The round-robin algorithm, known for its simplicity and efficiency in fair allocation, can be extended or adapted to accommodate more complex fairness criteria beyond EF1. One approach is to introduce additional constraints or objectives to the allocation process. For example, one could incorporate constraints on diversity, such as ensuring a diverse distribution of items among the agents based on certain characteristics or preferences. This could involve modifying the agent ordering or introducing additional rules for item selection to promote diversity in the allocation.
Another way to enhance the round-robin algorithm is to consider different notions of fairness, such as envy-freeness up to any number of items (EFx) or maximin share fairness. By adjusting the criteria for evaluating the fairness of allocations, the algorithm can be tailored to meet these specific requirements. This may involve redefining the utility functions of the agents or introducing new mechanisms for resolving envy or ensuring fairness.
Furthermore, the round-robin algorithm can be extended to handle more complex preferences or utility functions. Instead of relying on simple ordinal rankings, agents could express their preferences in a more detailed or nuanced manner, such as through cardinal utilities or partial rankings. This would require modifications to the algorithm to accommodate the increased complexity of the preference information provided by the agents.
Overall, by incorporating additional constraints, objectives, or fairness criteria, and by adapting the algorithm to handle more intricate preferences, the round-robin algorithm can be extended to address a wider range of fairness considerations in allocation problems.