Long-term fairness with bounded worst-case losses

How does one repeatedly choose actions so as to be fairest to the multiple beneficiaries of those actions? We examine approaches to discovering sequences of actions for which the worst-off beneficiaries are treated maximally well, then secondarily the second-worst-off, and so on. We formulate the problem for the situation where the sequence of action choices continues forever; this problem may be reduced to a set of linear programs. We then extend the problem to situations where the game ends at some unknown finite time in the future. We demonstrate that an optimal solution is intractable, and present two good approximation algorithms.