Im trying to model the following problem using the core and the shapley value but I can't understand how to define the characteristic function.
Problem:
Let S be a team consisting of 3 players A,B,C and an enemy team F.Both teams contest in 18 games and each player takes part in 6 games.Finally S team won.Player A managed to win in 5 out of 6 games.Player B in 3 out of 6 games and player C in 2 out of 6 games.The price was 18 meals of food.The contest committee is in a dilemma.Should they award the team with as many meals as many wins they had in total.Meaning each player of the winning team will get as many meals as many wins he/she had on the games?Or they should give each player an equal amount of meals(meaning 6 for each)? The players after the games ended wanted to get the maximum meals they can get(meaning 6 meals).What the committee should do?
Can anybody shed some light on how to define the charactiristic function(meaning the payoff v(m) of each coalition m)?