I'm new to the topic and currently only introduced to Normal Form Games. So about this rational player in game theory... I was wondering if the player could still be considered rational by choosing an irrational answer to the game to be be able to better position them self in the later game? Or would this never be the case since that would still be considered rational? At what point does uncertainty about the behaviors of a player come in?

Thank you

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    It's paradoxical for an rational player to choose a choice that is irrational with full knowledge. Perhaps you want irrational to imply unpredictability, which rational players can be. Uncertainties, like having mixed strategies where it is rational to mix up ones strategies, is accounted for. – Paul Burchett May 5 '17 at 14:28
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    If there are multi-tier games in game-theory, the overall expected utility (including the expected reaction functions of every other player) is taken into account. Depending on how expected utility is computed, this may include uncertainty variables. So if he can position himself extraordinarily well in a higher-tier game, whether he chooses the seemingly irrational choice in the first game still depends on how much to gain and how probable it is overall. But he NEVER chooses irrationally. It just may seem so from a standpoint of different informations. – Philip Klöcking May 5 '17 at 17:57
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    When you're playing chicken, it's rational to take your hands off the steering wheel to convince the other player that you're crazy. This works in real life too. See Richard Nixon's madman theory. en.wikipedia.org/wiki/Madman_theory – user4894 May 5 '17 at 20:14
  • Thank you for all your comments. I enjoyed being introduced to these new concepts (i.e. multi-tier games). Haha, @user4894. How can this mad man strategy be reflected in the analytical construction describing a game? Can uncertainty only be represented in the utility function of a particular player? – ThunderVault May 8 '17 at 12:03
  • @PhilipKlöcking where can I get some nice reading on multi-tier games in game theory? – ThunderVault May 8 '17 at 12:16

It would never be rational to be irrational. In Rational Actor Theory, a rational actor is goal-oriented, reflective and consistent. If you act irrationally, you will not achieve one of these goals.

However, there is nothing which prevents a player from choosing to act in a way that appears irrational because they perceive a long term benefit to others perceiving that apparent irrationality. This would qualify as rational thought. The phrase for this is "there is method to my madness."

The uncertainty about players would be most likely incorporated into the reflective side. If it is clear that the other players are not being affected by your apparent irrationality, and you do not believe you are going to be able to sell it any better than you already had, then it is irrational to continue acting apparently irrational. You would either no longer be goal-oriented or you would no longer be reflecting enough to realize that your actions were not accomplishing the goals.

  • Factually wrong. en.wikipedia.org/wiki/Madman_theory – user4894 May 5 '17 at 20:14
  • @user4894 What about that link disproves my argument. In fact, when I read it, it seemed like an exact perfect match for what I wrote. Nixon appears to have walked the exact same line I did, between irrational behavior and apparently irrational behavior. – Cort Ammon May 5 '17 at 20:21
  • Sorry, misread your post. It's rational to act irrational. – user4894 May 5 '17 at 20:28
  • Thank you @CortAmmon for your answer. To summarize, it is not possible to be irrational if your strategy is goal oriented. I'm still curious, do you know if it is possible to describe the goal of a game that rewards an irrational strategy? Are there games where it is best to pick a random strategy because the end goals are not achievable? – ThunderVault May 8 '17 at 12:17
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    That's a good question. My answer did assume that, at some point, you would switch away from a random approach at the opportune moment (to use a Jack Sparrow terminology). I do, however, know of at least one study which showed that the best way to organize security movements to stop terrorists is a completely random walk. That would suggest that, indeed, a random strategy can be the best choice for a rational actor. However, that one anecdote is the only example I have to suggest that that "irrational strategy" counts as a rational strategy. – Cort Ammon May 8 '17 at 13:48

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