Serendipity and the Game Theory of Innovation in the Anthropocene

Climate and sustainability science increasingly confronts a choice of innovation strategy: costly, complex technological interventions promoted under a resource-based view, or nature-based approaches that capitalize on ecological laws and coexistence with nature. This note constructs a two-player game formalizing that choice. One player follows a resource-based view (RBV), investing in projects whose net benefit is concave in scale but whose implementation carries a compounding, quadratic penalty for cost overrun and unintended consequence, capturing what has been termed the "innovation curse": costly technologies (Carbon Capture and Storage, bioplastics, glacier geoengineering) that are prioritized despite high cost, speculative efficacy, and occasionally absurd outcomes. The other player follows a nature-based view (NBS), whose payoff is linear in ordinary ecological investment but carries an additional nonlinear term representing serendipity capacity, the ability to notice, evaluate, and capitalize on unexpected ecological information. We prove two propositions. The first shows the resource-based player's optimal investment is a bounded dominant strategy, strictly decreasing in the compounding risk of its own technology, so that unconstrained ambition is not rational even on its own terms. The second shows that the nature-based player's serendipity-driven strategy reduces a shared measure of ecological risk at a rate that saturates as serendipity capacity grows, and that once this capacity exceeds an explicit threshold, the game's equilibrium delivers a strict net reduction in aggregate ecological risk relative to a no-intervention baseline, regardless of how much the resource-based player continues to invest. Applied together, the two propositions give a precise, mechanism-level sense in which ecological intelligence, aided by serendipity capacity, can help reduce the ecological risks of the Anthropocene: not by outcompeting technological innovation directly, but by supplying a saturating, compounding-risk-free channel of risk reduction that technological strategies structurally cannot replicate.