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In a context that future return is discounted by a constant parameter, one-shot deviation principle holds for both repeated games and dynamic programming.

Because, in repeated games, a one-shot deviation refers to one history, so on equilibrium path, a one-shot deviation could produce a play that differs on more than one stages from the original equilibrium path.

Is it true for the sequence of state variables and control variables in dynamic programming? In other words, can a one-shot deviation generate an aforementioned sequence that differs for more than one stage?

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I don't understand what the question is asking. Can you expand or explain more formally? Dynamic programming is just a general technique that is only useful for solving some problems. When it is useful, it is because the optimal solution has the form of optimally solving subproblems, then making the optimal decision at the current "level" given the subproblems' solutions. Since we make the optimal decision at each step or level, of course any other decision or "deviation" would be no better.... –  usul Feb 19 at 14:14

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