What is the price of stability of game

Reference no: EM133199124

Question: Five commuters A, B, C, D, E, must choose between their own car with a fixed travel cost, or the public bus, where the charge to each user decreases with the number of users. Let ce denote the cost/travel time of using his own car for commuter i E {A, B, C, D, E} and let cA = 1, cH = 3, co = 5, en = 7, ck = 9. Regarding the bus, if 1 person uses it his cost will be 10, if 2 people use it then each of them will have cost 8, if 3 people use it then each of them will have cost 6, if 4 people use it then each of them will have cost 4, while if all 5 people use it then each of them will have cost 2. Naturally, each player wants to minimize his own cost.

a. Is there any dominated strategy (ies) in this game? If yes, perform an iterated elimination of all dominated strategies. Explicitly mention the sequence iu which the corresponding strategics are eliminated and present the resulting game.

b. Find (and clearly present) all pure Nash equilibria (NE) of the game.

c. What is the Price of Stability of this game (assuming that the objective function is the total travel time)?

Reference no: EM133199124

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