Laura, Sheena, and Grace, three students at DMU, are the owners of the start-up firm LSG in Leicester. They will join forces with two other start-ups, B1 and S2, to expand their portfolio of products and increase their market share.

(Coalitional games). Laura, Sheena, and Grace, three students at DMU, are the owners of the start-up firm LSG in Leicester. They will join forces with two other start-ups, B1 and S2, to expand their portfolio of products and increase their market share. LSG generates a total of £420 in profits on its own, while B1 produces £260 in profits alone and S2 reports £140 in profits. All measures are in thousands. The three firms have collaborated before, generating joint profits of £680 for LSG and B1, for LSG and S2 of £600, and for B1 and S2 were able to make £420 together. After the merger happens, it is estimated that the three firms together will generate a total profit of £1400.

Table 1 summarises the profits

 (v(S)) for each joint venture S.

1. To meet the rationality condition for each firm, how should the £1400 joint profit be split? (5 marks)

2. If the £1400 joint profits are split among the three firms according to the Shapley value, how much should each of the firms get? (15 marks)

3. Are coalitions that split payoffs according to the Shapley value always part of the Core? (5 marks)