Deming and The Prisoner's Dilemma

Revisiting Deming's Theory of Transformation Through Game Theory

We have been taught by economists that competition will solve our problems. Actually, competition, we see now, is destructive. It would be better if everyone would work together as a system, with the aim for everybody to win. What we need is cooperation and transformation to a new style of management.

Deming, Dr. W.E. The New Economics. 2nd ed (p. xv), 3rd ed (p. xix)

A system must be managed. It will not manage itself. Left to themselves in the Western world, components become selfish, competitive, independent profit centres, and thus destroy the system.

The secret is cooperation between components toward the aim of the organization. We cannot afford the destructive effect of competition.

Ibid. 2nd ed (p. 50), 3rd ed (p. 36)

… American management must still learn that in order to compete, they must learn to cooperate (William W. Scherkenbach, Deming’s Road to Continual Improvement, SPC Press, Knoxville, 1991). The Clayton Act had effectively prohibited this kind of cooperation.

Ibid. 2nd ed (p. 56), 3rd ed (p. 40)

Interdependence and interaction. An important job of management is to recognize and manage the interdependence between components. Resolution of conflicts, and removal of barriers to cooperation, are responsibilities of management.

Ibid. 2nd ed (p. 64), 3rd ed (p. 45)

THE AIM for this newsletter is to share some thoughts with you that occurred to me after viewing Dr. Derek Muller’s explainer video on The Prisoner’s Dilemma, particularly its implications with respect to Dr. Deming’s thoughts on how to catalyze a transformation toward his theory, supported and powered by cooperation. It’s another one of those neat convergences that you come across as you refine and develop your thinking through a Deming lens and see the world in a different perspective.

In this post, we’ll learn about Deming’s heuristic for creating a critical mass of minds to trigger a transformation and how it links with the work of Dr. Robert Axelrod in the 1980 to test one of the most famous games in game theory.

How Many People Does it Take to Start a Transformation?

Pop-quiz scenario: You’ve been invited to speak with the CEO of a mid-cap company about the benefits a Deming transformation can bring to their operations. Over the course of your conversation, you broadly explain Dr. Deming’s theory predicated on a systems-view and the superior productivity that comes from working together as a system rather than apart as individual profit centres.

The CEO mentions that they are really interested in getting the SLT on-board, along with their employees but simply can’t afford to stop operations entirely while everyone learns how to cooperate and begin PDSAs. They ask you: “How many people do we need to get started?”

Assume the company has 850 employees. What do you say? The SLT? 25? 40? 100?

This very question was asked of Dr. Deming by David Langford many years ago, who remarked that as few as the square root of an organization’s headcount would be enough to form a critical mass to cause a transformation. In other words, our CEO could begin with around 30 well-chosen people in an area we want to transform first.

But, what’s critical mass? Isn’t that supposed to be something large?

Being a physicist, Dr. Deming would often reach for metaphors grounded in physics to explain his ideas and theory. When he speaks about “critical mass”, he’s making a comparison to the minimum amount of fissile material to set off a nuclear reaction, or transformation. It’s not about how many people, but how few.

So, we could explain all of this to our CEO who might push back: “This sounds great in theory, but are you sure we could begin with so few people? How do we know this can happen? Do you have anything I can share with the SLT to build their confidence?”

You might at this point ask if they know about game theory and The Prisoner’s Dilemma…

Refresher: The Prisoner’s Dilemma

For the purposes of our scenario, we’re going to use a variation of the Prisoner’s Dilemma based on the one Dr. Muller presents in the video above, which you should set some time aside to watch as it’s really excellent. In a nutshell, this is one of the most famous examples of game theory that was developed by researchers at RAND Corp. in the 1950s to better understand the dynamics of conflict and cooperation, particularly in the context of the Cold War, however it also proved effective in many other scenarios such as politics and business.

You explain to the CEO that instead of a jailor and two prisoners wagering on jail sentences depending on who will betray whom, you’ll substitute a banker with a chest of coins who awards them based on how cooperative or self-interested you believe your opponent (colleague) to be.

Source: What Game Theory Reveals About Life, The Universe, and Everything

The banker explains three rules that will govern your payouts:

• If both you and your colleague opt to cooperate with each other, you will each be awarded three gold coins;

• If one of you cooperates but the other chooses to defect, the defector gets five gold coins, and the cooperator gets none;

• If both of you choose to defect, you each get one gold coin.

You explain to the CEO how these rules are similar to the faulty practices of management Deming warns about in The New Economics like merit increases and performance pay in how they bias your behaviour toward self-interest over cooperation. However, they can also represent other rewards like promotions or access to resources, favours, or prestige.

You then ask: “How would you choose to play?”

The CEO thinks on this for a moment and concludes that under these rules it’s better to defect than cooperate, at worst they get one coin, at best five.

You might then ask the CEO: “Ok, now imagine you need to play this game with the same opponent (colleague) multiple times per day, almost every day. How would you choose to play?”

Our CEO would think again on this before responding: “It depends on my aim, I suppose. If I’m there to win, I’ll defect because my colleague already knows I’ve done so in the past and will likely do so into the future. If I try to cooperate, I basically let them have the five coins.”

Expecting this response, you lean forward and say, “Now imagine this game played out hundreds of times per day between your employees who you are wanting to work together, cooperatively as a team. Not everyone is the same, there is variation in how they think and manage their work with each other, which means many competing strategies. If your aim is to move toward a Deming transformation, what is the best strategy for building cooperation over reciprocity?”

At this point, you smoothly segue into explaining how this very question was tested by a university professor over forty years ago…

Axelrod’s Dilemma Tournaments

In Muller’s video we learn about Dr. David Axelrod, a political scientist at the University of Michigan who set up a series of computer tournaments in 1980 to find the best long-term “strategy” for the Prisoner’s Dilemma that would win the most points (coins) over 200 rounds, repeated five times over. He invited top game theorists from around the world to submit their “strategies” as programs that could be loaded in to a computer and played off against one another along with a “control” program that randomly cooperates or defects 50% of the time.

Axelrod received fourteen entries, each with unique modes of play, such as:

• Friedman, which started off cooperative but would flip to permanently defecting if its opponent defected just once;

• Joss would start cooperating, but randomly defect 10% of the time, creating an unstable relationship;

• Graaskamp worked similarly to Joss, but would defect in the 50th round to probe the opponent’s strategy for weakness.

After all the programs competed, a simple strategy called Tit-for-Tat emerged as the overall winner. It started by first cooperating, then mimicked its opponent's last move, and would only retaliate against a defecting opponent once, returning to cooperation if its opponent did so first.

When played against Friedman, both obtained perfect scores; however, when Tit-for-Tat played the unstable Joss, a run of back-and-forth defections ensued with both doing poorly. Nevertheless, because Tit-for-Tat cooperated well enough with the other strategies, it emerged the winner.

Axelrod’s Discoveries

Keen to validate his findings, Dr. Axelrod created a second tournament to give participants an opportunity to refine their strategies based on what was learned in the initial tourney. He also introduced a twist where runs would last an average of 200 rounds to inject some unpredictability and prevent gaming to the last round.

Sixty-two entries were received, which fell into two broad camps: “nice” (cooperative) and “nasty” (self-interested). Once again, Tit-for-Tat emerged as the overall winner—in fact, of the top-fifteen entries, fourteen were “nice”. Based on the results of both tournaments, Axelrod made two important discoveries, the first being the four key traits that successful, long-term strategies had over their opponents, in that they were:

1. Nice, ie. biased toward being cooperative;

2. Forgiving, ie. don’t hold grudges;

3. Retaliatory, ie. when crossed, struck back immediately and weren’t overly-cooperative pushovers;

4. Clear, ie. exhibited a transparent, predictable pattern of trust.

His second discovery came from running simulations to emulate natural selection among strategies, ie. those which could accumulate the most points and replicate themselves over multiple generations. In these simulations, the worst-ranked strategies (nasty) from the tournaments quickly went extinct within one hundred generations, while the top-ranked ones (mostly nice) became more common. A notable exception was Harrington, the only nasty strategy in the top-fifteen of the second tournament, which initially grew rapidly but declined as its prey went extinct:

Source: What Game Theory Reveals About Life, The Universe, and Everything (00:16:51)

In contrast, the proportion of “nice strategies” like Tit-for-Tat rapidly increased and stabilized over hundreds of generations, dominating the field:

Source: What Game Theory Reveals About Life, The Universe, and Everything (00:17:18)

You can now pull everything together for the CEO: “Here’s what this means and what you can share with your SLT: Axelrod’s simulations reinforce Dr. Deming’s heuristic for the number of people needed to create a critical mass for transformation as the square root of total headcount. If they are well-chosen, taught new theory, and have actively-involved leadership who continually remove barriers to cooperation, they can out-compete, out-last, and overtake the selfish ones and begin to build toward critical mass.

You don’t need to start with thirty people, but build towards it.

However, there is a catch: It needs to begin with you.”

The CEO, suitably impressed (hey, it’s an imaginary scenario…) asks: “When can we begin?” You hand them a copy of The New Economics and say: “As soon as you are ready. Read the Preface and Chapter 1, your transformation starts now.”

And… SCENE!

Cooperation Over Competition

In The New Economics, Dr. Deming mentions cooperation and management’s responsibility to enable it over fifty times. Axelrod’s computer tournaments and simulations provide us with a model to not only appreciate why Deming was adamant about the need to work cooperatively instead of competitively, but also how adversarial competition (defection in the game) leads to sub-optimal results over time.

Moreover, the four key traits of successful game strategies that are “nice” give us a high-level view of what cooperation could look like: transparent, fair but firm, and not afraid to push back or defend a position rather than caving-in. I think this aligns really well with the traits Deming describes an individual gaining when they internalize his theory, as he writes in the fourth chapter of The New Economics on his System of Profound Knowledge;

Once the individual understands the system of profound knowledge, he will apply its principles in every kind of relationship with other people. He will have a basis for judgment of his own decisions and transformation of the organizations that he belongs to. The individual, once transformed will:

• Set an example

• Be a good listener, but will not compromise

• Continually teach other people

• Help people to pull away from their current practice and beliefs and move into the new philosophy without a feeling of guilt about the past.

2nd ed (pp. 92-93), 3rd ed (pp. 63-64)

If we build towards having thirty people who continually exhibit these traits, it’s quite possible that our CEO and SLT will ignite an irresistible transformation.

Reflection Questions

Consider your organization through the lens of the Prisoner’s Dilemma: What is the prevailing style of interaction? Cooperative or biased to defection? How well are you or your leadership and management recognizing and removing barriers to cooperation? How well-understood is the connection between cooperation and productivity? What is enhancing or degrading this ability?

Do you agree with Dr. Deming’s thoughts on creating the critical mass for a transformation with as few as the square root of an organization?

Miro Board Notes

As per usual, paid tier subscribers can access my Miro board where I plan out my thinking on posts, along with transcriptions and links to resources that can be accessed via the link below. I reserve the right to add to this board as new information and ideas come to me or are suggested by readers.