The best replacement for perfect competition is monopoly.

The best alternatives to perfect competition are rated as following:
★★★★★  monopoly
★★★★  monopolistic competition
★★★  oligopoly
★★★  imperfect competition
★  pure competition
★  free market
★  monopolistic
★  pure monopoly
★  monopolies
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Speaking about perfect competition, one probably shouldn't forget about long run equilibrium.

Other search terms related to perfect competition and their ratings are:
★★★★★ long run equilibrium
★★★★ in a market
★★ demand curve
★ monopolistic competition
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