Which Inequality? The Inequality of Resources Versus the Inequality of Rewards

We consider a tournament arising out of a matching market. On one side of the market, aspirants who are differentiated in ability choose a level of output. Under assortative matching, higher output leads to a better match. Thus, rather than a “winner-take-all” tournament, there are multiple ranked rewards. That is, the participant with the highest output gets highest reward (the best match), the second placed competitor gets second-highest reward and so on. In this model, equilibrium strategies and payoffs depend on the distributions of types of the competitors and the distribution of rewards. An increase in the inequality of competitors’ resources tends to reduce output and can make all competitors better off. However, an increase in the dispersion of the rewards increases output and can make all worse off. We use these results to investigate the effect of inequality on individual welfare.