Quality patterns and critical mass effects in an evolutionary game of public contracting

We study an evolutionary game of public contracting in which firms are randomly matched in pairs from an infinite population to play a public contracting contest, e.g. to build bridges. Price is fixed; firms must choose quality, which may be Low, Normal or Outstanding. The highest quality wins the contest; however, the higher the quality offered, the less the profit. We show how selection of a quality pattern at the population level occurs via replicator dynamics, i.e., relatively more rewarding strategies are adopted with increasing frequencies. A complete characterization of the dynamics is provided.