John Maynard Smith applied the zero-sum contests and win-win evaluation schemes from game theory to show that competition among males of a species would not tend to be lethal, but would have limited actual fighting and a large quantity of posturing and other non-aggressive display behaviour. This game-theoretic explanation has been largely accepted by theorists and other biologists in the field. In 1982, his book Evolution and the Theory of Games explained the application of game theory to biological science. This book explained how evolutionarily stable strategy is relevant to the field.
After the war he studied genetics under the famous J. B. S. Haldane at University College London.
With Eors Szathmary, he wrote a book The Origins of Life: From the birth of life to the origin of language about a mathematical model that applied equally to the molecular biology and chemistry of very early evolution of life, as well as social group evolution.
In his honor, the European Society for Evolutionary Biology has an award for extra-ordinary young evolutionary biology researchers named The John Maynard Smith Prize. It has been awarded every other year since 1997.
The 1997 winner was Marie-Charlotte Anstett for Facilitation and constraints in the evolution of mutualism The 1999 winner was Nicolas Galtier for Non stationary models of nucleotide substitution and the evolution of base composition.