Sink equilibria and convergence

@article{Goemans2005SinkEA,
  title={Sink equilibria and convergence},
  author={Michel X. Goemans and Vahab S. Mirrokni and Adrian Vetta},
  journal={46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)},
  year={2005},
  pages={142-151}
}
We introduce the concept of a sink equilibrium. A sink equilibrium is a strongly connected component with no outgoing arcs in the strategy profile graph associated with a game. The strategy profile graph has a vertex set induced by the set of pure strategy profiles; its arc set corresponds to transitions between strategy profiles that occur with nonzero probability. (Here our focus will just be on the special case in which the strategy profile graph is actually a best response graph; that is… 

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