Sunday, October 24, 2010

Nash equilibrium Part I

The Nash equilibrium?

The "Nash equilibrium" is a game theory idea that is used to evaluate or forecast the responses of two or more independent, intelligent, and uncoordinated decision makers compelled to participate in solving a common problem or address a common issue.

It is also assumed that in some way the parties are adversaries, and, as a matter of strategy,  knowledgeable of the other's likely reactions and preferences.

Does your project face uncoordinated adversaries?  I use the word adversary in the sense that each party has interests they feel duty bound to protect; each perceives something to lose if they agree whole heartedly with the other's position.   

I use uncoordinated in the sense that each party has a vested interest in being--and maintaining themselves as--an independent decision maker.  As such, they address the issue or problem without coordinating their actions in advance with the other party; in fact, they may have no knowledge of when the other party will act. However, there the game and in informal  'order' or sequence to the decision making among parties, although who goes first is often part of the 'game' strategy,  given knowledge of the other party's preferences or known reactions. 

And, here's another point: each party has little incentive to 'move off' their position once adopted.

Contract negotiations between the project and a contractor, or the project and a customer, come immediately to mind.  In theory and practice negotiations are adversarial.  And, there is always a strategy of who goes first; and the other's preferences are usually understood in advance. 

But all manner of value clashes also come to mind.  Stakeholders resist other stakeholders;  and stakeholders fuss with the project manager.  Here's another example: If you've ever tried to implement wide sweeping change, like installing a system that changes and disrupts myriad processes all at once, you will understand the motiviation for this posting.

So, what is game theory and how does it apply to project management? Game theory posits certain situations are worked somewhat like making moves on a game board. The board is open and evident to all; the rules are known. There are competing interests. However, in most board games, there is a clear winner and a clear loser. In the project domain, the interesting games are the non-zero-sum games where everyone gets something and no one loses everything. Non-zero-sum is particularly the objective in negotiation: everyone needs to walk away with something.

To survive in such a 'game, it's a little like 'reading the defense' when faced with a challenge, threat, or opportunity.

The Nash equilibrium, named for its inventer, Nobel laureate John Nash, presumes that in cases of non-zero-sum--that is, neither party needs to lose and both parties may claim a win--then:
....each player does what he would if he knew what the other player was going to do. It is an equilibrium in the sense that the two resulting strategies are consistent with one another; once the game is played, neither player has any desire to change his decision. Not all games have a unique Nash equilibrium"
according to a 1982 paper by economist Alan Blinder
Blinder went on to develop something that has come to be called "Alan Blinder's matrix" that he himself called a 'payoff matrix'.  It's described on page 23 of the paper under the link given above.

We'll discuss Blinder's matrix as it applies to project management in the next part in this series

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