Nash Equilibrium In Game Theory

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ash equilibrium named after the person (John Forbes Nash) who proposed it. Nash Equilibrium gives a stable condition of strategies in game theory. If each player is playing with its strategy and the combination in which no player can get additional benefit by changing its strategy while other players’ strategies remain same. The combination of these strategies and corresponding payoffs are Nash equilibrium.
The Nash equilibrium in the payoff conditions of table 2 is determined and different combinations in this regard are shown in table 3.

In table 3 it is visible that the best strategy for SC1 is D, best strategy for SC2 is also D and best strategy for MC is also D. The outcome is similar as in case of Prisoner’s Dilemma. The best strategy for each player is Don’t cooperate, irrespective to the strategies of other players. So if all the players go for “D” then no one will get any payoff as shown in table3. On the other side the best option for all players is when all of them cooperate. If everyone goes to play safe then all of them will play “D”. If there is situation that every one is sure
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. . . PN } then the value of characteristic function of coalition of all player (υ (S)) will be υ (S) ≥
If υ (S) =
Then the game is called inessential game. In case of inessential game there is no advantage of formation of coalitions. In our case above the value of υ for coalition of all the players is 14 and sum of individual values of υ is 0.
Therefore it is essential game because: υ (S) >
Therefore in our case the game is essential and formation of coalition is beneficial than playing alone.

VII. CONCLUSIONS

It is general awareness that co-operation certainly proves beneficial. There is an old saying that “one and one make eleven”. In this paper cooperation among parties of construction supply chain, means to explore the practices by which productive relations can be developed among these

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