Ethics in business - Game Theory

Game theory is a dynamic field of mathematics, although still relatively young. It has already brought several Nobel prizes, and its discoveries are applicable practically everywhere. One of its research methods is to build the so-called dilemmas. These are situations of conflict in which different strategies are investigated, obviously looking for the winning one. The objective is simple, a success; calculated and cold. In terms of the purpose of this mini-cycle of articles, this is exactly what we need. Researching what behaviour is advisable from a mathematics perspective (that is, a natural perspective) to achieve success and compare it with ethical postulates/feelings. Do these approaches support each other or exclude themselves; that is the question... Hypothetically, the more contradictory they are, the worse news it is for ethics, I'm afraid. Mathematics will prevail. "Mister, you can’t change the laws of physics..." In this case, mathematics.

The key conclusion of the previous article was that the aggressive scenario doesn’t pay off in the long-term perspective. The theory of probability is brutally unambiguous, especially in the case of a growing business, with increased complexity, dependent on the behaviours of many players. In such cases (length in time + scale), continuous risk and bidding high statistically leads to a fall. Some will succeed, as in statistics, but there will be few of them. Each of us makes decisions on our own, whether we want it this way, what probability and what stakes we want to bid. What’s important here - this doesn’t mean that mathematics supports ethics 100%. It can still be criminal behaviour. I deliberately used this “business” sector as an example. However, whether we want it or not, even gangsters are more effective using variants of cooperation and minding the needs of other stakeholders. That is, moving from the most ordinary brutal banditry towards being more civil (with a pinch of salt towards the latter statement). It's always something. Mathematics in the simplest approach has helped us filter processes and allowed us to roughly evaluate strategies.

All this has led me to the question, which I phrased at the end of the previous article:

What is minding others, possible cooperation and interaction with other market participants really about?

So we're back to mathematics and the game theory. The results of the so-called prisoner's dilemma experiment will come very useful here. I will not go into the details of the assumptions, although from the mathematical point of view it is crucial; you can find them easily on the web. We're interested in results. As the name of the dilemma implies, we have two prisoners locked separately in isolated cells. No one knows what the other would do, this is the key assumption. They have two scenarios. The first is to say nothing at the interrogation, that is to accept the variant of cooperation with the other, not knowing what he would do (will he betray us, or will he remain silent). The second scenario is to betray the fellow prisoner. The results of the calculations are simple and unambiguous. Whatever the other one (silence or betrayal) would do, the winning scenario for us is... betrayal. So bidding only on yourself, without cooperation. So much for mathematics.

Is the prisoner's dilemma such an abstract concept? Well, no. Every now and then it appears in our lives and we have to make decisions. A simple example is doping in sports. We have no idea if our competitor is doping. What does mathematics say according to the prisoner's dilemma? It says dope yourself. If the competitor dopes too, you have evened out the odds; if he doesn’t, you will beat him. Can ethics alone overcome this? Hmm. Looking at the history of the sport (people), I would bet on the technological victory of detection over doping and the inevitability, immediacy and weight of the punishment as perhaps more effective than ethics. There is one more important auxiliary factor, decisive even, but let’s talk about it later.

The second example is the arms race. We sign treaties over what is allowed and what is not; however, we have no idea whether our alleged opponents are plotting something forbidden in their secret labs. What does the prisoner's dilemma say? Set up your own secret lab and plot. If they do, you will even out the odds; if they don’t, then when it comes down to it, we have an advantage. Here, apart from the "normal" ethics of an individual, another factor comes in. After all, the wellbeing and survival of "our" nation is a supreme value and one cannot risk it with any treaties that we are not sure "the others" follow. Simple as that. But how do we try to prevent this? For example, by agreeing on the possibility of checking the other side, signed in a treaty; but only in designated places, with a certain time advance, so we still cannot be certain that they aren’t plotting somewhere in the mountains or underneath them or in the desert. International treaties prohibit not only possession but also research on biological weapons. Somehow I am strangely calm(less) that in somewhere in the world something must be happening in this matter. It’s mathematics. Because if they are plotting...

What about business? Oh, there are plenty of examples. For obvious reasons, we have poor knowledge of what our competition plans, just as we protect our plans against them, after all. For example, we don’t know if they employ children in their factories, or dispose of toxic waste without purification somewhere on a different continent, because we’re no longer allowed it here. For the same reasons as above, it is more profitable for us to employ children and not spend money on wastewater treatment. In these two cases, we have already been quite successful; however, resulting from ethical (children) or pragmatic reasons (sewage). We have also introduced, just like in the case of an arms race, systems of mutual control of the entire process from acquiring materials to production and sales (also through designated external institutions). It took us about two hundred years, but it works. I'm also very happy about it myself. In everyday business, however, we operate permanently without knowledge of actions/plans of competitors, so we regularly receive information about market collusions, violations of accepted commitments, etc. Well, if they are plotting...

So far, it looks quite bad from the point of view of ethical postulates, doesn’t it? Postulates being postulates, the reality is a reality. Mathematics says not to cooperate and bid only on yourself. If you have read through this far and have not yet jumped up to shoot me, strangle me, bury me and park a tank on top of it, I have some good news. The first one is a reminder – don’t shoot the messenger. I am only writing down what nature itself suggests. The second is even better. Fortunately, there is a knight on a white horse who is coming to the rescue. His name is... mathematics. The prisoner's dilemma works only in a one-off situation when there is no tomorrow (the game has one or a predetermined number of turns), and/or decisions are made without knowledge of the results of choices made by other participants of the game. Are there any special cases in business with no tomorrow or knowledge of the past? Of course, and we do know them. Let’s have a historical example. We sometimes watch westerns. Apart from the gunslingers, one of the recurring characters is a travelling salesman, who offers potions that cure everything (water + nettle, to make it taste bad). He is, quite obviously, a hoax. He comes to town, he talks smoothly, he sells, and he leaves. After a while, people realize that what they bought is useless and doesn’t treat anything. It doesn’t matter for the salesman, because he won’t be back in town. There is no tomorrow. His business exists as long as there are still new towns to visit, full of new, naive people. Wild West was a huge area, so this kind of business could last for years. And if you can talk smoothly and you have finished a few NLP courses... the world is your oyster! There may be trouble when one of the deceived residents will move to another town, and the salesman would arrive there; then tar and feathers would be the best case scenario, but an angry mob with stones and ropes is a different matter. Nowadays these traditions are still followed; the simplest example is the great opportunity of two toothpaste tubes for the price of one. As a customer, you are interesting for the seller only once. Once you bought it, he says goodbye and moves on to looking for more gullible ones, never coming back to you again. Business exists as long as it reaches new, naive people. The deluxe version is a financial pyramid scheme... It works, as long as we pay. In such pyramids, the additional key factor is the operator (and only him, not us), who usually knows that the number of turns is limited and at the right time the business must close. He even plans ahead towards it. And in this case, the system is always the one-off prisoner’s dilemma, that is, the winning scenario is the lack of cooperation or a fraud. But frequently the operator’s greed clouds his judgement (emotions! remember the previous article?), he does a few rounds too many and he falls into a trap. Bernie Madoff managed his Ponzi scheme for many years because he combined it with effective manipulation techniques. Now he has to spend 150 years behind bars, and his son has committed suicide... well, Mr Madoff stands a possibility of parole after perhaps 108 years…

Luckily, a huge part of the business, most of it actually, operates in different conditions. There is a tomorrow because we want our customers to return. There is a past, because competitors, clients, legislators, taxpayers, etc. remember our previous behaviour and plan their subsequent movements according to ours. What’s more, the number of turns is unlimited, or at least unknown. We want our company to last as long as possible. It is a so-called iterated prisoner's dilemma. The search for the winning scenarios for such assumptions was made in various ways. Finding the answer is extremely important here. After all, this is a situation that perfectly describes the reality around us. One of the aforementioned ways was to build and launch computer programs operating according to several specific models; all that in order to see which program, or business model, wins. Here are the basics:

- always cooperate (whatever competitors do); the so-called naive strategy

- bid only on yourself, that is, never cooperate; nasty strategy

- repeat every move of the other party (they cheat so you cheat; they cooperate, so you cooperate, etc.)

- start with cooperation, react to cooperation with cooperation but when they cheat you, retaliate in the next move and return to cooperation in the next (show strength, and then forgive and return to cooperation); a nice and forgiving strategy.

Ah, the tension is building up, right...? Well, the scenario that always loses badly is the first one. Well, the idea of turning the other cheek, regardless of the circumstances, is beautiful, but it leads us to a certain loss. I'm beginning to understand why all countries that have good gods in their constitutions or on their banknotes, still maintain armies and police forces.

Two scenarios go head to head for a long part of the experiment. This is the second model (never cooperate) and the fourth (cooperate, retaliate when cheated, forgive and cooperate until betrayed again, etc.). However, the moment comes when one of them falls. Now, you can relax... The losing scenario is the nasty one. The answer to the question of how long they are going head to head and when the aggressive one begins to lose is very interesting. All the more interesting that it is consistent with previous business examples. Well, the aggressive program is just as effective as the fourth one, as long as there are still representatives of the first model. That is, as long as there is anyone you can eat with no consequences because they will always turn the other cheek. When the nasty eat the naive, they run out of fuel and so long, farewell; second place. For many, the silver medal is still a very attractive perspective in this best of all worlds. Therefore, there may be a need for a market regulator, because its invisible hand will work of course thanks to mathematics, but why so much blood must be spilt on the way?

So, the final conclusion, which model wins in the long-term:

- be friendly (cooperate) – don’t cheat as long as you haven’t been done so

- when you are betrayed, show strength and retaliate accordingly (once!)

- return to cooperation mode, giving the other side a chance to do the same.

We know such models very well, only we don’t always take notice. A hot example is a relationship between the European Union/USA and Russia after the latter's attack on Ukraine: first, economic and political sanctions; then opening doors for possible cooperation in solving the problem - a classic example of the iterated prisoner's dilemma. Of course, the devil is in the detail, such as defining "proper" revenge, that is, what the other side would feel and affect its further actions. But the principle is clear. By the way, I'm sure of one thing; Polish politicians haven’t even heard of the iterated prisoner's dilemma. That makes the country what it is right now.

What makes it difficult, and often even impossible, to act according to the winning scenario? We already know this from previous considerations: emotions. Are there no wise people in Israel and Palestine who know mathematics? There are many of them. And yet there is no chance of agreement. Of course, when I say "emotions" I mean a broad spectrum of their causes, including attachment to symbolism, founding myths, beliefs, etc. If there were two AI programs set up there (their creation is still to come), they would find a solution in no time. And people would stop dying. The same emotions are also the reason that Poles often quite differently assess EU/US policy towards Russia. The policy I do not necessarily glorify, because it often lacks consequences as it is led by people: subject to emotions, trapped by here and now, to the mini-interests of groups of influence, the pressure of the upcoming elections, etc.

And now as promised we return to the issue of doping in sport. I mentioned a new factor, perhaps decisive, for this matter. Well, in the past, doping in sport was subject to the rights of a one-off prisoner's dilemma. ?I took, I won the competition, the control didn’t detect anything, case closed, the end, there is no tomorrow, only here and now”. In the last years, however, the rules have changed. The samples are frozen and can be inspected again many years later, using the latest methods to detect prohibited substances. The non-existent "tomorrow" has entered the game! The number of turns increased to unlimited. There was also "yesterday". We’ve caught you for the second time? Well, you’re banned for life! It means no less than a change of paradigm from one-off to iterated dilemma of a prisoner. A side effect is the growing number of medals won by Poland at various championship events. Medals won after the event because competitors have been disqualified for doping, detected after a long period of time. Being honest starts to be fun!

What would be the best example illustrating the prisoner's dilemma in sport? Lance Armstrong, formerly seven-time Tour de France champion; today, zero-time. He was stripped of everything, including money (well, part of it) and his good name, and rightly so. Apart from the obvious assessment of his doping behaviour from the point of view of ethical postulates, he has broken all three key mathematical principles mentioned in this and the previous article. First of all, he was arrogant, for whom other people were only pawns. He antagonized other participants of his game and thus reduced the probability of success of individual choices. Secondly, no one told him that the probability of events multiplies and he had overdone the sequence of these events. That's why he made extreme choices for years. Meanwhile, absolute mathematics indicated that the probability of success of his entire career is already close to zero. He wanted to beat over the record of the number of victories in Tour de France while exposing himself to all spotlights. Thirdly, he hasn’t noticed that the dilemma definitely is changing from one-off to iterate. "Tomorrow" and "yesterday" made the game. It was a very spectacular fall and an equally important lesson for our argument.

To conclude, a true story from last year, to let it close the discussion about ethics and mathematics. My friends took me to the Alps. One of them lost his wallet somewhere between 2,000 and 3,000 meters. It held quite a lot of money and a credit card because he volunteered for the role of a temporary payer of current expenses during the trip. Despite several attempts, we were unable to find the wallet. We have comforted ourselves saying that at such routes, in these higher and more difficult parts of the mountains, there is a specific group of people and we stand a good chance that there will be something like group solidarity and the finder will let us know. So, we have made ethical assumptions against mathematics, because it is nothing more than a one-off prisoner's dilemma. There is no yesterday, no tomorrow, high mountains, I anonymously find a wallet, I put it in my pocket, I go home: pure profit with zero chance for punishment. About three months later, my friend received a message from Switzerland: I found your wallet, please tell me how to return it...

Here I have a thought that will be one of the subjects of article number five. If at the beginning you "only" take an opportunity when it arises, then with time openness and temptation to create them increases. In this course of thought, I will use the help of Hemingway and Giuliani, among others.

That's what cold mathematics has to say. Let me remind it once again - it does not state what is ethical. Instead, it brings very important elements to our decision-making process. Provided you learn these elements. Eventually, each of us makes a personal decision. We will see in part four of the series what decisions are influenced by, how "obvious" they are and embedded in our "fixed and unchangeable" value system.

PS Ethics being ethics, mathematics being mathematics, but what if their battleships have invaded our port, and we only have a fishing boat...? But it's a different game model, for another article, although there are some points that they share.

PPS In all of this, it turns out that social media are very useful. They help in the rapid and mass flow of information. For example, bad products, services, business behaviour. It's more of a nuclear bomb than a scalpel that painfully makes everyone aware that there is yesterday and there will be tomorrow. Like any weapon, this can be used for good and for evil purposes. It's a well-known thing.