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Friday, January 6, 2012

Game Theory – From the perspective of a project team

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1 Introduction





In a project, people having various roles and responsibilities of executing the project at different level, have the control and impact on the project at varying stages. Each of them (Project Members) can affect the project in many ways.


The successful navigation of the project depends a lot on each of them. The contribution of each of them in a holistic view gives a greater picture than when seen it as an individual contributions from each of them. In this paper, we have presented a project, comprising of a Customer, a Project Manager, a Quality Coordinator and a Team Member. Smooth sailing of a project requires co-operative contributions and interactive activities and interactive initiatives taking place at each players level and hence the strategies followed by each of the project member makes it that more critical for a project’s successful completion and implementation.


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The set of activities and strategies pursued by each player in the project can be identified and related to courses of actions involved in a game and hence a project composition can be identified as a bunch of players and the interactive situation in the project can be considered as a game. Our effort in this paper is a small step to discuss about the application of Game Theory to a project scenario, to determine the strategy followed by each of the players, such that each one of them gains highest returns and also everyone’s interest is preserved implicitly leading to successful completion of the project.


Assumptions


ü A successful completion of a project is mainly a function of three parameters namely cost incurred, time taken to complete the project and bugs involved.


ü Payoff for each player largely depends on the preferences to the above-mentioned parameters.


ü In a scale of 10, depending on the preferences of the player, following figures can be assigned to parameters of the project outcome for each of the players.


Cost Time Bugs


Customer 5 4 1


Project manager 4 4


Quality coordinator 4


Team member 1 4 5


Detailed sections


Definitions


Game Theory Game theory can be defined as a formal study of decision-making where several players must make choices that potentially affect the interests of the other players. In the current scenario each of the player’s i.e. the customer, project manager, quality coordinator and team member has his/her own objectives towards their work. The decisions they make to achieve their objective affects the interests of the other players. Since decision making of each player is a simultaneous action, the game is a normal form game.


Payoff A payoff is a number, also called utility that reflects the desirability of an outcome to a player, for whatever reason. A project outcome can give different payoffs to different players depending on his preferences.


Nash Equilibrium A Nash equilibrium, also called strategic equilibrium, is a list of strategies, one for each player, which has a property that no player can unilaterally change his strategy and get a better payoff.





Solution


An ideal Project scenario can be considered as a game with following players


Ø Customer


Ø Project manager


Ø Quality coordinator


Ø Team members





The objective of each of the players differs from one another. The strategies of each player to achieve their objective can be put as follows. A player can implement only one of his strategies in a project.


Player Objective Strategy


Customer Maximum earning from minimum investment 1. Reduce investment/ expenditure. (C1). Reduce through put time. (C)


Project Manager Minimize risk 1. Ensure that all the requirements are captured. (P1) . Ensure that all the relevant risks are identified and contingency plan is put in place required in the crunch time. (P)


Quality Coordinator Maximize conformance to quality 1. To ensure that all the deliverable to the client conforms to the standards and has all the features and components that makes it a superior quality deliverable. (Q1)


Team Maximize learning on the amount of effort put 1. Do it right at the first time. (T1). Do it the first time. (T)





The conceivable outcome of the project can be any of the following.


Outcome Project Status Cost Time Bugs


O1 Project Completed Within Cost Within Time With Bugs


O Project Completed Within Cost Not within Time Without Bugs


O Project Completed Within Cost Within Time Without Bugs


O4 Project Completed Within Cost Not within Time With Bugs


O5 Project Completed Not within Cost Within Time With Bugs


O6 Project Completed Not within Cost Not within Time Without Bugs


O7 Project Completed Not within Cost Within Time Without Bugs


O8 Project Completed Not within Cost Not within Time With Bugs


O Project Scrapped


Each of the project outcomes has following payoffs for each player depending on their preferences for the parameters (namely cost incurred, time taken and bugs) involved in the project outcome.


Customer Project Manager Quality Coordinator Team member


O1 8 6 5


O 6 6 7 6


O 10 10 10 10


O4 5 4 1


O5 5 4 4


O6 1 4 5


O7 5 4 7


O8 0 0 0 0


O 0 0 0 0


Various combinations of the strategies adopted by each player can be tabulated as follows. Having 8 combinations from variables i.e. =8.


C1 C1 C1 C1 C C C C


P1 P1 P P P1 P1 P P


Q1 Q1 Q1 Q1 Q1 Q1 Q1 Q1


T1 T T1 T T1 T T1 T


O O4 O1 O1 O7 O5 O5 O5


4 Results


Let us consider the strategy combination C1-P1-Q1-T1. The outcome of the project is O and the payoffs are 6 for customer, 6 for project manager, 7 for quality coordinator and 6 for team member. When the Team member changes his strategy to T then it leads to the strategy combination C1-P1-Q1-T that has project outcome of O4. If we observe, the payoff of Team member has increased from 6 to , which means he has gained by unilaterally changing his strategy. So, it cannot be Nash equilibrium.


Similarly analyzing other combinations (except the one explained below) and determining the outcome of each combination does not result in Nash equilibrium.


Let us consider the strategy combination C1-P-Q1-T1 giving the output O1. The payoffs are for Customer, 8 for Project manager, 6 for quality Coordinator and 5 for Team member. When the customer changes his strategy from C1 to C while others keep their strategies constant, the new strategy combination formed is C-P-Q1-T1 giving the output O5. Payoff for the customer has gone down to 5.


When the project manager changes his strategy from P to P1 while others keep their strategies constant, the new strategy combination formed is C1-P1-Q1-T1 giving the output O. Pay off for the project manager goes down to 6.


When the Team member changes his strategy from T1 to T while others keep their strategies constant, the new strategy combination formed is C1-P-Q1-T giving the output O1. Pay off for the Team member remains same.


Since no one is going to benefit by unilaterally changing his/her strategy, the strategy combination C1-P-Q1-T1 represents Nash equilibrium.


Since the outcome of the equilibrium state is O1, which is when the cost incurred is least, project is executed within time and with bugs.


5 Conclusion


The Nash equilibrium for all the players is reached when


1. Customer has spent the least


. Project is completed within time


. Team member has done the things right at the first time


6 Acknowledgements


We would like to acknowledge the following individuals who contributed information and their professional expertise towards the completion of this paper.


Dibyendu Chakraverty, Systems Manager.


Siddhartha Sarkar, Senior Systems Engineer.


Arjun Thayyil, Systems Engineer.





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