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