Dynamic Reference Points, Strategic Gambles, and Cognitive Fatigue in High-Frequency Contests: Field Evidence from Online Chess

Neoclassical models of labor supply and contest theory assume that forward-looking agents balance marginal effort costs against expected marginal payoffs. In competitive settings, decisions depend on backward-looking reference targets, emotional reactions to recent losses, and cognitive stamina. We analyze 3,000,000 competitive games, 5,999,360 post-game rating observations, and 1,561,866 playing sessions from the Lichess platform to track how goals, standings, and fatigue alter player decisions. We document five empirical findings. First, players bunch above round-number rating milestones (1200 to 2100). A regression discontinuity design across 3,356,232 observations reveals that crossing a milestone increases the odds of session termination by 18.5% (coef = +0.1700, z = 33.91, p < 0.0001). Placebo tests at 50-point midpoints show no discontinuity. Second, session termination is asymmetric: multi-game sessions end on a loss 53.48% of the time, compared to 42.71% on a win (p < 10^-300). Suffering an unexpected defeat against an opponent rated at least 100 points lower prolongs the session by 0.83 games (t = 24.35, p < 0.0001). Evaluating session lengths across 30-minute, 45-minute, and 60-minute pause thresholds confirms this pattern is stable. Third, sequential game analysis across 4,437,482 transitions reveals a persistent tilt penalty: losing game t reduces the win rate in game t+1 from 51.59% to 48.88% (coef = -0.0268, t = -57.36, p < 0.0001). This decline occurs despite the matchmaking algorithm pairing losing players against lower-rated opponents. Fourth, decomposing stopping behavior across all 24 hours of the day shows that the 53% terminal loss rate remains consistent globally, ruling out local bedtime artifacts. Fifth, in arena tournaments with convex streak multipliers, holding an active two-game winning streak suppresses the odds of sacrificing clock capacity (the Berserk decision) by 31.3% (coef = -0.3758, z = -28.91, p < 0.0001), showing strong loss aversion over accumulated multiplier capital. Finally, using Stockfish 19 evaluations across objective blunders, post-blunder deliberation latency contracts as sessions lengthen, while 33.16% of defeats end in clock-bleed time forfeitures rather than resignation. JEL Classification: D91, C93, D81, J22.