Game Theory

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Strictly dominant strategies

Strictly dominated strategy is where a player takes a strategy to suit him or herself, no matter what anyone else is doing.

There are two choices, A and B. if A strongly dominates B then A is always superior to B, no matter what the opponents do. If A weakly dominates B then in at least one option A is superior to B, but in all the other options the payoff for A and B are the same.

If both players have a dominant strategy then they will stick to their guns and there will be one unique Nash equilibrium. However, this may not be the best choice (or “pareto optimal”), meaning there are non-equilibrium outcomes that would be better for both players. The Prisoner’s dilemma is one example.

Weakly dominated strategies are best in Nash equilibrium games. Take C, which weakly dominates D. If the both players choose C, both get one point. If either of them choose D, they both lose.

From this it can be seen that rational players will not play strictly dominant strategies as a result.

SDS for companies

Iterated elimination of dominant strategies (IEDS)

Minimax

Backward induction

Forward induction