tag:blogger.com,1999:blog-1780806945960886534.post3515019701354556885..comments2024-03-28T05:47:54.177+00:00Comments on Philosophical Disquisitions: Game Theory (Part 6) - The Penalty Kick GameJohn Danaherhttp://www.blogger.com/profile/06761686258507859309noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-1780806945960886534.post-63241937720325478592019-01-02T22:21:23.684+00:002019-01-02T22:21:23.684+00:00Good job. Good job. Mathsmanhttps://www.blogger.com/profile/02756334750349311484noreply@blogger.comtag:blogger.com,1999:blog-1780806945960886534.post-5396863922438168632011-06-10T10:39:27.299+01:002011-06-10T10:39:27.299+01:00Assuming I keep up with this series, evolutionary ...Assuming I keep up with this series, evolutionary game theory will be covered at some stage. For the time being the focus is on single-shot games. I think I mentioned that at some stage. If I didn't, I am now. Calculations are different when dealing with multi-round games or repeated games (e.g. iterated Prisoners' dilemma).<br /><br />As for your other point, you can incorporate risk aversion into models of decision making. This can then account for the preference for the more reliable strategy.John Danaherhttps://www.blogger.com/profile/06761686258507859309noreply@blogger.comtag:blogger.com,1999:blog-1780806945960886534.post-17692086087455583402011-06-10T03:58:42.168+01:002011-06-10T03:58:42.168+01:00I wonder about this rule:
"If you want to ma...I wonder about this rule:<br /><br />"If you want to maximise your expected payoff...You should not choose a strategy that is never a best response."<br /><br />Some work in evolutionary biology indicates that it is sometimes better to choose a strategy that pays-off well under a wide variety of conditions, rather than a strategy that pays-off well under a narrow set of conditions.<br /><br />They call it "survival of the flattest":<br />http://devolab.msu.edu/survival_of_the_flattest/<br /><br />Of course, game theory is not evolutionary theory, so I'll try to phrase this in terms of the penalty-kick game. I wonder if the above rule is linked to the fact that the payoff function is linear in the given example.<br /><br />Imagine that one strategy has a moderate payoff under all conditions (i.e. all choices by the opponent), but for each condition there is another strategy that has a slightly higher payoff. The catch is that each of these alternative strategies has 0 payoff under any other condition.<br /><br />In this scenario, it would be best to chose the reliable strategy even though there is always another strategy that provides a better outcome, because given the uncertainty about the opponent's actions, there is an infinitesimal chance that any of the alternative strategies will have a payoff. True?Ricketsonhttps://www.blogger.com/profile/02579799843541826447noreply@blogger.com