Two players decide simultaneously whether or not to enter a lottery. The payoff from sinning the lottery is b > 0.

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Question 5. [9 points out of 45] Two players decide simultaneously whether or not to enter a lottery. The payoff from winning the lottery is b > 0. The cost of entering is ce (3,6). If both players enter this lottery, each player wins with probability 0.5. If only one player enters the lottery, that player wins with probability 1. a.) Find all the pure-strategy Nash equilibria. b.) * Find the symmetric mixed-strategy Nash equilibrium. That is, find the equilibrium probability p with which each player enters the lottery as a function of the known parameters b and c. c.) What happens to the equilibrium p from part (b) as c tends to ? What happens as c tends to b? Explain intuitively. d.) Is the sum of the players' payoffs higher in the pure-strategy Nash equilibria from part (a) or in the mixed-strategy Nash equilibrium from part (b)? Explain intuitively. Question 5. [9 points out of 45] Two players decide simultaneously whether or not to enter a lottery. The payoff from winning the lottery is b > 0. The cost of entering is ce (3,6). If both players enter this lottery, each player wins with probability 0.5. If only one player enters the lottery, that player wins with probability 1. a.) Find all the pure-strategy Nash equilibria. b.) * Find the symmetric mixed-strategy Nash equilibrium. That is, find the equilibrium probability p with which each player enters the lottery as a function of the known parameters b and c. c.) What happens to the equilibrium p from part (b) as c tends to ? What happens as c tends to b? Explain intuitively. d.) Is the sum of the players' payoffs higher in the pure-strategy Nash equilibria from part (a) or in the mixed-strategy Nash equilibrium from part (b)? Explain intuitively