  This paper is concerned with exploring the microscopic basis for the discrete
versions of the standard replicator equation and the adjusted replicator
equation. To this end, we introduce frequency-dependent selection -- as a
result of competition fashioned by game-theoretic consideration -- into the
Wright--Fisher process, a stochastic birth-death process. The process is
further considered to be active in a generation-wise nonoverlapping finite
population where individuals play a two-strategy bimatrix population game.
Subsequently, connections among the corresponding master equation, the
Fokker--Planck equation, and the Langevin equation are exploited to arrive at
the deterministic discrete replicator maps in the limit of infinite population
size.
