3. Two vendors simultaneously choose a location. Then the customers choose the closest vendor to buy from. The profit for each vendor equals the number of customers that it attracted. Assume that the vendors choose a location from the set {1,2,3,4,5} of natural numbers, viewed as points on a real line, and that at each location there is exactly one customer. For example, for n = 5 there are 5 locations and when the players choose respectively the locations 2 and 5, their payoffs are u(2,5) = 3 and u2(2,5) = 2. When the vendors share a customer, for instance, when they choose respectively the locations 2 and 4, they end up with a fractional payoff, in this case u(2,4) : 2.5 and u2(2,4) 2.5. In general, each vendor's strategy set is Si = {1,2,3,4,5} for i 1, 2. The outcome of IESDS is
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- Suppose Rashard and Alyssa are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Rashard chooses Up and Alyssa chooses Down, Rashard will receive a payoff of 4 and Alyssa will receive a payoff of 5. Alyssa Up Down Rashard Up 8, 4 4, 5 Down 5, 4 6, 5 In this game, the only dominant strategy is for to choose . The outcome reflecting the unique Nash equilibrium in this game is as follows: Rashard chooses and Alyssa chooses.Q14. Do players have perfect information in the above game? Yes, all of them have perfect information No, player 2 has imperfect information No, player 3 has imperfect information No, no player has perfect information Q15. If we want to describe the above game with a strategic form representation, what would the strategy sets for the three players be? Player 1={a, b, c} ; Player 2={x, y}; Player 3={r, s} Player 1={a, b, c} ; Player 2={xx, xy, yx, yy}; Player 3={r, s}Please 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. Suppose player 2 could move before player 1 (i.e. has a first mover advantage). In your explanation to the questions below, please do refer to the figures in the matrix. What strategy would (s)he select? Is it really an ‘advantage’ for player 2 to move first? Or does player 2 benefit from being the second mover (and hence player 1 moving first)? I.e. for this question, do not make a comparison to the outcome of the…
- Theo and Addy are deciding what toys to pick out at the toy store. Depending on what toys they pick, they can play different games together, but they can’t coordinate their choices. They can’t talk to one another at all until after that make their choice. Below is their payout matrix which shows their utility for each choice. All the bold figures are for Theo and all the non bold figures are for Addy. Addy Strategies Theo Strategies Toy Gas Pump Jump Rope Toy food 20 10 10 3 Ball 7 3 9 4 a) If Theo chooses Toy Food, what would be the possible outcomes for Addy? What would be best for Addy? b) If Addy chose a Toy Gas Pump, what are the possible outcomes for Theo? What would be best for Theo? c) Does Addy have a dominant strategy? If yes, what is her strategy? If not how can you tell? d) Does Theo have a dominant strategy? If yes, what is her strategy? If not how…Suppose that Kim and Nene are both in the public eye. They get offers to sell secrets of the other to tabloids. If both keep the secrets, they are both better off than if they get exposed. If only one is exposed, the other person is better off than if no one was exposed. Their payoffs from each option are given in the payoff matrix. Suppose that Nene and Kim play the game over four television seasons, where each season is a new game. Consider the scenarios. Remember, a tit‑for‑tat strategy is one where the person starts by cooperating and then plays whatever strategy the other firm played last. Over four seasons, how much will Nene make if she and Kim both play tit‑for‑tat? $ Over four seasons, how much does Nene make if she always exposes and Kim plays tit‑for‑tat? $ Over four seasons, how much will Nene make if she plays a tit‑for‑tat strategy and Kim always exposes? $ Over four seasons, how much will Nene make if she and…Exercise 7: The facility location game. Our example is a game in which two firms compete through their choice of locations. Suppose that two firms A and B are each planning to open a store in one of six towns located along six consecutive exits on a highway. We can represent the arrangement of these towns using a six-node graph as in Figure 1 Now, based on leasing agreements, Firm 1 has the option of opening its store in any of towns 1, 3, or 5, while Firm 2 has the option of opening its store in any of towns 2, 4, or 6. These decisions will be executed simultaneously. Once the two stores are opened, customers from the towns will go to the store that is closer to them. So for example, if Firm A open its store in town 3 and Firm B opens its store in town 2, then the store in town 2 will attract customers from 1 and 2, while the store in town 3 will attract customers from 3, 4, 5, and 6. If we assume that the towns contain an equal number of customers, and that payoffs are directly…
- Consider the following dynamic game. There are two players (P1, P2). Player 2 tries to rob Player 1. If Player 1 pays $100, the game is over with Player 1 (victim) paying $100 to Player 2 (robber) (P1: -$100, P2: +$100). If Player 1 refuses to pay $100, then Player 2 has two choices: one is to hurt Player 1 (P1: -$5,000, P2: -$1,000) and the other is to walk away (P1: 0, P2: 0). Explain how to find an equilibrium in this game.Two individuals each receive fifty dollars to play the following game. Independently of each other, they decide how much money to put in a common pot. They keep the rest for themselves. As for the money in the pot, it is increased by 80% and then distributed equally among the two individuals. For instance, suppose that the first individual puts $10 in the pot while the second individual puts $20. Increasing the total pot of $30 by 80% gives $54 to share equally between the two individuals. So the first individual’s payoff in this case is $(40 + 27) = $67, while the second individual’s payoff is $(30 + 27) = $57. (a) Compute the Nash equilibrium. (b) Is the Nash equilibrium Pareto efficient? ExplainEach actor has two possible actions: reduce greenhouse-gas emissions or increase emissions. Each player's payoffs for various combinations of actions are shown in the cells: by convention, the row player (EU)'s payoffs are shown first, and the column player (China)'s payoffs are shown second. Based on this matrix, which of the following statements are true? A.The EU is better off reducing its emissions, but only if China also reduces its emissions B. China is better off increasing its emissions, but only if the EU also increases its emissions C.Both China and the EU are better off increasing their emissions, whatever the other player does D.All of the above E.None of the above