Use the following one-shot, normal game to answer ...
Use the following one-shot, normal game to answer questions below:
|Strategy |D |E |F |
|A |100, 125 |300, 250 |200, 100 |
|B |250, 0 |500, 500 |750, 400 |
|C |0, -100 |400, 300 |-100, 350 |
a. Find each player’s dominant strategy, if it exists.
b. Find each player’s secure strategy.
c. Find the Nash equilibrium
2. In a two-player, o ne-shot simultaneous-move game each player can choose strategy. A or Strategy B. If both players choose strategy A, each earns a payoff of $500. If both players choose strategy B, each earns a payoff of $100. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1 earns $0 and player 2 earns $650. If player 1 chooses strategy B, and player 2 chooses strategy A, then player 1 earns $650 and player 2 earns $0.
a. Write the above game in normal form.
b. Find each player’s dominant strategy, if exists
c. Find the Nash equilibrium (Or Equilibra) of the game
d. Rank strategy pairs by aggregate payoff(highest to lowest)
e. Can the outcome with the highest aggregate payoff be sustained in equilibrium? Why or why not?
4- Use the following one-shot, normal game to answer questions below:
|Strategy |C |D |
|A |10,10 |60, -5 |
|B |-5, 60 |50, 50 |
a. Identify the one-shot Nash equilibrium
b. Suppose the players know this game will be repeated exactly three times. Can the players achieve payoffs that are better than the one-shot Nash equilibrium? Explain
c. Suppose this game is infinitely repeated and the interest rate is %5. Can the players achieve payoffs that are better than the one-shot Nash equilibrium? Explain
d. Suppose the players do not know exactly how many times this game will be repeated. But they do know that the probability the game will end after a given play is θ . If θ is sufficiently low, can players earn more than they could in the one-shot Nash equilibrium?
6- Consider a two-player, sequential move game where each player can choose to play right or left. Player 1 moves first. Player 2 observes player 1’s actual move and then decide to move right or left. If player 1 moves right, player 1 receives $0 and player 2 receives $15. If both players move left, player 1 receives -$10 and player 2 receives $8. If player 1 moves left and player 2 moves right, player 1 receives $10 and player 2 receives $10.
A. Write the above game in extensive form.
B. Find the Nash Equilibrium outcome to this game
c. Which of the equilibrium outcomes is most reasonable? Explain
10 – According to the recent article in the Wall Street journal, side-impact crashes are among the deadliest, accounting for nearly 10,000 deaths per year Child safety concerns have kept auto manufactures from making side impact airbags standard equipment, though they are optional on most middle- to higher-market automobiles. Openly critical comments by General Motors’s Ron Zarrella that other manufactures’ airbag systems inflate too powerfully and present a potential hazard to children have led to an industrywide study aimed at devising a common set of safety standards for side-impact airbag systems. Part of the trick of developing a set of standards that will protect both adults and children equally is getting the industry to agree on single set of standards. Suppose that such standards are developing and that Ford and GM must simultaneously decide weather to make side-impact airbags standard equipment on all models. Side-impact airbags raise the price of each automobile by $500. If both GM and Ford make side-impact airbags standard equipment, each company will earn profits of 1.5 billion. If neither company adopts side-impact airbag technology, each company will earn $.5 billion (due to lost sales to another automakers). If one of the company adopts the technology as standard equipment and the other does not, the adopting company will earn a profit of $2 billion and the other company will lose $1 billion. If you were a decision maker at GM, would you make side-impact airbags standard equipment? Explain
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