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Establish whether there exists a two-player game in extensive form with perfect information, and possible outcomes I (Player I wins), II (Player II wins), and D (a draw), whose strategic-form description is
If the answer is yes, describe the game. If not, explain why not.
Suppose that some players are indifferent between some pairs of houses. Specifically, suppose there are three players, whose preferences are given in Figure 1. - Find the core and show that the strong core is empty.
Find the mixed strategy Nash equilibria of the game (depending on c and Π). Does the existence of a friend make it more or less likely that you decide to go swimming on the first day?
Find all subgame perfect equilibria of this game. Now suppose player 2 has found a way of cheating, getting to observe player 1's hand. Represent the extensive form of this game and find its subgame perfect equilibria.
Radon levels in a house vary from week to week. In one house a sample of 8 weeks had the following readings for radon level ( in pCi/L): 1.9, 2.8, 5.7, 4.2, 1.9, 8.6, 3.9, 7.2
Draw the game tree and the matrix of this game, and find all the Nash equilibria. - Find all the subgame-perfect equilibria of this game.
Is there a Nash equilibrium in which more than k people contribute? One in which k people contribute? One in which fewer than k people contribute?
Determine the critical discount factor above which cooperation between the two firms can be sustained (i.e., playing grim trigger strategy by both firms is an equilibrium in the repeated game).
Does this game have a subgame perfect Nash equilibrium? - Do you think any one of the players has a strategy that guarantees him a win (a payoff of 2)?
Show this sequential-play game in strategic form, and find all the Nash equilibria. Which is or are subgame perfect and which is or are not? If any are not, explain why.
Which firm produces more output in an equilibrium? What is the effect of technical change that lowers firm 2's unit cost c2 (while not affecting firm 1's unit cost c1) on the firms' equilibrium outputs, the total output, and the price?
Calculate the right-hand-side of constraint 1 to 11 (instead of 10) and solve the problem. How much did the profit increase as a result of this?
Suppose your friend is creating a game about Lewis and Clark's expedition. Provide a list of 10 possible elements she should include in the game in order to make it as informative and exciting as possible
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