pp 10-22 (Vol 12 2019)

E. Nocon 1,*, and
K. NocumΒ 2

1 Mathematics and Statistics Department, De La Salle University, Manila
2 Mathematics Department, Batangas State University, Batangas City

* Corresponding author: ederlina.nocon@dlsu.edu.ph

ABSTRACT

We focus on a game that involves two sets of players, 𝑆 and 𝑇 . The members of 𝑆 (referred to as sponsors) aim to induce cooperation among the members of 𝑇 (called team players). Each member of 𝑆 offers a reward system in the form of a characteristic function giving
the reward of each coalition (a subset of 𝑇 ). On the other hand, a member of 𝑇 may choose to join a coalition 𝑀. The aggregate actions of members of 𝑆 and 𝑇 affect the rewards not only of the members of 𝑇 but also of 𝑆 who expect payoffs as well.

We take a look at the formation of an equilibrium that is supposed to define an efficient outcome resulting from the strategies of the players from both 𝑆 and 𝑇 . We also tackle possible strategic moves of a sponsor and a team player that are motivated by their desire
to increase current payoffs. Lastly, we discuss some allocation concepts that allow team players to divide among themselves the reward that they receive from the sponsors. These concepts discussed in this paper present a new game that models a real-life situation
wherein collaborations are being motivated by outside forces. Moreover, the allocation concepts provide various practical ways of dividing rewards among the members of the coalitions.