Suppose 2 players play the following game infinite times in the future. What should be the minimum value of the time discount so that the equilibrium strategy is (Cooperate, Cooperate)? Player 2 Player 1 Cooperate Defect Cooperate (10, 10) (12, 2) Defect (2, 12) (4,4)
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- If you played the game in Exercise 1 many times, then you would expect your average payoff per game lo be about $ ____________.Let x1 and x2 be the payoffs of two investmentThere are three players in a public good game. Each player (i=1,2,3) has 100 dollars to contribute the amount of money cı, i=1,2,3, for a public good. Each player's payoff depend on the following: (i) The amount of her remaining wealth 100-c, i=1,2,3, for spending in private good. 3. (ii) The amount of public good is equal to the sum of contributions from all players. (iii) Each person cares about the amount of public good and her consumption of private goods. Based on the above assumption, each players ui-(100+c)+(c1+c2+c3)(100-c), i=1,2,3 (a) What is the amount of each player contribute to the public good for Nash equilibrium for the non-cooperative simultaneous game? .What is total payoffs for all players in the non-cooperative simultaneous game? What is the amount of each player contributes to the public for social optimum if (b) (c) there are no discrimination of all players? Hint: The social optimum is the maximum total payoff if all players cooperate together. You might think…
- For numbers s and 6. A model used for the yield Yof an agricultural erop aS a funetion of the ritrogen level Nin the soil (measured in appropriate units) is given by: 1+ N where k is a positive constantWhich of the following statement(s) is true about a strategy that is played in some pure str equilibrium? i. it cannot be eliminated by a mixed strategy ii. it can be Pareto optimal iII. it can be eliminated by iterated elimination of strictly dominated actions iv. it always survives iterated elimination of weakly dominated actions O a. (ii) and (iii) b. (1) and (iii) OCo and (i) and (iv) d. (i) and (ii)Let's consider the following game: Player 1 chooses a (potentially negative) number x, and player 2 chooses a (potentially negative) number y. The payoff for player 1 is given by U1 = 100x - x2 - 2xy. The payoff for player 2 is given by U2 = 130y - 2y2 - 2xy. Solve for the Nash equilibrium in pure strategies. What is Player 1's payoff in the equilibrium? Enter a numerical answer below. You may round to the second decimal if necessary.
- 2. Consider a version of the shirking game with U, 3D 5p - w+ (1 — р)mw - т UA = p(w-2) +(1-p)(1-m)w A. Find the equilibrium p and m as a function of w B. Find the equilibrium w C. Why is the equilibrium in this game inefficient?Exercise 2. Marginal and Conditional Relationships can be Very Different. For 100 mild cases of eczema, a new treatment had a higher cure rate than the old treatment (33.3% of 90 vs. 20% of 10). For 100 severe cases of eczema, again the new treatment had a higher cure rate than the old treatment (60% of 20 vs. 50% of 80). Over all 200 eczema cases, however, the old treatment had a higher cure rate than the new treatment- i.e. Simpson's Paradox strikes again. (a) Compute the overall cure rates for the new and old treatments. (b) Which treatment, old or new, would you choose and why?Kataleigh company manufactures dining room tables and chairs each table requires 50 board feet and 3 hours of labor. Each chair takes 20 board feet and 4 hours of labor.The manufacturer has 3,300 board feet of lumber available and a staff table to provide 380 hoursof labor. Finally, the manufacturer has determined that there is a net profit of P100 for each chairsold and P200 for every table sold.For simplicity, we assume that needed materials (such as nailand varnish) are insufficient quantities. How many table and chairs should the companymanuffacture in order to maximize its profits, assuming that each item manufactured is sold.Use Simplex Method to solve the problem.
- Using Equation g >= 1-1/N, graph the relationship between the number of firms in the market, N, and probability, g, that the game continues from one period to the next, needed to sustain collusion in an indefinitely repeated game. What is the greatest number of firms for which collusion would be sustainable. if g = 0.95You are analyzing stocks of three companies you are interested in investing in. Suppose that these three stocks are Apple stock (AAPL), Microsoft (MSFT), and Tesla (TSLA). At the end of this month, each month may move up (increase in value), move down (decrease in value) or stay the same. In this case, an experiment consists of observing the price condition across the three stocks. Each of the three conditions (move up, move down, stay same) are equally likely. How many outcomes are in the sample space? List 7 of the outcomes. (use U for move up, D for moving down and S for staying the same) Let A be the event that all the stocks have the same performance. List the outcomes in A. Let B be the event that all of stocks are different. List the outcomes in B. Let C be the event that at least two stocks move up. Are events A and C mutually exclusive? Are events B and C mutually exclusive? What is the probability of ? What is the probability of ? What is the probability of ? What is the…maximize Subject to Z = 50x₁ + 80x2 +64x3 + 80x4 5x₁2.5x₂ + 4.5x3 +3.99x4≤ 600 2.6x₂ +5.5x3 +1.9x4500 22x₂ +18x3 +25x4 ≤ 400 12.6x2 +9.7x3 +10.55x4≤ 1700 4.1x₁ + 15x₁ + 8x₁ + x₁ + X₂ X₁ + X₂ + x3 + X4 ≥ 0.60 X1, X2, X3, X4 20 (a) Transform the problem into standard form. (b) Solve the problem by using the computer. (c) What is the effect on the optimal solution if the 2nd constraint were discarded from the formulation?