Lack of Robustness
Markov perfect equilibria are not stable with respect to small changes in the game itself. A small change in payoffs can cause a large change in the set of Markov perfect equilibria. This is because a state with a tiny effect on payoffs can be used to carry signals, but if its payoff difference from any other state drops to zero, it must be merged with it, eliminating the possibility of using it to carry signals.
Read more about this topic: Markov Perfect Equilibrium
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