discussion_of_duel

# discussion_of_duel - Discussion of\Duel Econ 159a/MGT522a...

This preview shows pages 1–2. Sign up to view the full content.

Discussion of \Duel" Econ 159a/MGT522a Ben Polak November 1, 2007 The argument below is a little more formal (and a little less direct) than the one we used in class, but the gist of the message is the same. Some of you may °nd it useful. The Rules. There are two players, each with a wet sponge. They start at either side of the room. The players have alternate turns. Each turn, the player can either shoot or take a step forward. If she shoots and hits then she wins. If she misses, then the game continues so e°ectively she loses (since the other player can wait and shoot point blank). The Strategic Decision. When to shoot? Extra structure to make the analysis tractable. Assume that the abilities of the players are known. In particular, ° let P 1 ( d ) be player 1’s probability of hitting if she shoots at distance d ; and ° let P 2 ( d ) be player 2’s probability of hitting if she shoots at distance d ; In addition, let us make two plausible assumptions: ° P 1 (0) = P 2 (0) = 1; that is, they hit for sure from point blank. ° Both P 1 and P 2 are decreasing; that is, the probabilities of hitting go down with distance. Notice we do need not assume that the players are equally good shots, or even that one is better than the other at all distances, just that their abilities are known. Speculations. We might think that a better shot will shoot ±rst since she has a better chance of hitting. Alternatively, we might think that a worse shot will try to pre-empt the better shot.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern