One such example is the infamous "which is the poisoned cup?" scenario, in which, for example, if the poisoner picks the strategy "he thinks I'm going to put it in his cup, so I'll put it in mine", then the poisonee is incentivized to move to the strategy "he thinks I think he's going to put it in my cup, so he'll put it in his, so I'll pick mine," and the poisoner then is incentivized to change to "he thinks I think he thinks..." and so on and so forth.
However, there are strategies that, once adopted, force a local equilibrium, that is, the players involved have no incentive to change strategies.
Now let's make this slightly more interesting...let's say that one cup contains water and the other coffee, which, due to its antioxidant properties *cough* makes the poison 20% less effective, that is, it will only kill you 80% of the time. Find equilibrium strategies for this scenario.
Edited by Yoruichi-san, 08 June 2012 - 06:59 PM.