In Cooperative game Theory, a 3 player model is presented: Please identify if the game can be modeled as written, if yes, model and discuss the shapley value and at least one core model. If no, please list what information would be needed to model the problem.

A game that focused on the idea of 3 railroads (players) with a seasonal rush coming. Railroads have fixed assets (tracks) and mobile assets (locomotives and cars). Corporate South (CS) has a large quantity of tracks covering the southernmost part of the country and access to the Mexican market. Corporate Northern has access to a larger quantity of locomotives and cars as well as the Canadian market. Corporate Pacific has access to the largest part of the market, reaching the most people and access to the ocean imports. Due to the combination of the assets and access to the market a value can be assigned to each individual railroad. The value of CP is 3 million dollars, CS is 2.5 million dollars, and CN is 1.5 million dollars." The feedback received on this concept was that it would make a good final report problem, taking into account the single players, player coalitions, and the grand coalition.

The Single Players:

Corporate Pacific (CP) = 3 V(1) = 3

Corporate Northern(CN) = 1.5 V(2) = 1.5

Corporate South(CS) = 2.5 V(3) = 2.5 Player Coalitions: V(12) = 4.5

V(13) = 5.5

V(23) = 4.0 Grand Coalition:

V(123) = 7

S₁ = CN = P1 N c(S₁) = c({1}) = C1

S₂ = CP = P2 N c(S₂) = c({2}) = C2

S₃ = CS = P3 N c(S₃) = c({3}) = C3

S₄ = CN + CP ={P1, P2} N c(S₄) = c({1,2}) = C12

S₅ = CN + CS ={P1, P3} N c(S₅) = c({1,3}) = C13

S₆ = CP + CS ={P2, P3} N c(S₆) = c({2,3}) = C23

S₇ = CN + CP + CS = {P1, P2, P3} N c(S₇) = c({1,2,3}) = C123

S₈ = c(S8) = 0