Econ 398 Homework 6 Suggested Solutions 1) Use the characterization from class to check for mixed-strategy Nash Equilibria. First note that there are four pure strategy equilibria, each where one person drives Straight, and the other person either swerves Left or swerves Right. Next notice that Stop is dominated for Daisy by, for instance, a strategy that puts probability weight of .4, .2, .4 respectively on the strategies Left, Straight, and Right. So Stop won’t be used in any Nash Equilibrium. Consider strategies where one player plays a pure strategy and the other randomizes over two or more strategies. Notice that if Billy-Jo drives Straight, Daisy is willing to randomize over Left and Right. Furthermore, if she randomizes over Left and Right, Billy-Jo will drive Straight. There is therefore a whole component of equilibria where Billy-Jo plays Straight (with probability 1), and Daisy plays Left with probability q and right with probability 1-q, where q∈[0,1].
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