A Meta-heuristic Approach for Strategic Fair Division Problems

Fair division of resources emerges in a variety of different contexts in real-world problems, some of which can be seen through the lens of game theory. Many equilibrium notions for simple fair division problems with indivisible items have been considered, and many of these notions are hard to compute. Strategic fair division is a branch of fair division in which participants may act uncooperatively to maximize their utility. In the presence of participants who have strategic behavior, it is essential to have a suitable algorithm in place to allocate resources in a fair and equitable manner. We propose a new approach to solve strategic fair division problems where fairness is attained by finding a constrained Nash equilibrium in a specific game. We show that computational complexity barriers also hold. More broadly, the theoretical results of this paper could potentially be applied to related general game theory problems and complex fair division problems. Finally, we propose an algorithm for finding a constrained Nash equilibrium in the game that we introduce. Our focus will be on one particular meta-heuristic – the bus transportation algorithm – as an approach to improve the running time of the search.