The origins of quasi-concavity: a development between mathematics and economics

The origins of the notion of quasi-concave function are considered, with special interest in some work by John von Neumann, Bruno de Finetti, and W. Fenchel. The development of such pioneering studies subsequently led to a whole field of research, known as “generalized convexity.” The different styles of the three authors and the various motivations for introducing quasi-concavity are compared, without losing sight of economic applications characteristic of the whole field of generalized convexity.