While artificial intelligence (AI) and machine learning (ML) have been increasingly used for decision-making, issues related to discrimination in AI/ML have become prominent. While several fair algorithms are proposed to alleviate these discrimination issues, most of them provide fairness by imposing constraints to eliminate disparity in prediction results. However, the use of these fair algorithms may change the behavior of prediction subjects. As such, even though the disparity in prediction results might be removed by fair algorithms, behavioral responses to the use of fair algorithms can still create disparity in behavior which may persist across different groups of prediction subjects. To study this issue, we define a notion called "strategic best-response fairness" (SBR-fair). It is defined in a context that includes different groups of prediction subjects who are ex-ante identical in terms of abilities and conditional payoffs. We utilize a game-theoretic model to investigate whether different types of fair algorithms lead to identical equilibrium behaviors among different groups of prediction subjects. If yes, such an algorithm is considered SBR-fair. We then demonstrate that many existing fair algorithms are not SBR-fair. As a result, implementing these algorithms may impose fairness on prediction results but actually induce disparity between privileged and unprivileged individuals in the long run.

The unfairness of a regressor is evaluated by measuring the correlation between the estimator and the sensitive attribute (e.g., race, gender, age), and the coefficient of determination (CoD) is a natural extension of the correlation coefficient when more than one sensitive attribute exists. As is well known, there is a trade-off between fairness and accuracy of a regressor, which implies a perfectly fair optimizer does not always yield a useful prediction. Taking this into consideration, we optimize the accuracy of the estimation subject to a user-defined level of fairness. However, a fairness level as a constraint induces a nonconvexity of the feasible region, which disables the use of an off-the-shelf convex optimizer. Despite such nonconvexity, we show an exact solution is available by using tools of global optimization theory. Furthermore, we propose a nonlinear extension of the method by kernel representation. Unlike most of existing fairness-aware machine learning methods, our method allows us to deal with numeric and multiple sensitive attributes.