[EM] Plurality equilibria

[Forest Simmons]

On Fri, 20 Sep 2002, Rob LeGrand wrote in part:

> 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.
>

The game of chicken is symmetrical, but this example isn't.  One faction
has nothing to lose and a very probable gain while the other may lose or
gain, and most likely lose, when taking into account that the other has
nothing to lose by defecting.

I know that some games have no deterministic optimal rational strategy,
but I think that this one does.

I know that in real life not all players will follow the unique optimal
rational strategy when one exists. But the original question only asked
about the result of applying near optimal strategy.

Perhaps I should have left out the word "near" to avoid the issue of
irrationality altogether.

But this brings up another question.  When there is no optimal
deterministic strategy, is there a case where the optimal stochastic
strategies give superior expected results for IRV over plurality?


Forest

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