Requirements

  • 0-sum game
  • indifference condition
    • agents must be indifferent to which strategy they use
    • e.g. rock-paper-scissors
      • there is no clear profit-maximizing strategy
      • any response is the best response in pure strategies

Equilibrium

  • no Nash Equilibrium in pure strategies
  • BUT there is an equilibrium with mixed strategies
    • mixed strategy … taking probabilities of actions into account
      • i.e. preferences of other players
    • players are only willing to change their preferences “randomize” when there is otherwise no chance for profit
      • e.g. during rock-paper-scissors one might pick one option multiple times to get an edge
    • with symmetrical games they will always randomize always equal probabilities
    • with asymmetrical games they will only randomize when chances are equal, otherwise players have dominant strategies