Open-ended innovation arm-race in zero-sum games

This note discusses zero-sum games with open-ended innovation, whereby each player may introduce new strategies. The innovation process is modelled as a draw of new strategies form a distribution. It is argued that, when the cost of innovation is vanishingly small, this setting can lead to an everlasting innovation arm-race. In particular, the introduction of new technologies of the advanced player increases the marginal utility for technological innovation of the backward one, whereas innovation of the backward player disincentivizes the more advanced one to innovate.