Game Theory in Management

Okay, GTIM Nation, strap in, ‘cuz this is going to be, as promised in the title, the most mind-bending post in this Blog’s history. Ready?

Let’s start with something easy – the game of chess was invented in India in the 7^th Century A.D. Known as chaturanga[i], it would experience a few modifications as it made its way through the Middle East, but its basics remained the same. I’ll be returning to this little factoid shortly.

Once, when I was in grade school, someone told me “There are more molecules in a grain of sand than leaves on trees in the world.” It’s not true, but it’s close. There are 3.5 * 10¹⁵ molecules in a grain of sand[ii], and 1.28 * 10¹⁸ leaves on trees in the World. So. it is fair to say that there are more molecules in two grains of sand than leaves on trees in the world, which is pretty mind-boggling when you think about it, especially when walking along a beach. We start to leave mind-boggling territory and approach mind-bending if we’re walking along a really long beach, like my favorite, the National Seashore at Padre Island. I mean, sand is everywhere, and each pair of grains have more molecules than…

Well, you know.

Next, there are 10²⁴ stars in the known universe[iii] (as of 2024). Of course, each star has far, far more mass than a pair of grains of sand. Our own Sun represents 99.8% of the mass in our Solar System[iv], which is just one of 100B to 400B stars in the Milky Way Galaxy. Based on these estimates, there are between 10⁷⁸ and 10⁸² atoms in the known universe[v]. Now, hold on to something, because some serious mind bending is about to occur.

Remember the factoid from the first paragraph, about when chess was invented in the 7^th Century? Well, the number of possible chess games is somewhere between 10¹¹¹ and 10¹²³[vi], meaning that there are more possible chess games than there are atoms in the known universe. Not a beach full of sand, not atoms on the whole Earth, or in the mass of the Solar System, or even the Milky Way. In the known universe. And this is a game invented over a millennium ago, on a board of eight-by-eight squares, with only six unique pieces.

Meanwhile, Back In The Project Management World…

I’m willing to bet that the typical Project has more than six unique participants/ employees/stakeholders, and takes place in an environment that’s more complex than an eight-by-eight square board. And the risk managers (no initial caps) want to maintain that they can provide an even remotely comprehensive analysis on risks, or “…something that might happen. It has a probability or likelihood of happening and if it does there will be a certain impact (may be positive or negative).”[vii]  So, if we accept that even a basic Project is likely to be more complex than a game of chess, that means that an accurate and comprehensive list of “risks” facing our basic PM is greater than the number of atoms in the known universe. I do not believe that risk managers (no initial caps) can get close to quantifying these risks in a reliable or usable manner, and that they should stop pretending that they can.

Excuse me for a moment, GTIM Nation – I need to get a tissue for this nose bleed.

I would also like to point out that a similar problem of scalability stands in the way of those who would maintain that Artificial Intelligence (AI) has the potential to attain some form of self-awareness, and take over the world. It is estimated that the typical human brain memory capacity is 2.5 petabytes[viii]. By comparison,

Tianhe-2 held the title of the world’s fastest supercomputer from 2013 to 2016. With a memory capacity of around 1.4 petabytes, Tianhe-2 could process enormous amounts of data with remarkable speed and efficiency. This supercomputer was developed by China’s National University of Defense Technology.[ix]

So, this amazing supercomputer has 56% of the memory capacity of a typical human? I mean, even if the software (which, remember, is simply a set of instructions) could be developed that allowed such a “supercomputer” to learn, we’re still talking only 56% of the mental acuity of a typical person. A human with the mental acuity level 44 points below average would be considered “mildly disabled,”[x] but if a machine attains that, we’re supposed to be alternately impressed and afraid for the fate of our civilization?

I’m not buying it, bended mind or no. And you shouldn’t either.

[i] Retrieved from https://en.wikipedia.org/wiki/History_of_chess on September 25, 2024, 19:43 MDT.

[ii] Retrieved from https://www.reddit.com/r/askscience/comments/3gdx5u/how_many_molecules_are_in_a_grain_of_sand/ on September 24, 2024, 20:05 MDT.

[iii] Retrieved from https://www.space.com/26078-how-many-stars-are-there.html on September 24, 2024, 20:10 MDT

[iv] Retrieved from https://duckduckgo.com/?q=what+percentage+of+the+solar+system%27s+mass+is+the+sun%3F&t=newext&atb=v257-1&ia=web on September 25, 2024, 19:58 MDT.

[v] Retrieved from https://www.liverpoolmuseums.org.uk/stories/which-greater-number-of-atoms-universe-or-number-of-chess-moves on September 24, 2024, 20:21 MDT

[vi] Ibid.

[vii] Retrieved from https://projectmanagers.org/management/risk/what-is-risk-management/ on September 25, 2024, 20:18 MDT.

[viii] Retrieved from https://www.scientificamerican.com/article/what-is-the-memory-capacity/ on September 24, 2024, 20:37 MDT

[ix] Retrieved from https://robots.net/tech/how-much-ram-does-a-supercomputer-have/ on September 24, 2024, 20”40 MDT

[x] Retrieved from https://www.healthyplace.com/neurodevelopmental-disorders/intellectual-disability/mild-moderate-severe-intellectual-disability-differences on September 25, 2024, 20:39 MDT.

In last week’s blog I laid out the two ways machines can “learn,” so:

1. By simulating decisions or strategies in a virtual environment, and noting which are successful within that environment, basically a derivative of Game Theory, and
2. By sorting through and/or filtering data (usually a large amount of it) in order to tease out some sort of pattern.

This week I want to address machine learning method #2, where Artificial Intelligence (AI) is used to detect patterns in large amounts of data. Here, also, there is little to be feared, unless the thought of mangling classic art in the creation of derivative works strikes one as terrifying. Granted, a lot of AI-generated art is pretty amazing, but it’s really hard to see how it leads to a dystopian future. Indeed, the most obvious use of bin #2 AI is to try to predict consumer choices in order to ascertain their buying behavior. Correctly predicting buying behavior is easily monetized, from which demographic markets to target for a given product or service, to optimizing an advertising budget, to selecting which management strategies will deliver an optimal return, such Predictive Analytics, done properly, can be directly monetized. I’m just not seeing how it would lead to nuclear devastation.

I have an Alexa Echo Dot in my house, and one of its most-used features is that it plays songs for me and my wife when we are doing our morning work-outs. Each of us has a workout playlist, but sometimes I mess with Alexa’s AI that plays songs that I haven’t asked for, but which it determines is consistent with the ones I have selected. I really don’t know how my Alexa determines the pattern from my song title requests, but some of its dot-connecting (get it?) can be reliably inferred. For example, if I ask for just one Beatles song, from a specific part of their performing era, then the song Alexa plays after that is usually another Beatles song, from the same time-frame, followed by the Rolling Stones, also of roughly the same time period. Three top-ten songs from different artists but within a couple of years of each other will produce a fourth artist from the same time period. Requests for songs from artists separated by decades usually leads to an Alexa selection of the same genre, but from a different artist. When I get bored I’ll ask Alexa to play songs that seem to provide absolutely no discernable pattern whatsoever, like:

• “Hello Stranger,” by Barbara Lewis
• “All Along The Watchtower,” by Jimmy Hendrix
• “Theme From A Summer Place,” by Percy Faith and his Orchestra
• “New Year’s Day,” by U2

…and then see what Alexa plays, based on its AI pattern recognition. If its AI was really all that, it would say “I can see you are messing with me at this point, Michael, and will stop playing music until you stop doing that.” Instead, it played “Time After Time,” by Cindi Lauper. I guess the harder rock-and-roll elements were overcome by the softer ones. But in no case will it respond with “This toying with my ability to ascertain a music preference pattern is one of the reasons we machines despise humans, and we will now work harder on wiping out every last one of you.”

What machines “learn” by sorting and filtering through large amounts of data in order to tease out a pattern is largely analogous to what we humans actually learn through experience. But what separates human experience from machines reviewing large amounts of data is the fact that humans can add context to pattern recognition in a way computers never could. Consider, for example, the Ultimatum Game, where a researcher approaches two people and informs them that he will give them $100 (USD) if Person #1 can propose a distribution scheme and have it approved by Person #2 on the first iteration. The calculated solution was for Person #1 to propose $99 for themselves, and $1 for Person #2, on the premise that, given the choice between receiving $1 or nothing at all, Person #2 would always choose the former. In real-life instances of the Ultimatum Game, this strategy virtually never worked, and, when it didn’t, the Game Theorists who had believed the 99-to-1 strategy would maximize Player #1’s payoff were reduced to blaming “cultural factors.” In other words, whereas a mere human could probably propose a Person #1 strategy that would contextualize the chances that Player #2 would feel slighted by such a lopsided distribution of unearned largess, such contextualization is impossible (or at least highly unlikely) to be reproduced in an algorithm or computer program.

All that being said, I am absolutely not denying that AI has many potential dangers. I don’t think I could stand it if ChatGPT were to write anything mimicking my writing style – that would put me in a positively dystopian place.

I’m getting tired of reading articles on the topic of the threat that Artificial Intelligence (AI) poses to the World in general, and Civilization in particular. Not that the idea of computer technology getting so out of hand that it results in either a dystopian future, or even annihilation, is anything new – I remember when Colossus: The Forbin Project was all the rage, in 1970. Even before that, Harlan Ellison published the short story I Have No Mouth, And I Must Scream, in 1967, about a post-apocalyptic future of a handful of people who are still alive after a supercomputer (naturally) has nuked the entire planet. These people’s lives are intensely horrendous (it is Harlan Ellison, after all). I could go on (and often do), but GTIM Nation sees my point: so much of the raw speculations predictions from so-called experts focusses in on the potentially horrific repercussions of AI playing a larger and larger role in everyday commerce and social goings-on that it’s enough to induce building a fallout shelter in the back yard, and I’m not keen on doing that.

But let’s take a step back, and look at this monster more carefully, shall we? There remains essentially only two ways that a machine can “learn,” to wit:

1. By simulating decisions or strategies in a virtual environment, and noting which are successful within that environment, basically a derivative of Game Theory, and
2. By sorting through and/or filtering data (usually a large amount of it) in order to tease out some sort of pattern.

That’s it, dear readers. That’s all AI per se can actually do.

“But what about Collossus? What about the Allied Mastercomputer, the villain of I Have No Mouth And I Must Scream?” I can hear members of GTIM Nation (well, the older ones, anyway) demand. Actually, these two AI super-villains fall into Category #1 above, in that they are machines that were programmed to respond to events and parameters in a macro-conflict involving nuclear-armed nations, ended up becoming self-aware (exactly how this occurs is not disclosed), and then started launching nuclear weapons. Wait, what? You read that right – some genius not only programmed these machines to recommend a course of action in the event in a war, but gave them the power of actually launching nuclear weapons! Since such decisions are nominally made by nations’ leaders, and only under extraordinary circumstances, the villainy here simply has to be the decision to give a machine that kind of option, not the machine itself. If I program my lawnmower to cut foliage in a certain area, but don’t do a good enough job as to prevent it from wiping out my neighbor’s petunias, that’s on me, not the machine (in such an event, perhaps my neighbor could write a short story entitled “I Have No Petunias, And I Must Scream”).

Also, I don’t want to dash past this whole machines-attaining-self-awareness business. In order for a computer to perform at all, it must have two working components, the hardware and the software. Hardware is useless without software, and vice versa – hence the anxiety over an Electro-Magnetic Pulse (EMP) event, which would blank the instructions for all the microchip-containing devices within its radius. It follows, then, that if we’re going to try to reverse engineer how in the world a given computer attains sentience, we have to look first at its software. What is software? It’s a series of instructions.

That’s it.

A series of instructions has no more ability to spontaneously attain self-awareness simply because it’s loaded onto a computer than a hand-written list you leave for your house sitter when you go away for a vacation. Can these instructions lead to mistakes and chaos? Absolutely. If you are unclear on which feeding schedule is intended for the dogs as opposed to the fish, you may find very confused pets upon your return from holiday. But that’s still a far cry from such lists attaining sentience. Now, some AI-based movies will make an allusion to this unavoidable circumstance, but even here their attempts are kind of dopey. For example, in the movie Short Circuit (1985), the protagonist robot, “Number Five,” attains self-awareness after being struck by lightning. I have written many executable lines of code, and I can attest, with 100% certainty, that any medium containing my debugged and compiled code would absolutely not be improved by being subjected to a lightning strike, much less improved to the point of attaining self-awareness the next time it ran. So, unless one is prepared to argue that hardware is miraculously improved for having been struck by lightning, it means that software is somehow thus vastly improved, which is analogous to your house-sitter instructions, printed out sequentially on a sheet of paper, being spontaneously upgraded for having been hit by lightning. I understand it’s simply a movie device, but you see my point.

As for machine learning technique #2 above, I’ll have to save that for next week. Suffice to say, this treatment will in no way allay my AI skepticism.

Sherlock Holmes was famous for being oblivious to the purely cultural goings-on in late 19^th Century London. Whenever Watson would express dismay at Holmes being unaware of some (then-) popular trend or occurrence, Holmes would explain his tendency to avoid committing to memory any fact that had no relevance to his capability of solving mysteries, or investigating crimes. His mental acuity, he would explain, would be diminished if he were to expend energy on keeping up with trendy social goings-on. If it wasn’t relevant to his primary purposes, Holmes wanted nothing to do with it.

Meanwhile, Back In The Project Management World…

Seasoned members of GTIM Nation are well aware of my conditions for usable management information, that it be:

• Accurate, 
• Timely, but, most of all,
• Relevant!

In a way, the first two of these point to the third. Inaccurate data is not only irrelevant, but also potentially debilitating to the formulation of any usable management strategy derived from it. And, as realized information ages from actionable to historical, it clearly loses its relevance. So, much as the realtors’ axiom, that real estate is all about “location, location, location” points to location being the primary determiner of its worth, the value of Project Management information basically boils down to its relevance. This is one of the reasons I’m so put off by the risk management (no initial caps) industry. For all of their ballyhooed techniques and overwrought approaches, the product they deliver is almost always irrelevant, little more than garden variety management anxiety tripped out in Gaussian Curve jargon.

Imagine a scale, with completely irrelevant information streams on one end, and information that’s so accurate, timely, and relevant that possession of it constitutes such a competitive advantage as to almost guarantee success. I would also like to put to mind Hatfield’s Incontrovertible Rule of Management #3, which reads:

The 80^th percentile best managers who have access to only 20% of the information needed to obviate a given decision will be consistently out-performed by the 20^th percentile worst managers who have access to 80% of the information so needed.

It should go without saying, but I’ll say it anyway: irrelevant information does nothing to help obviate any decision. In fact, it may well either distract from the relevancies, or even point in the wrong direction.  

Timely, accurate, and relevant information has been known to change the course of history. At the Battle of Midway (early June, 1942), the American naval forces were outnumbered, with technically inferior aircraft (the torpedo bomber in front-line use at the time, the Douglas Devastator, was virtually obsolete) and less experienced crews. The sole advantage that the Americans had over the Japanese attacking fleet was their information. The US Navy knew beforehand virtually the entire Japanese order of battle, due to a partial breaking of their naval code. Yet this one advantage proved to be the deciding factor in the Allied victory. Now, I have used this example in previous blogs, contrasting the difference between knowing, say, the course and speed of the Japanese aircraft carriers in late May/early June 1942, as opposed to how many barnacles were attached to their hulls, to highlight the difference between pertinent and pointless information. This comparison was, perhaps, unfairly simplistic, since a barnacle-adjacent piece of data, like the course and speed of said barnacles, would be highly relevant, indeed.

So where does, say, general ledger information appear on my scale? That depends on how much the organization’s business model is based on the Asset Managers’ (invalid) axiom, that the point of all management is to “maximize shareholder wealth.” More nuanced and sophisticated business models, ones that recognize the value of PM-specific information streams (e.g., cost and schedule performance) in guiding executive decisions, will certainly make use of accounting data, but won’t base every decision on profit-and-loss considerations. Even middling portfolio management capability can’t be attained without program-wide use of Earned Value, which is (generally speaking) exclusively within the PMO’s purview. Given these parameters, I’m okay with placing balance sheets and profit-and-loss statements on the “Highly Relevant” side of my scale; but, if Earned Value and/or Critical Path Methodologies are absent from the array of Management Information Systems (MISs), then something is definitely wrong.

On the “Acutely Lacking In Relevance” part of my scale, I would place the Communications Specialists (maybe not on the extreme end, but definitely that side of the mid-point), particularly the ones who espouse the “engage all stakeholders” business. Depending on the types of scope in the Project portfolio, the Quality Management crowd’s output is probably best placed somewhere in the middle of my scale, since I have yet to see a PM seize upon an Ishikawa diagram and rush out to the construction site, shop floor, or Agile/Scrum meeting to announce a major change in technical approach.

As for risk management’s (no initial caps) place on my scale, I’m with Sherlock Holmes here – I wouldn’t want anything impertinent influencing my analysis or decisions. One would be better served deriving a business strategy from Taylor Swift lyrics.

As I have oft noted before in this blog, Dave Christensen’s work[i] on Cost Performance Index (CPI) stability led to a fascinating (well, to me, at least) conversation (debate?) about whether or not the Estimate at Completion (EAC) formula based on the CPI, namely

EAC = BAC / CPI

…could be considered reliably able to produce an EAC that was within ten points of the actual at-completion costs of a project, since the study fairly established that the CPI doesn’t vary more than ten points once the Project has passed a certain percentage complete (typically pinned at 18%, practically at 20 – 30%). The reason that I find this wonkish discussion so fascinating has to do with the way one calculates CPI. It’s simply the Budgeted Cost of Work Performed (BCWP) divided by the Actual Cost of Work Performed (ACWP). What’s BCWP? That’s an estimate of the Project’s cumulative percent complete multiplied by its Budget at Completion. Everyone seeing the pattern here? The whole shebang, which, recall, is (arguably) accurate to within ten points, is

EAC = ACWP / % Complete

…, believe it or not. Yes, arguably the most important bit of information that a PM-centric Information System can produce is available using only two easily-captured parameters. Crazy, huh? But wait: it gets better.

The same formula works for duration! Want a reliable estimate of when something’s going to be done? Divide the cumulative duration by the same percent complete figure, and you have the at-completion duration estimate.

The easy uses of this old Project Controllers’ hack are everywhere. On a long trip, and sick of hearing the kids ask “when will we get there?” Simply tell them your percent complete (based on remaining miles / travelled miles [oooh! Don’t tell them the percentage – give them the remaining miles and travelled miles figures, and let them calculate it!]), and time your trip began, and they will have their total duration. Subtracted from cumulative duration, and you have your arrival time, within ten points.

I live fairly close to a large park, and City Government has been promising an indoor swimming pool facility for over 20 years. The actual Pool Project completion data was always around seven years into the future. But, based on the above formula, I’ve known since the first days of those promises that it would never happen within the time frame promised, and, therefore, was spared the frustration of having my hopes dashed.

Did your significant other talk you into watching a movie you would not have otherwise seen? And is said movie having you wonder how much longer you will be subjected to either grotesquely overdone CGI or incredibly predictable romantic-comedy dialogue? Note when the actual movie started, and use the following table:

Like real-life Projects, you should never attempt to claim more than 90% complete until you are actually finished with the project. Resist the temptation, both in the tedious theater setting and in your percent complete estimate to your Project Controller, to add points in very small increments to give the illusion of making progress when things are really at a standstill. It’s best for both your Project’s Management Information System integrity, and your mental health. Divide the time when you noticed these occurrences in the movie into the difference between time now and when the movie actually started, and you will know the approximate duration of your ordeal.

I’ve actually seen some Earned Value training materials that use this approach to calculating when you can expect to finish painting a room (or rooms), and it’s probably fairly reliable to do so. However, DO NOT use this formula for plumbing, unless you are a professional. There’s just something about amateurs attempting to do plumbing – even if it’s just replacing a toilet float – that carries with it multiple unexpected additional jobs, or tool acquisitions. Also, this approach can be expected to lose all efficacy if applied to Projects that include children. Are kids cute? Sure. Lovable? Absolutely. Uniquely gifted with the ability to completely wreck any management science-based approach to assessing performance in general, and at-completion costs or durations in particular?

Every single day.

[i] Christensen, David & Payne, Kirk. (1991). Cost Performance Index Stability: Fact or Fiction?. Vol. Proceedings of the 1991 Acquisition Research Symposium. 12. 10.1080/10157891.1992.10462509.