  I consider a family of games with corresponding payoff matrices, parametrized
by the parameter The informal question of interest is: what game is the best?
Instead of attempting to suggest a more or less arbitrary definition of the
best game, I allow natural selection to find it through honest competition
between games. Specifically, I consider a model of a community composed of
populations with different payoff matrices and study the natural selection
between the populations. The outcome of the community evolution determines the
best game. I develop here a mathematical toolbox, that allows the study of
evolution of parametrized games. The developed approach is applied to three
examples of parametrized games from the literature: local replicator dynamics,
pairwise competition and the game of alleles in diploid genomes.
