 As an alternative, one might consider a learning rule where the rate players switch to strategy \(S_i\) only depends on whether the expected payoff of \(S_i\) exceeds the average payoff of the population at the current time. Notice that such a learning rule attributes a higher degree of rationality to the individual players than the learning rule which generates the replicator dynamics. Why? This learning rule requires people to know the entire set of possible strategies, as well as the associated payoff matrix, so that they can determine if a strategy presently absent from the population would be worth adopting. When this learning rule is plugged into the above schema, one obtains the Brown-Nash-von Neumann (BNN) dynamic (see Brown and von Neumann, 1950). Unlike the replicator dynamics, the BNN dynamic can introduce new strategies into the population which are not represented. When the population is started in the states where everyone plays Rock, Paper or Scissors, the BNN dynamic will eventually end up in a state where all strategies are represented.