Game theory

• Dominance
  • Strict Dominance
  • Weak Dominance
• Best Response
• Nash Equilibrium
• Mixed Strategy

Dominance

The idea of dominance is to do with the selection of a strategy based on the its outcome versus the other players strategies. If a strategy is always better than another strategy, then it is said to strictly dominate that strategy. If it is sometimes better, then it is said to weakly dominate that strategy.

Best Response

When dominance isn't found in the strategies we next look at best response. The player selects the stragegy that maximises their utility given the other players strategy.

Nash Equilibrium

A nash equilibrium is a pair of strategies where no player has an incentive to change their strategy. It's easiest identified by looking at the best response for each player. If they are both playing their best response in a given cell then it is a nash equilibrium.

Mixed Strategy

A pure strategy is one that we can find from playing a single strategy, but a nash equilibrium may not exist. Instead we have to take a mix of strategies to find a nash equilibrium.