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Compute the Nash equilibria and subgame perfect equilibria for the following games.
Do so by writing the normal-form matrices for each game and its subgames. Which Nash equilibria are not subgame perfect?
Two players, Amy and Beth, take turns choosing numbers; Amy goes first. On her turn, a player may choose any number between 1 and 10 Who will win the game? What are the optimal strategies (complete plans of action) for each player?
Compute the probability that exactly five students are left-handed.
Write a program that produces random permutations of the numbers 1 to 10.
If player 2 rejects player 1s initial proposal, player 2 can make a counterproposal which, if rejected by player 1, ends the game with payoffs 0 for each player. Find SPNE of the game using backward induction. What if δ2 increases? What if δ1 incr..
The market for olive oil in new York City is controlled by 2-families, Sopranos and Contraltos. Both families will ruthlessly eliminate any other family that attempts to enter New York City olive oil market.
A hat contains three coins - one gold, one silver and one copper. You will select coins one at a time without replacement until you choose the gold coin. The outcome of interest is the sequence of coins that are selected during this process.
Show that the set of trembling hand perfect equilibria of this extensive game is disjoint from the set of behavioral strategy profiles associated with the trembling hand perfect equilibria of its strategic form.
Assume zero production cost for both firms. Find the Bertrand equilibrium prices for a simultaneous-move game. Draw the two demand curves in a graph, with price on the vertical axis and demand on the horizontal axis.
What is the payoff of a person whose number is the highest of the three? Can she increase this payoff by announcing a different number?
The "Prisoner's Dilemma" was the gateway to the strategic viewpoint of game theory. In this assignment, you will explore the applications of game theory to economic business decisions.
If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician's accuracy is within the target accuracy?
If so, find a payoff function consistent with the information. If not, show why not. Answer the same questions when, alternatively, the decision-maker prefers the lottery.
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