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For each of the following games, where Player I is the row player and Player II is the column player:
(a) Write out the mixed extension of the game.
(b) Compute all the equilibria in mixed strategies.
Write down an expression (in terms of w) for the wheel monopolist's profit. Show that for any w> 0, the total profits of the skate and wheel monopolists is lower than the integrated monopolist's profit.
What is the present value of a perpetuity that begins payment 10 years from today. The first payment is $1000.
Player 1 has the following set of strategies {A1;A2;A3;A4}; player 2’s set of strategies are {B1;B2;B3;B4}. Use the best-response approach to find all Nash equilibria.
A survey of 356 local drivers reveals that 18.7% of them car pool. Is there evidence that the actual proportion of local commuters car-pooling is less than national level. Also find and interpret the p-value of this test.
Analyze the renewable resource problem for N players. Is it true that all of the resource is extracted in the first period if N approaches infinity?
A supplier and a buyer, who are both risk neutral, play the following game, The buyer’s payoff is q^'-s^', and the supplier’s payoff is s^'-C(q^'), where C() is a strictly convex cost function with C(0)=C’(0)=0. These payoffs are commonly known.
Explain from firm A's perspective the expected decision that firm B will make and does situation have a Nash Equilibrium?
We expect two proportions to be about 0.20 and 0.30, and we want an 80% chance of detecting a difference between them using a two-sided 0.05 level test.
A sample set of 29 scores has a mean of 76 and a standard deviation of 7. Can we accept the hypothesis that the sample is a random sample from a population with a mean greater than 72? Use alpha = 0.01(1-tail) in making your decision.
Show that for any p ∈ [0, 100], there is a Nash equilibrium of the game in which an agreement is reached at this price. Describe the equilibrium strategy profile and explain.
Write the first-order condition and derive the best-response function for each player. - Find the Nash equilibrium of this game. What is the probability that the defendant wins in equilibrium.
Construct a game with payoffs that corresponds to situation - Can you solve the game through iterated dominance?
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