GT6-n players - Overview So far we have looked at More Than...

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1 1 More Than Two Players UGBA 143: Game Theory and Business Decisions 2 Overview So far, we have looked at: Normal form games Continuous games Typically, between two players Today: More complex strategic situations Many players 3 Cournot competition: More than two firms Unit cost is $1 per unit Market demand curve is: price = 8 – (total quantity produced) / 5,000 3 firms, producing quantities Q 1 , Q 2 , Q 3 . We can use the same technique as before (i.e. 2 firms) to solve for the Nash equilibrium quantities ( Q 1 *,Q 2 *,Q 3 *) and price P* What happens when there are 4 firms? 5 firms? More? 4 Cournot competition: More than two firms 3 firms: Given Q 2 ,Q 3 , Firm 1’s profit is Q 1 (7 – ( Q 1 + Q 2 + Q 3 ) / 5,000), so Firm 1’s best response is (35,000 – ( Q 2 + Q 3 )) / 2 Remember to apply symmetry when you can! The Nash equilibrium is: Q 1 * = Q 2 * = Q 3 * = 35,000 / 4 With n firms, the Nash equilibrium is Q i * = 35,000 / ( n +1) 5 Friends at the Bar Alice, Barb, Cindy are deciding between going to a bar and staying at home Staying at home yields payoff 1 Going to the bar yields: What is (are) the Nash equilibria?
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