Nash Equilibrium

Nash equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his or her chosen strategy after considering an opponent's choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. Nash equilibrium is named after an American mathematician John Forbes Nash Jr., who originally presented it.

Nash equilibrium is a situation in which one subject independently tries to maximize his/her own profit without collaborating with others. Under Nash equilibrium, even if only one subject changes its own act, the subject's profit will not increase from the current situation because each subject or organization has chosen an act that maximizes their own profits while taking others' acts into consideration. Therefore, no subject or organization has an incentive to change its own acts. Even though Nash equilibrium is caused as a result of each subject's act chosen to maximize its own profit, sometimes no one's profit is actually maximized. In addition, there could be more than one combination of subjects' acts that result in Nash equilibrium.

When we aim to improve business process, sometime we can reach the optimal state, but sometimes we settle in a non-optimal state. In other words, as a result of separate attempts for local optimization by each participant and department executing business process, the entire process is not necessarily fully optimized while each part of business process is optimized.

Let us think about a case in which BPM is separately executed by each department. If business process is managed in cross-departmental manner, even though each department concerning business process can optimize flows that the department is in charge, none of them can know whether the entire business process is optimized or not. We can easily imagine a case in which cooperation among departments is not done, and as a result, the entire business process remains in unfavourable state. This is exactly "Prisoner's dilemma," which is Nash equilibrium. Because business process in each department is optimized, no one is motivated to do global optimization.

In order to avoid falling into non-optimal Nash equilibrium when executing BPM, all departments need to cooperate to manage business process as a whole by means of cross-departmental collaboration for the sake of global optimization. In other words, unless BPM is not worked on across the company, it is not guaranteed that BPM surely takes effect. Without cross-departmental cooperation, we could easily remain in a non-optimal state and would not have any motivation to improve the situation.

An optimal state that is not Nash equilibrium is not a stable state, so we must monitor and manage the state continuously so that it will not fall into Nash equilibrium.