Wednesday, July 14, 2010

Nash Equilibrium to Team Management By Frazer Pereira

Nash equilibrium, named after John Nash, is a set of strategies, one for each player; such that no player has an incentive to unilaterally change their action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if they remained with their current strategy. For games in which players randomize (mixed strategies), the expected or average payoff must be at least as large as that obtainable by any other strategy.

In the world of management, teamwork is one of the most crucial and fundamental aspect for the appropriate functioning of an organization to accomplish desired aspirations within the constraints prearranged. These constraints include time, manpower, technology, inventory and other attributes which affect the working of the desired objective. Thus the popular saying in team management is “The best result comes when everyone in the group works for the best of the group“.  Another theory exists for an operational environment is given by Adam Smith. Adam Smith is known for his explanation of how rational self-interest and competition, operating in a social framework depending on adherence to moral obligations, can lead to economic prosperity and well-being. Modifying the popular explanation in accordance to Adam Smith, “The best result comes when everyone in the group works for their own benefit”.

Now both these concepts evidently have flaws. Working for your own self in accordance to Adam Smith creates what is termed as ‘parasites’ in the team who profit from the effort of others. On the other hand advancement at a personal level is inhibited by the principle of working for the group. This prevents the members from giving their paramount contribution due to an assortment of aspects, the chief reason being human personality and emotions.

To diminish these flaws we’ll apply Nash Equilibrium to the two concepts. In simple words the new adapted principle for the most effective team would be “The best result comes when everyone in the group works for their own benefit as well as for the benefit of the group” (As quoted in the movie “A Beautiful Mind”). This theory if used would effectively reduce the flaws in the existing system and construct an environment in the team where personal growth and team objectives can be coexisting. We will now see how to apply this principle to a Human Environment of a Team.

Based on this new principle we will define new-fangled objectives and subtasks for the team. These objectives comprise of strategies of individual contributors’ i.e. team members. These strategies can be classified as goals or needs of the members. Things like promotion, experience, recognition, working hour’s flexibility, etc. Experience can be classified as experience in a particular field, subject, software etc. We also need to divide the objective into various subtasks (A, B, C and so on), each subtask having a common background. These tasks for a general objective can be research, planning, inventory management, resource management, advertising, debugging etc. Combining these two simple policies we can define the parameters essential for the achievement of Nash Equilibrium into a Team Environment. Combining these two strategies based on the similarities and differences between the Personal Objectives and Subtasks, we will assign responsibilities suitable to each individual. For example, individuals seeking experience in management should be assigned management related duties. Those seeking promotion should be assigned objectives which will reflect their credentials for the promotion or payroll increase.  Family people seeking flexible hours would be assigned those hours at the cost of increased responsibility or lack of choice in the task assigned. Thus the individual will be motivated to accomplish the task at maximum efficiency as it will benefit the individual to the maximum. Diverting away from the strategy assigned will cause a stoppage in the personal goal and characteristic human nature will prevent this from stirring. Now since the tasks when combined are the final goal, maximum efficiency in the task would lead to maximum efficiency in the final output. People striving for their own personal gain while providing assistance for the ambition of others would further maximize the final output efficiency, as it would feel good to doing good for others as well as achieving personal goal due to Human Nature.

In the above proposed theory we have Task A assigned to Personnel (1). Circumstances may arise where the goals of individuals would be similar which would prevent the division of task in the above manner.  For this, Task A needs to be further divided so it would be effectively distributed amongst the individuals having similar objectives. This complicates the planning stages but if used effectively would increase the efficiency of the particular task and thereby increasing the efficiency of the overall objective.

The proposed theory involves increase in planning and control over the team and would need a first-rate manager to accomplish it effectively. But if applied the output gain would be much higher than by the normal procedure. What’s left is to implement this principle in a research environment and find the effectiveness compared to current methods.

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