From Finite to Infinite: The Mathematical Case for Non-Competitive Prosperity Beyond Musical Chairs: Why Playing to Continue Beats Playing to Win

Modern economies operate as vast games of musical chairs: participantscompete for finite positions, winners claim rewards, losers are eliminated. Thispaper argues that this finite-game structure is mathematically incapable ofproducing universal prosperity and proposes a transition to infinite-gameeconomics. Drawing on James Carse's distinction between finite games (playedto win) and infinite games (played to continue), we demonstrate that finite-gamecompetition necessarily produces losers regardless of economic growth. Theselection paradigm--meritocracy, technocracy, competitive education--embedsfinite-game logic into social infrastructure, systematically excluding participantsrather than cultivating them. We formalize the conditions under which infinitegames outperform finite games: when value creation is relational rather thanextractive, when circulation matters more than accumulation, and when diversityenables emergence. The paper connects to previous work on economiccirculation (Ishibashi, 2026g) and cognitive diversity (Ishibashi, 2026f), showingthat the pathologies identified there--extraction without circulation,homogenization without emergence--are symptoms of finite-game thinking. Thealternative is not eliminating competition but reframing it: from playing to win toplaying to continue, from selection to cultivation, from zero-sum to generative.Keywords: finite games, infinite games, competition, meritocracy, selection, cultivation,prosperity, circulation, emergence