A. Atay, C. Trudeau
Cooperative game theory studies how to allocate the joint value generated by a set of players. With externalities, coalition values can be defined through various approaches, notably by trying to determine the best and worst-case scenarios. Optimistic and pessimistic perspectives offer insights into strategic interactions, often corresponding to the coalition either choosing first or choosing after the complement coalition. In a general framework, we explore this relationship and show that it always holds in the presence of negative externalities, but only partly with positive externalities. If choosing first/last corresponds to these extreme values, we also obtain a useful inclusion result: allocations that do not allocate more than the optimistic upper bounds also do not allocate less than the pessimistic lower bounds. Finally, we explore applications to illustrate how our findings yield new results and offer a means to derive results from the existing literature.
Keywords: Cooperative games, optimization problems, cost sharing, core, anti-core, externalities
Scheduled
Jovenes Investigadores en teoría de juegos
June 12, 2025 11:30 AM
Mr 2