How to Solve an Allocation Problem?

Game theory proposes several allocation solutions: we know (a) fairness properties, (b) how to develop (c) methods building on these properties, and (d) how to calculate (e) allocations. We also know how to influence the perceived fairness and realization of allocation solutions. However, we cannot explain properly that theoretically fair allocation methods are rarely used. To obtain more insight into these issues we solved an allocation problem in a purchasing cooperative case study by confronting theory with perceptions. We find large theoretical and perception differences and inconsistencies between and within the five steps from a to e. We note that theoretically fair methods tend to be more complex than theoretically unfair methods. In addition, the allocations of some simple methods are perceived fairer than the allocations of complex methods in our case study. To improve theoretical solutions the focus should be on a and c. To influence perceptions the focus should be on b, c, and d. Finally, all five steps are modeled into comparable fairness measures and a general model. Using this model implies that both theory and perceptions are considered in solving allocation problems.