The Game is On … Except When It Isn’t

 

From the time John Von Nuemann and Oskar Morgenstern wrote Theory of Games and Economics (Princeton University Press, 1944 – a date, incidentally, that indicates that Von Nuemann was working on this book while he was also working on the Manhattan Project), there has been this notion in the management science world that Game Theory, either on its own or in combination with statistics (or some other, complimentary area of scholarship), could help generate some sort of grand unifying theory that would enable those who developed such a theory to precisely calculate economic behavior. Put another way, there’s been this hope that some super-sophisticated formula, that took into account a sufficient number of parameters (by necessity, would have to be myriad), might lead to an ability to predict a macro-economic future with a usable degree of accuracy. As I’ve mentioned often time before, any reasonably competent stock broker or commodities trader, if handed a copy of next week’s Wall Street Journal, could begin picking out the color of his new Jaguar right away, so it’s easy to see why such a formula could be hoped for. It’s the management science equivalent of knowing the upcoming PowerBall numbers – placing Game Theory squarely at the very tip of management’s cutting edge.

As I discuss (at length) in my recently-released, must-have book, Game Theory in Management (https://www.ashgate.com/default.aspx?page=641&calctitle=1&pageSubject=1966&title_id=11616&edition_id=11979) , this quest to be able to calculate the future was even at the heart of Isaac Asimov’s famous Foundation trilogy. In Foundation, we are introduced to one Harry Seldon, who has actually developed a Code of Nature, which can calculate the future with a reasonable degree of accuracy. The most common analogy employed is that of gas (I swear I am not making this up): it would be admittedly impossible to predict the behavior of one molecule of a gas. But, given billions and billions of such molecules, their macro-behavior becomes predictable through scientific calculations and observations. Similarly, the Foundation trilogy occurs far into the future, when humans have populated much of the Milky Way and their population numbers in multiple billions. What’s notable about the fictional Seldon Plan is that it is nearly undone by the uncalculated appearance of a character known as The Mule, who can telepathically change people’s minds. Since The Mule is a mutant, his appearance could not have been anticipated through the calculated structure of the Seldon Plan.

The problem with developing a business version of the Seldon Plan, of course, is that it’s wildly impossible. I mean, the notion makes for great science fiction, but the genre of science fiction is usually chosen because the author needs to present a version of reality that’s completely impossible in the present, or even in the past. And that’s certainly the case here.

Consider that extremely simple game, the Ultimatum Game. In it, two participants – Player A and Player B – are offered $100 (USD), and they only need to do one thing to get it: Player B must agree to Player A’s initial plan for distributing the money between them. If Player B does not approve, neither player receives anything. Game Theory analysts calculated that Player A maximizes his payoff if he offers Player B just $1, and tries to arrange to keep $99 for himself, under the theory that, since Player B’s alternatives are to accept one unearned dollar, or nothing at all, they will always accept the former.

But a funny thing happened on Player A’s trip to deposit his $99. The scheme calculated to maximize Player A’s payoff was almost never accepted in actual experimental iterations of the Ultimatum Game. In fact, Player Bs didn’t come close to accepting the proffered split from Player A until the arrangement approached 60 – 40. Game Theory analysts offered explanations on why they were so dramatically wrong, often centered on unforeseen “cultural influences.” As far as I’m concerned, invoking “cultural influences” was a way of trying to get around the fact that, even when the parameters are as stark and hard as those in the Ultimatum Game, it’s simply impossible to exclude factors outside of those anticipated from having a profound influence on the selected strategies of the game’s participants.

Ultimately, (pun intended) Game Theory is next to useless when invoked to help predict the future strategies most likely to be invoked by participants in either artificially constructed zero-sum games, or in the behaviors of players in the macro-economic “game.” However, Game Theory is extremely valuable in the furthering of management science, since it plays the central role in…

Oops! I’m butting up against my word limit. To find out how Game Theory is of extremely valuable use in evaluating management strategems and tactics you will either have to purchase my previously-referenced book (I told you it’s must-have!), or else wait for me to disclose more in this blog in future postings. What do you suppose are the odds that I will select a strategy to tell you what you crave to know in the next couple of weeks?