Predicting the distribution of contest success under the illusion of proportionality

Understanding disparities in contest success is central to explaining how competition shapes the distribution of rewards, influence, or market shares. We introduce the Proportional Play Equilibrium (PPE), a boundedly rational alternative to Nash Equilibrium (NE) grounded in the Illusion of Proportionality, and show that it results in more unequal outcomes by exaggerating the success chances of stronger contestants. Laboratory evidence strongly supports PPE's predictions for success dispersion while rejecting those of NE. Our results highlight how equilibrium analysis under full rationality may mischaracterize the inequality-generating effects of competition, with further implications for understanding inequality in markets or political contests.