Show that there is no equilibrium of the bidding game

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Show that there is no equilibrium of the bidding game in pure strategies. c) Let B denote the bid of a player. Assume that the bid distribution is symmetric among players, i.e. all players use the same bid distribution in equilibrium. Show that the mixed strategy equilibrium must satisfy: F ( B ) = B V 0 . 5 (HINT: If the equilibrium strategies of players 2 and 3 are given by the equation above, any bid B of player 1 must yield an expect utility of zero, i.e. player 1 must be indifferent among any pure strategy.) d) What is the expected bid of any player in the mixed strategy equilibrium? What is the expected revenue of the city government?
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Problem 3: (20 percent) Read the attached article ”In Auto Test in Europe, Meter Ticks Off Miles, and Fee to Driver” by Elisabeth Rosenthal in the NYT. a) What are two advantages of taxing people based on the actual car use compared to a gasoline or carbon tax? b) What would be a potentially simpler and less intrusive alternative that can also reduce congestion in cities? Explain your answers.
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