Suppose that 5 risk neutral competitors participate in a rent seeking game with a fixed prize of $100. Each player may invest as much as he wishes in the political contest, although those investments have an opportunity cost equal 1. The probability of winning is directly proportional to the candidate’s share of the total rent-seeking investment. What is the profit-maximizing investment by player 1 as a function of the investment by all the others? What is a Nash equilibrium investment by each player in a symmetric game?
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Suppose that 5 risk neutral competitors participate in a rent seeking game with a fixed prize of $100. Each player may invest as much as he wishes in the political contest, although those investments have an
- What is the profit-maximizing investment by player 1 as a function of the investment by all the others?
- What is a Nash equilibrium investment by each player in a symmetric game?
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- Suppose that 20 risk neutral competitors participate in a rent seeking game with a fixed prize of $500. Each player may invest as much money as he wishes in the political contest. The probability of winning is directly proportional to the candidate's share of the total rent-seeking investment. 1. What is the expected net benefit of a player if all other players invest $20 each? Write the net benefit as a function of the player's investment. 2. Solve the maximization problem to arrive at the profit-maximizing investment. Round to the nearest cent.Assume that two people are bargaining over how to split the surplus of their joint efforts, which total $100. The only difference between the two is that player A has an associated interest rate of 5 percent and player B has an associated interest rate of 20 percent. Based on Nash bargaining theory, what share of the $100 ill Player A wind up with? (Please provide your answer in $ style format)Ten commuters must decide simultaneously in the morning to use route A or route B to go from home (same place for all) to work (ditto). If a of them use route A, each of them will travel for 10a + 40 minutes; if b of them use route B, each of them will travel for 10b minutes. Everyone wishes to minimize his/her commuting time. Your tasks: Describe the pure Nash equilibrium (or Nash equilibria) of this ten-person game. Compute the corresponding profile of commuting times. Explicitly list all equilibrium conditions that are satisfied. à. b. What is the traffic pattern (strategies) minimizing the total travel time of all commuters (the sum of their travel times)? Describe the corresponding profile of commuting times (individual payoffs/cost). What does this mean about the Price of Anarchy of this game (assuming that the objective function is the total travel time)? с.
- lease find herewith a payoff matrix. In each cell you find the payoffs of the players associated with a particular strategy combination: The first entry is the payoff of player 1, the second entry is the payoff of player2. Player 2 t1 t2 t3 Player 1 S1 3, 4 1, 0 5, 3 S2 0, 12 8, 12 4, 20 S3 2, 0 2, 11 1, 0 Suppose both players select their strategies (S1, S2 or S3 for player 1 and t1, t2 or t3 for player 2) simultaneously and that the game is played once. In your explanation to the questions below, please do refer to the figures in the matrix. Does player 2 have a dominant strategy? If so, which one? Does player 1 have a dominant strategy? If so, which one? No explanation required. Is there one or more Nash equilibria in the game? If so, which one(s)?Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.9. There are four agents who are trying to decide whether they will buy a publicly shared TV, of which the total cost is $200. The valuations of the TV are $30 for agent 1, S35 for agent 2, $70 for agent 3, and $70 for agent 4. Let c; be how much agent i will pay if the TV is purchased. Suppose c = 20, c2 = C3 = C4 = 60. According to Groves and Clarke mechanism, which one could not be the pivotal agent? A. agent 1 B. agent 2 C. agent 3 D. agent 4
- on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.a) Write out the extensive form of a game between a farmer (playing in the first round) and nature (playing a mixed strategy in the second round). Assume that the farmer can either pay a cash rent of $1500 for land (English system) or 1/2 of crop production to the landlord (sharecropping). Assume the farmer is planting corn and will produce 2 tons of corn. Assume that nature has a 50% chance of playing a strategy in which the price of corn is $3500/ton and a 50% chance of playing a strategy in which the price of corn is $500/ton. The farmer keeps any money left after paying cash rent and sells any corn left after paying the landlord in sharecropping. b)What is the most that a risk neutral farmer would be willing to pay for an accurate prediction of the price of corn in problem 1 before choosing whether to pay cash rent or sharecrop?Section 1: Two Romantics Ann and Bob had their first date. Each either felt romantic chemistry (C) or no chemistry (NC) with the other person. Each person knows his/her own feeling but does not know the feeling of the other person. Assume a common prior belief that the other person felt chemistry with probability Pr(C) = p and no chemistry with probability Pr(NC) = 1-p. Ann and Bob are old-fashioned romantics and they made the following rule after the first date: No texts/calls/DMs. Instead, they can choose whether to appear (A) or not appear (NA) under the USyd Quadrangle clock tower at sunset on the next day. Their payoffs are given as follows: (From a first-person perspective) If I felt chemistry (C) and I appear (A) under the clock tower, my payoff is 100 if the other person also appears (A) and -100 if the other person doesn't (NA). If I felt chemistry (C) and I choose not to appear (NA) under the clock tower, my payoff is -30 regardless of the other person's action (because I…
- Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land. Farmer 2 Farmer1 1 cow 2+ cows 1 cow 8,8 2,10 2+cows 10,2 4,4 What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off) The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…Consider the following payoff matrix B R U 7, 7 4,17 A 17,4 6,6 Players A and B repeatedly play this game with an infinite horizon. Future payoffs are discounted with 1/(1+r), where r is the long-term interest rate. Determine the interval of r for which the Carrot-and-Stick strategy does form a Nash-equilibrium when the opponent can discover any deviation immediately. Remember the following relation TA+Lt-1 (14+t) TB TB = TA + O r>0.1 O r0.2 Or-1 O r1Jagtar and Ravi both grow mangoes, which they sell in the same local market. They are deciding whether to pick 5 baskets worth of mangoes or 10 baskets, and have the following profit matrix: Jagtar 5 1 17 5 1 22 16 14 Ravi 1 24 14 a. What is the Nash equilibrium if both individuals make their decisions simultaneously? b. Does your analysis change if the local market charges a lump-sum fee of 12 to set up a stall and sell the mangoes in the space it provides? c. What would happen if the local market were instead to charge a lump-sum fee of 18?