Nash Equilibrium

Nash equilibrium is a state in which each subject independently tries to maximize his/her own profit (without cooperating with others). In other words, the equilibrium state in which the subjects do not (cannot) discuss a state where there’s “maximum profit total for everyone” even though they could reach this state through discussion.

 

1. Overview

Nash equilibrium is a result of each subject’s thinking about maximizing their own profits (just in the same way others think).
Therefore, subjects lack motivation to change the state. (The equilibrium is being maintained.)

When looking down from a perspective of overall optimization, however, the equilibrium state is not always a result of maximizing the total profits.

In the example of the “Prisoner’s dilemma”, two prisoners are separated and forced to choose either to “keep silent” or “betray” his accomplice. However, there is a condition that “If one keeps silent and the other betrays, the one who betrays will not be imprisoned”. Even though the optimal solution would be for “both of them to keep silent”, they fall into the equilibrium state (Nash equilibrium) where “Both of them betray” in the end.

Nash equilibrium is named after an American mathematician John Forbes Nash Jr., who originally presented it.(devised in 1950, received the Nobel Prize in Economics in 1994.)

 


2. Nash Equilibrium in Each Department of Organization

When each department within the organization tries to optimize Business Process independently, the optimization is performed only from the perspective of each department. However, there is a possibility that these Business Process do not be optimized from the viewpoint of entire organization.

  • Operation of Material Code: From the viewpoint of sales department, material codes are not written into slips since it requires additional cost to maintain material codes. (As a result, order contents are reconfirmed in manufacturing process. In bill issue process as well.)
  • Notice of quality defects: In manufacturing department, the occurrence of defectives in subtle level is not reported since it raises manufacturing cost or needs to take much labor on procedures. (As a result, some final products evolve into customer complaint and cause losses as company.)

By discussing with a cross-organizational perspective, we must get out from non-cooperative game. If “Two parties cooperation”(Nash bargaining solution) or “N person coalition” can be obtained, the optimization from the viewpoint of entire company will be promoted.

 


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