How To Find Nash Equilibrium Payoff Matrix

Payoff Matrix for Nash Equilibrium

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Nash equilibrium refers to the level of outcome where alter of strategic would not provide extra benefits to a actor if other players do not alter their strategies.

Nash equilibrium can occur multiple times in a game. It is invented past John Nash and can exist practical in many fields, such equally ecology and economics.

Let us understand the concept of Nash equilibrium with the help of an case. Suppose two organizations, P and Q desire to increase their profits past increasing their advertising expenditure. In such a case, each of the organization can adopt 2 types of strategies. One is to increase the advertising-expenditure and the other is to keep ad-expenditure constant or no change in the ad-expenditure.

The payoff matrix of 2 organizations is shown in Tabular array-eight:

Payoff Matrix for Nash Equilibrium

In Table-8, neither of the organization has a ascendant strategy; therefore, their strategies depend on each other's strategies. For case, if organization P increases the ad-expenditure, then system Q as well needs to increase its ad-expenditure. In case, organisation Q does not increase its ad-expenditure, then the outcome of P increases.

Therefore, in the present case, it tin be concluded that both the organizations, P and Q should follow the same strategy increase in ad-expenditure) to become the maximum benefit. This is because if none of them increases their advertisement-expenditure, then organization P has the sales increase of Rs. 25 million, while the sales of arrangement Q would exist Rs. v million just.

Nonetheless, if arrangement Q increases its advertizing-expenditure, its sales increase to Rs. 10 million. Therefore, information technology is good for organization Q to increase its ad-expenditure. Now, organizations P also need to follow system Q. This is the case similar to an oligopolistic market condition. In an oligopolistic market place, if 1 system reduces its product prices, and so other rival organizations too need to reduce their prices, so that they can retain customers.

Prisoners' Dilemma :

Prisoner's dilemma refers to the game in which even by adopting all-time strategies, players are not able to get the best outcome. In dilemma, every player wants to minimize his/her hazard on the cost of increasing the run a risk for the other role player(s). In the reducing the run a risk for oneself, the players become into a worst situation, which may be avoided if they cooperate with each us understand the prisoner'south dilemma with the help of an instance.

Suppose in that location are two individuals, named John and are involved in drug smuggling. They are arrested by police as per the information provided by ane of the informers of Now, the police are interrogating both of them separately.

They were told three outcomes of their responses, which are equally follows:

i. If both of them remain silent, then they would be set gratuitous because there is no prove of their involvement in drug smuggling.

2. If they confess about their evil activities, they would be imprisoned for five years.

iii. If one of them confesses and the other remains silent, then the confessor would be imprisoned for two years, while the other would be imprisoned for 10 years.

Now, the problem with John and Mac is that they are not aware whether their partner would remain silent or confess. Therefore, it is a situation of defoliation.

The payoff matrix in the present case is shown in Table-9:

As shown in Table-9, the 2 individuals take two options either to confess or remain silent. The decision of confessing by both the individuals depends on the period of imprisonment. The best pick for both of them is to remain silent. Yet, due to uncertainty about each other's decision, they are non able to remain silent. Therefore, information technology is a situation of dilemma for John and Mac.

In the present case, it tin can be anticipated that both of them would confess to reduce their time catamenia of imprisonment. Therefore, the best pick in this situation would be to confess and become imprisoned for five years. This is because if in case one partner confesses and the other denies, then the 1 who denies would be imprisoned for 10 years.