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The non-cooperative game in ESCM

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In the non-cooperative game, there is no formal contract between the players to cooperate. Also, the players are rational to select the best strategies selfishly. Therefore, the players are aware of the other players’ selfishness and rationality. So, the players choose the best strategy to maximize their expected payoff based on their perception of the other players’ strategies. The best response of players is developed based on the best responses of other players. So, the system of linear equations is developed for determining the best response of each player and the Nash equilibrium point in the game, as shown in Eq. (4).

After equations differentiation based on the variables of QoS value ($qi$) in the system of linear equations, the new system of linear equations is determined and shown in Eq. (5).

Therefore, the best response of players ($qi∗$) is determined after solving the new system of linear equations, as shown in Eq. (6).

The Nash equilibrium point is determined based on Eq. (6) in the Non-cooperative game, as shown in Eq. (7).

By supposing $k=6$ and $c=19$, the Nash equilibrium point is $(0.4,0.4,0.4)$ based on the first answer. Also, the second answer is impossible according to the $qi$ acceptable range in Eq. (3). Therefore, the expected payoff of players is 0.7, as shown in Eq. (8).

The players don’t assure the other players’ cooperation in the Non-cooperative game. Therefore, the players select the lower level of the QoS as the strategy in the Nash equilibrium point. So, the players obtain low payoff value in the non-cooperative game.

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