3 ms·

I haven't down voted anyone. Setup your own experiment and let me know what you find.

• nostromo95 9y ago
  You’re mixing up equilibrium payoff and Nash Equilibrium (which is a strategy profile). Yes, the payoffs of player A randomizing and player B playing scissors is the same as both players randomizing, but observe that this profile of strategies fails the ex-post facto definition of Nash Equlibrium, i.e. in retrospect player A would want to change their strategy choice to “play rock every time.”
• qubex 9y ago
  Then I apologise for thinking it had been you. I’m going to sound very arrogant but: I don’t need to set up the scenario you describe because optimal strategies in identical games have been proven since the 1940s when Oskar Morgenstern and John Von Neumann published their seminal Theory of Games and Economic Behaviour (1944). If you are getting results that are in conflict with that which is mathematically proven (provided certain circumstantial criteria are met), then you can be sure that you have not exactly matched the circumstantial criteria assumed as a perquisite for the proof. So basically you’re in another situation where the theorem makes no claim to hold and, unsurprisingly, doesn’t.
• Yeikoff 9y ago
  Lets do then. Player 1 randomizes (1/3, 1/3, 1/3). Player 2 randomizes (1, 0, 0). Does player 1 want to deviate? Yes! Randomizing is not the best strategy if player 2 is going to be playing the same pure strategy all the time, player 1 would be better off if she were to play the best response to whatever (1, 0, 0) is. -> Not an equilibrium.