Evolutionarily stable investments in recognition systems explain patterns of discrimination failure and success.

Many animals are able to perform recognition feats that astound us-such as a rodent recognizing kin it has never met. Yet in other contexts, animals appear clueless as when reed warblers rear cuckoo chicks that bear no resemblance to their own species. Failures of recognition when it would seem adaptive have been especially puzzling. Here, we present a simple tug-of-war game theory model examining how individuals should optimally invest in affecting the accuracy of discrimination between desirable and undesirable recipients. In the game, discriminating individuals (operators) and desirable and undesirable recipients (targets and mimics, respectively) can all invest effort into their own preferred outcome. We demonstrate that stable inaccurate recognition will arise when undesirable recipients have large fitness gains from inaccurate recognition relative to the pay-offs that the other two parties receive from accurate recognition. The probability of accurate recognition is often determined by just the relative pay-offs to the desirable and undesirable recipients, rather than to the discriminator. Our results provide a new lens on long-standing puzzles including a lack of nepotism in social insect colonies, tolerance of brood parasites and male birds caring for extra-pair young in their nests, which our model suggests should often lack accurate discrimination. This article is part of the theme issue 'Signal detection theory in recognition systems: from evolving models to experimental tests'.