3. Consider a football stadium that has 3 seating sections (S1, S2, S3) in a row....

Transcribed Image Text:

3. Consider a football stadium that has 3 seating sections (S1, S2, S3) in a row. The distance between section S1 and S2 is the same as the distance between sections S2 and S3. Each of the sections seats 100 people. Now, consider two hotdog vendors who have to decide the sections in which to set up their shop in order to sell as many hotdogs as possible. Since the fans do not want to miss any part of the game, they will buy from the hotdog vendor in the sections closest to them (assume the distance inside the section does not matter to them). We will also assume that this is a hungry crowd in a popular game, so every seat is occupied and every person will buy one hotdog. If both the vendors are in equally distant sections, then half the fans buy from one vendor and half from the other. For example, if one vendor is in S1 and one vendor is in S3, half the people in S2 will buy from the first vendor and half from the second vendor. Similarly, if both vendors are in the same section, half of the fans will buy one vendor and half from the other vendor. a. Construct a payoff matrix showing the payoffs of the vendors for each of their strategies. b. Is there a dominant strategy for this game? If so, is it strictly dominant? c. Find the pure-strategy Nash Equilibria of this game. Section 1 100 fans Section 2 100 fans Section 3 100 fans 4. For each of the following, either (i) give an example of the payoff matrix of a game with 2 players and 3 strategies per player that satisfies the requirement (please make all payoffs integers between 0 and 9, and underline the best responses in the payoff matrix), or (ii) explain why the requirement is impossible to satisfy. Do not choose examples of games covered in class, discussion, or in the textbook. a. There are exactly 3 pure-strategy Nash equilibria. b. One player has no best response to one of the other player's strategies. c. One player has a strictly dominant strategy, the other player has a dominant strategy but not a strictly dominant strategy, and there is exactly one pure-strategy Nash equilibrium. d. One player receives the same payoff regardless of the chosen strategies and neither player has a dominant strategy. e. There are no pure-strategy Nash equilibria. 3. Consider a football stadium that has 3 seating sections (S1, S2, S3) in a row. The distance between section S1 and S2 is the same as the distance between sections S2 and S3. Each of the sections seats 100 people. Now, consider two hotdog vendors who have to decide the sections in which to set up their shop in order to sell as many hotdogs as possible. Since the fans do not want to miss any part of the game, they will buy from the hotdog vendor in the sections closest to them (assume the distance inside the section does not matter to them). We will also assume that this is a hungry crowd in a popular game, so every seat is occupied and every person will buy one hotdog. If both the vendors are in equally distant sections, then half the fans buy from one vendor and half from the other. For example, if one vendor is in S1 and one vendor is in S3, half the people in S2 will buy from the first vendor and half from the second vendor. Similarly, if both vendors are in the same section, half of the fans will buy one vendor and half from the other vendor. a. Construct a payoff matrix showing the payoffs of the vendors for each of their strategies. b. Is there a dominant strategy for this game? If so, is it strictly dominant? c. Find the pure-strategy Nash Equilibria of this game. Section 1 100 fans Section 2 100 fans Section 3 100 fans 4. For each of the following, either (i) give an example of the payoff matrix of a game with 2 players and 3 strategies per player that satisfies the requirement (please make all payoffs integers between 0 and 9, and underline the best responses in the payoff matrix), or (ii) explain why the requirement is impossible to satisfy. Do not choose examples of games covered in class, discussion, or in the textbook. a. There are exactly 3 pure-strategy Nash equilibria. b. One player has no best response to one of the other player's strategies. c. One player has a strictly dominant strategy, the other player has a dominant strategy but not a strictly dominant strategy, and there is exactly one pure-strategy Nash equilibrium. d. One player receives the same payoff regardless of the chosen strategies and neither player has a dominant strategy. e. There are no pure-strategy Nash equilibria.

Answer rating: 100% (QA)

Hotdog Vendor Game a Payoff Matrix Vendor 1 Section 1 Section 2 Section 3 Section 1 100 100 50 150 0 200 Section 2 150 50 100 100 50 150 Section 3 0 2... View the full answer