Forest wrote: > Very informative examples, but the existence of different equilibria > doesn't quite answer the original question, which was formulated in > terms of near optimal strategy given near perfect information.
Zero-sum games always have optimal strategies, whether simple or mixed, for each player, but non-zero-sum games, which include most elections, are more complicated. Knowing the other voters' sincere preferences just isn't enough. You have to know their thought process too. > Given the sincere preferences of your example it seems more likely to > me that optimal (and near optimal) strategy for plurality would lead to > the other equilibrium that you mentioned: > > 45:Anderson <--- insincere > 35:Carter > 20:Anderson Depends. What if the Anderson voters know that the Reagan and Carter voters will stick to their favorites? You might say that that's irrational, but in non-zero-sum games rationality can be elusive. Consider the game of chicken, where two trucks drive straight at each other on a skinny road. You can swerve at the last second or not. The best outcome is to watch your opponent swerve while you don't; next best is for both to swerve; third best is to swerve and give your opponent the glory; worst is to die together in a ball of flame. One extremely effective strategy is to convince the other driver that you're insane. Scream, drink beer, throw the steering wheel out the window. The other driver will realize that swerving is a good strategy, even if he loses face. Being known as a rational player can be to your disadvantage. The game of chicken is symmetrical and has two mutually exclusive equilibria. There's an excellent treatment of zero-sum and non-zero-sum games in Philip Straffin's Game Theory and Strategy. Straffin also analyzes the above election under plurality; he gives three equilibria. ===== Rob LeGrand [EMAIL PROTECTED] http://www.aggies.org/robl/ for Texas State Representative, District 50 __________________________________________________ Do you Yahoo!? New DSL Internet Access from SBC & Yahoo! http://sbc.yahoo.com ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
