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# hw6a - Homework 6 ISyE 4803 1 For the following three games...

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Homework 6 – ISyE 4803 1. For the following three games, find the Nash equilibria (if any) and the Pareto efficient outcomes (note, in the tables I am only writing the payoffs, but these are for two players): 1,1 3,0 0,3 2,2 2,1 0,0 0,0 1,2 2,6 -2,8 4,4 5,5 2. Consider the following basic Cournot game: There are two firms and market demand is P=1-Q (where Q=q1+q2). Do the following: a. Find the Cournot equilibrium. (Call this output level M). b. Find the equilibrium where both collude. (Call this output level L) c. Find the output level for firm 2 if it knew firm 1 would pick level L (call this level H). d. Write out a payoff matrix (it will be 3 by 3) where the actions of each firm are M, L, and H. Fill in the payoffs for each outcome. e. Find the Nash equilibrium (if any) of this matrix and the Pareto efficient outcome(s) (if any). 3. Suppose two firms face a market demand of P=100-Q (where Q=q1+q2) and the total cost for a firm is 2+Q 2 . Find the Cournot equilibrium. 4.

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hw6a - Homework 6 ISyE 4803 1 For the following three games...

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