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- Provide an example of a 2-player normal form game where each player has 3 (pure) strategies such that: (i) There is no pure strategy Nash equilibrium.Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C), Player 2’s choices are shown in the column headings (D, E, F). The first payoff is for the row player (Player 1) and the second payoff is for the column player (Player 2). Player 2 Player 1 D E F A 6, 8 4, 7 2, 9 B 2, 3 2, 6 4, 7 C 5, 4 7, 5 3, 6Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C, D), Player 2’s choices are shown in the column headings (E, F, G). The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 7 7, 2 2, 6 B 5, 5 5, 4 8, 4 C 4, 6 8, 4 7, 5 D 1, 6 3, 5 6, 4 Highlight the correct answer: Player 1: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy Player 2: Has a dominant strategy to choose E Has a dominant strategy to choose F Has a dominant strategy to choose G Does not have a dominant strategy The Nash equilibrium outcome to this game is: A/F B/E B/G C/F C/G There is no pure strategy Nash…
- Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C, D), Player 2’s choices are shown in the column headings (E, F, G). The first payoff is for the row player (Player 1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 4 7, 7 2, 6 B 10, 6 1, 7 12, 4 C 4, 6 8, 8 7, 7 D 1, 6 3, 9 6, 7Consider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A/B), Player 2’s choices are shown in the column headings (C/D). The first payoff is for the row player (Player1) and the second payoff is for the column player (Player 2). Player 2 Player 1 C D A 8, 3 2, 4 B 7, 4 3, 5 Pick the correct answer: Player 1: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy Player 2: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy The Nash equilibrium outcome to this game is: A/C A/D B/C B/D There is no pure strategy Nash equilibrium for this gameProve that in a 2 × 2 zero-sum game, if equilibrium strategies exist then one of the players has a dominated strategy.
- Consider this market that is dominated by two airlines, American and United. Each can choose to charge a high price (and restrict capacity) or charge a low price (and expand capacity). If one of the airlines reduces the price and the other does not, then the airline that reduced the price can capture customers from the other airline. The profits for each outcome is shown below: a. Does United have a dominant strategy? If so, what is it? Explain. b. What is the Nash equilibrium in this game? Explain. c. Is this game an example of a Prisoner’s Dilemma? Explain.Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 7 and Deborah will receive a payoff of 6. The only dominant strategy in this game is for ____ to choose ____ . The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses ____ and Deborah chooses ____ .