year before the income tax season begins, they will each earn $3 per return. If neither one of them advertises, they will each earn $10 per return. If one advertises and the other one doesn’t, the one who advertises will earn $150 per return and the one who doesn’t advertise will only earn $1 per return. What interest rate would make it so that both of them had the incentive to not advertise? A. 10% and below B. 5% and above C. 5% and below D. 10% and above E. none of the above
- 3. Consider a game with the following payoff table for player 1: Strategy Player 2 Player 1 1 2 1 4 6 2 0 -5 3 -2 0 4 -2.5 0 (a) Without eliminating any dominated strategies, use the graphical procedure from the viewpoint of player 1 to, first find the maximin point, then determine the optimal mixed strategy for player 1 according to the minimax criterion. (Do not need to find the optimal mixed strategy for player 2.) (b) Now eliminate all dominated strategies, if resulting in a 2 × 2 payoff table, use the Oddments Method directly to find the optimal mixed strategies for both players. (c) What is the corresponding value of the game?Table 17-6 Two home-improvement stores (Lopes and HomeMax) in a growing urban area are interested in expanding their market share. Both are interested in expanding the size of their store and parking lot to accommodate potential growth in their customer base. The following game depicts the strategic outcomes that result from the game. Increases in annual profits (in millions of dollars) of the two home-improvement stores are shown in the following figure. Lopes Do notincreasethe size of store and parking lot Increase the sizeof store and parking lot Lopes = 1.0 Lopes = 0.4 Increasethe size of store and parking lot HomeMax = 1.5 HomeMax = 3.4 HomeMax Lopes = 3.2 Lopes = 2.0 Do notincreasethe size of store and parking lot HomeMax = 0.6 HomeMax = 2.5 Refer to Table 17-6. When this game reaches a Nash equilibrium, annual profit will grow by a. $0.6 million for HomeMax and by $3.2 million for Lopes. b. $2.5 million for HomeMax and by $2.0 million for Lopes. c. $3.4 million for HomeMax and…... EOC 17.06 ✓Answered-Correct Jim and Cheryl are competitors in a small town and each is trying to decide if it is worthwhile to advertise. If both of them advertise, each will earn a profit of $10,000. If neither of them advertises, each will earn a profit of $20,000. If one advertises and the other doesn't, then the one who advertises will earn a profit of $30,000 and the other will earn $14,000. What is the Nash equilibrium in this game? A B D Neither of them should advertise. Both of them should advertise. There is no Nash equilibrium for this game. X Jim should advertise and Cheryl should not advertise. Your answer
- 9. Consider the following parlor game to be played between two players. Each player begins with three chips: one red, one white, and one blue. Each chip can be used only once. To begin, each player selects one of her chips and places it on the table, concealed. Both players then uncover the chips and determine the payoff to the winning player. In particular, if both players play the same kind of chip, it is a draw; otherwise, the following table indicates the winner and how much she receives from the other player. Next, each player selects one of her two remaining chips and repeats the procedure, resulting in another payoff according to the following table. Finally, each player plays her one remaining chip, resulting in the third and final payoff. Winning Chip Red beats white White beats blue Blue beats red Matching colors Payoff ($) 90 70 50 0 Formulate this problem as a two-person, zero-sum game by constructing a payoff table for Player 1. Do not need to solve this problem.1. Consider the two-player game with the following matrix form representation a 3.2 y -1.0 b 1,3 1,-1 с -1.1 4.2 where player 1 is the "row player,” player 2 is the “column player,” and, for every cell, the left-most number is the utility that player 1 obtains from the corresponding (pure) strategy profile and the right-most number is the utility that player 2 obtains from the corresponding (pure) strategy profile. (a) Find the pure-strategy Nash equilibria of this game. (b) Find the other Nash equilibria of this game.7 In bargaining theory, sometimes an individual’s patience level can affect his or her bargaining power. Consider a simple repeated game in which Person 1 makes an offer to purchase a good that Person 2 is selling; Person 2 can either accept this offer or reject it and make a counteroffer. This game continues until one player accepts the other’s offer. Explain how incorporating the rate of time preference (ββ) into such a repeated game might alter the outcome.