AbstractMales usually compete to gain access to prospective mates. Through this male–male competition, superior males have a higher chance of passing on their traits to the next generation of male offspring. One category of male traits is armaments, which are weapons used during competition, for example, the chelae of fiddler crabs and the antlers of deer. One consequence of intrasexual selection is the exaggerated evolution of armaments, which can be limited by trade‐offs, such as trade‐offs with male body size. Here, we formulate a game‐theoretic sexual selection model to explore the exaggerated evolution of armaments through male–male competition. The model is used to determine how competition affects the evolution of an armament that is subject to trade‐offs. Our simulation can be used to support the exaggerated evolution hypothesis, that is, male–male competition escalates the rate of evolution of armaments.