Wage Differences, Bonus and Team Performances: A parametric non-linear integer programming model

We formulate a non-linear integer programming model and use plausible parameters to examine: (i) the effects of wage differences between Super- and Normal- players in the performance of four teams which participate in the UEFA CL group matches; (ii) whether the expected qualification bonus received by UEFA and paid to the players of the non-qualified teams, enhances effort and the teams manage to qualify. When performance is measured by points’ maximization, higher wage equality seems to improve the performance of three teams, irrespectively if the elasticity of substitution between Super- and Normal- players is high or low, while the most efficient team of the tournament is not affected by the wage structure. The U-formed performance for that team is not excluded. When performance is measured by profits’ maximization, the performance depends on both the “production” technology and on wage differences. When all teams operate under increasing returns and all pay the same, but varying relative wages, or when they operate under decreasing returns and pay the marginal value product of their players, the most “balanced” team performs better. The most “unbalanced” team performs best under increasing returns to scale and egalitarian wages. In the last case, the non-qualified teams did not manage to improve their performance and qualify, even if their players should receive the expected qualification bonus that UEFA pays.