In mathematical terms, For any player i, a strategy weakly dominates another strategy if (With at least one strict inequality) (Remember that S − i represents the product of all strategy sets other than i's) On the other hand, s ...

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Dominance game theory, Dominance game theory - Terminology, Dominance game theory - Mathematical definition, Dominance game theory - Dominance and Nash equilibria, Dominance game theory - Iterated elimination of dominated strategies IEDS

Read more here: » Dominance game theory: Encyclopedia II - Dominance game theory - Mathematical definition

See also:

Dominance game theory, Dominance game theory - Terminology, Dominance game theory - Mathematical definition, Dominance game theory - Dominance and Nash equilibria, Dominance game theory - Iterated elimination of dominated strategies IEDS

Read more here: » Dominance game theory: Encyclopedia II - Dominance game theory - Iterated elimination of dominated strategies IEDS

If a strictly dominant strategy exists for one player in a game, that player will play that strategy in each of the game's Nash equilibria. If both players have a dominant strategy, the game has only one unique Nash equilibrium -- however, that Nash equilibrium is not necessarilly Pareto optimal, meaning that there may non-equilibrium outcomes of the game that would be better for both players. The classic game used to illustrate this is the Prisoner's Dilemma. Strictly dominated strategies cannot be a part of a Nash equilibrium, and a ...

See also:

Dominance game theory, Dominance game theory - Terminology, Dominance game theory - Mathematical definition, Dominance game theory - Dominance and Nash equilibria, Dominance game theory - Iterated elimination of dominated strategies IEDS

Read more here: » Dominance game theory: Encyclopedia II - Dominance game theory - Dominance and Nash equilibria

When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. B dominates A: choosing B always gives at least a good an outcome as choosing A. There are 2 possibilities: B strictly dominates A: choosing B always gives a better outcome than choosing A, no matter what the other player(s) do. B weakly dominates A: There is at least one set of opponents' action for which B is superior, and all other set ...

See also:

Dominance game theory, Dominance game theory - Terminology, Dominance game theory - Mathematical definition, Dominance game theory - Dominance and Nash equilibria, Dominance game theory - Iterated elimination of dominated strategies IEDS

Read more here: » Dominance game theory: Encyclopedia II - Dominance game theory - Terminology

When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. B dominates A: choosing B always gives at least as good an outcome as choosing A. There are 2 possibilities: B strictly dominates A: choosing B always gives a better outcome than choosing A, no matter what the other player(s) do. B weakly dominates A: There is at least one set of opponents' action for which B is superior, and all other se ...

See also:

Dominance game theory, Dominance game theory - Terminology, Dominance game theory - Mathematical definition, Dominance game theory - Dominance and Nash equilibria, Dominance game theory - Iterated elimination of dominated strategies IEDS

Read more here: » Dominance game theory: Encyclopedia II - Dominance game theory - Terminology