Computational complexity of evolutionary stable strategies
October 10, 2013 2 Comments
- For all
we have
, and
- If
then
.
Or we look at the contrapositive: a strategy can invade a host strategy
if (1) it has a better payoff in a population of
s than
s have against themselves, or (2) if they are neutral then a small population of
benefits themselves more than they benefit the host population. If some strategy
has no invading strategy
then it is an evolutionary stable strategy.
If you are an observant reader and familiar with classical game theory then you probably noticed that the first condition of the direct definition is equivalent to the definition of a Nash equilibrium (NE). The second clause joined with an “and” means that every NE is an ESS, but not every ESS is an NE. However, that second condition seems innocuous enough, surely it can’t change the the qualitative nature of the equilibrium concept?
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