tag:blogger.com,1999:blog-4535367891237919312.post762398479610243409..comments2017-05-20T15:49:01.867-04:00Comments on Man OverBoard: Game Theory: A simple multi-player casePaul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-4535367891237919312.post-54430379125035700952013-09-24T09:05:59.315-04:002013-09-24T09:05:59.315-04:00Games of Strategy by Avinash Dixit and Susan Skeat...Games of Strategy by Avinash Dixit and Susan Skeath. <br /><br />There are many editions of the book so you will be able to get an older edition at a reasonable price.Aaron Honsowetzhttp://www.blogger.com/profile/08648871127169061856noreply@blogger.comtag:blogger.com,1999:blog-4535367891237919312.post-44188020548718773742013-09-23T22:14:40.816-04:002013-09-23T22:14:40.816-04:00Excellent points, Aaron. As a player, my approach...Excellent points, Aaron. As a player, my approach will change if I'm only one space behind the leader and two spaces from the finish line, as opposed to trailing by five spaces. <br /><br />Exploring this topic has made me want to read up on game theory again. If you can recommend a good book on the topic, I'd be interested to know what it is.Paul Owenhttp://www.blogger.com/profile/02260814589584723033noreply@blogger.comtag:blogger.com,1999:blog-4535367891237919312.post-11164401020178927712013-09-22T20:02:39.959-04:002013-09-22T20:02:39.959-04:00You have done very well with your game theory so f...You have done very well with your game theory so far. <br /><br />I want to let you know that there is no proof that a 3 player zero-sum game must have a Nash Equilibrium. Or, I should say, there do exist three player zero sum games with no Nash Equilibrium. <br /><br />Part of what is making the 2nd game more complicated is that you are engaging in a game of repeated play. <br /><br />Another thing that increases the complexity is that there is a 4th conditional statement that you are exploring--the condition over what is the difference in length between the players. Not only does this dramatically increase the number of permutations to solving the game, but it forces you to look at one of your assumptions about the players not in first place. <br /><br />As a player am I indifferent about coming in 2nd or 3rd? The answer to that question alters the payouts in your payoff matrix. <br /><br />(Also, let's say more than one player crosses the finish line, does that count as a tie or does the runner that goes further win?)Aaron Honsowetzhttp://www.blogger.com/profile/08648871127169061856noreply@blogger.com