Open-ended innovation in zero-sum games

2026-07-28

AI Summary

This study investigates the open-ended innovation dynamics in zero-sum games driven by both players continuously introducing novel strategies. Modeling innovation as the sampling of new strategies from a strategy distribution, the work integrates game-theoretic and probabilistic methods to analyze how one player’s technological advancement increases the marginal returns for the opponent’s further innovation. Theoretically, under general conditions, this adversarial interaction inevitably triggers an unending innovation arms race, resulting in a perpetual cycle of strategic evolution. The analysis thus reveals an endogenous mechanism that sustains open-ended innovation in competitive environments, demonstrating that strategic interdependence alone can perpetuate continuous adaptation without external stimuli.

Abstract

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, under generic conditions, this setting can lead to an everlasting innovation arm race, because the introduction of new technologies of one player increases the marginal utility for technological innovation of the opponent.

Problem

• zero-sum games
• open-ended innovation
• innovation arms race
• strategic interaction
• technological innovation

Innovation

• open-ended innovation
• zero-sum games
• strategy innovation
• technological arms race
• marginal utility