Life in the fast lane

“You’re a rotten driver,” I protested. “Either you ought to be more careful or you oughtn’t to drive at all.”

“I am careful.”

“No, you’re not.”

“Well, other people are,” she said lightly.

“What’s that got to do with it?”

“They’ll keep out of my way,” she insisted. “It takes two to make an accident.”

—F. Scott Fitzgerald, The Great Gatsby

• Suppose that this is a static game, where both players move at the same time. Circle all payoffs corresponding to best responses, and find any/all pure strategy Nash equilibria.
• Now suppose that Jordan moves first, followed by Nick. (Jordan’s the “rotten driver”, so she has to react first if she wants to avoid an accident.) Draw the game tree.
• Use backward induction to find the subgame perfect Nash equilibrium. Be sure to describe each player’s complete “battle plan”, indicating what they would do in every possible situation. (Example: “Pfizer enters. Novartis only enters if Pfizer passes.”) What are the equilibrium payoffs (the payoff each player gets in this equilibrium)?
• The pair of strategies “Jordan Swerves, Nick plays Steady no matter what” isn’t subgame perfect. In your game tree, circle the subgame where this isn’t a Nash equilibrium.

Now suppose that Nick moves first, followed by Jordan. Assuming that both players are rational, which action will Nick choose, and how will Jordan