One-shot deviation principle

The one-shot deviation principle is the principle of optimality of dynamic programming applied to game theory. It says that a strategy profile of a finite extensive-form game is a subgame perfect equilibrium if and only if there exist no profitable one-shot deviations.[1] Ultimately, no player can profit from deviating from the strategy for one period and then reverting to the strategy. Furthermore, this principle is very important for infinite horizon games. In an infinite horizon game where the discount factor is less than 1, a strategy profile is a subgame perfect equilibrium if and only if it satisfies the one-deviation principle.


Definitions

A one-shot deviation for player i from strategy σi is a different strategy σ~i for only one period. A profitable one-shot deviation is one in which using a different strategy for one period (an one-shot deviation) yields a higher payoff.[2] A proof of how an unimprovable strategy must be optimal can also be done.[3]

References

  1. ↑ Tirole, Drew Fudenberg ; Jean (1991). Game theory (6. printing. ed.). Cambridge, Mass. [u.a.]: MIT Press. ISBN 978-0-262-06141-4.
  2. ↑ Rubinstein, Martin J. Osborne; Ariel (2006). A course in game theory (12. print. ed.). Cambridge, Mass. [u.a.]: MIT Press. ISBN 0262650401.
  3. ↑ Ray, Debraj. "One-Shot Deviation Principle" (PDF). Retrieved 5 February 2014.


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