Allocations in sponsored game

• Main Authors: Nocum, Karen P., Nocon, Ederlina G.
• Format: text
• Language: English
• Published: Animo Repository 2011
• Subjects: Cooperative games (Mathematics); Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/6930
• Institution: De La Salle University

One of the main problems in cooperative game theory is the fair division of the rewards that are jointly obtained by the cooperating members of a team. In the case of a particular game, known as sponsored game which consists of two sets of players; the sponsors S = {si|1 ≤ i ≤ k} and the team players T={tj|1≤j≤p},eachsponsorsi ∈Striestobring cooperation on the set of team players. Cooperation is attained by giving a corresponding reward system vi ∈ Svi to the formed coalition M ⊆ T such that vi : 2T → R≥0 with vi(∅) = 0 . Every team player tj ∈ T now decides to join or not to join in a coalition M ⊆ T . A formed coalition M will then receive a group reward of V (M) = X vi(M). Since the members of i=1 S and T act simultaneously, their decisions affect the benefits received by the team players, as well as the payoff of the sponsors. In this paper, we discuss some allocation schemes for the team players. Specifically, we consider schemes that are designed based on the concept of proportional allocation, min-max allocation, reasonable allocation set, the core and dominance core.