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Please model the 3 player game using Nash Equilibrium

3 railroads (players) with a seasonal rush coming. Railroads have fixed assets (tracks and facilities) 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 300 million dollars, CS is 250 million dollars, and CN is 150 million dollars.

If CP and CN decided to work together their overall payoff would be 500 million dollars, if CP and CS decided to work together their payoff would be 600 million dollars, if CN and CS decided to work together their pay off would be 400 million dollars, and if all 3 companies work together then their pay off would be 800 million dollars based on the value to their customer.

The Single Players:

Corporate Pacific (CP) = 3 V(1) = 300

Corporate Northern(CN) = 1.5 V(2) = 150

Corporate South(CS) = 2.5 V(3) = 250

Player Coalitions:

V(12) = 500

V(13) = 600

V(23) = 400

Grand Coalition:

V(123) = 800 million

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