When we’re about to make a decision, while playing a game whose result depends on the decisions of others, we should assume that, in most cases, the other players are as smart and as egotistical as we are. Game theory deals with formalising the reciprocity between rational players, assuming that each player’s goal is to maximise his or her benefit, whatever that may be.
Players may be friends, foes, political parties, states or anything that behaves interactively. The reward is not only measured in money, but it is the satisfaction players receive from the results of the game. These results could be positive (money, fame, clients, more ‘likes’ on Facebook, pride and so on) or negative (fines, wasted time, ruined property, disillusionment and so on).
There are many ways to apply game theory to life situations:
As you see, the list goes on.
The questions raised include: can game theory really help to improve the way people make their daily decisions? And do game players have an advantage over others?
This is where opinions vary. Certain experts are convinced of the game theoreticians’ crucial impact on almost everything; yet there are no lesser experts who believe that game theory is nothing more than handsome mathematics.
I believe the truth is somewhere in between… though not really in the middle. In any event, it’s a fascinating field of thought that offers numerous insights into a wide variety of issues in our lives.
I hereby present a game that will give us some insights about justice.
In 1982, three German scientists (Werner Güth, Rolf Schmittberger and Bernd Schwarze) wrote an article about an experiment they’d conducted whose results surprised economists (but almost no one else). Known as the ultimatum game, the experiment has since become one of the most famous and most studied games in the world.
The game goes like this. Two players who don’t know each other are in a room. Let’s call them Maurice and Boris. Boris (the proposer in this instance) is given $100 and instructed to share it with Maurice (who is the responder) in whatever way he sees fit. The only condition here is that Maurice the responder must agree to Boris’s method of division; if he doesn’t, the $100 will be taken away and both players will end up with nothing.
It should be noted that this is a game of two fully informed players. Thus, if Boris offers $10 and Maurice accepts, Boris ends up walking away with $90. Yet, if Maurice is displeased with this offer (remember, he knows Boris has $100), both will remain empty-handed.
In the past, mathematicians didn’t pay enough respect to people’s sense of justice. They do now
I believe that this game points to the huge tension that often exists between a decision based on mathematical principles (a ‘normative’ decision) and one based on intuitive principles and psychology (a ‘positive’ decision).
Mathematically, this game is easily resolved, but the wonderful easy solution isn’t exactly wise. If Boris wants to maximise his personal gain, he should propose one dollar (assuming that we play with whole dollars, not cents).
Presented with this proposal, Maurice faces a Shakespearean dilemma: ‘To take or not to take, that is the question.’ If Maurice is an ordinary Homo economicus mathematicus statisticus – that is, a maths buff and sworn rationalist – he would ask himself just one question: ‘Which is more: $1 or $0?’
In just a few moments, he’ll remember that his kindergarten teacher used to say that ‘One is better than none’ and he’ll take the dollar, leaving Boris with $99. There’s just one little problem: surely an actual game would never go this way.
It really doesn’t make sense for Maurice to accept the single dollar, unless he truly loves Boris and wants to be his benefactor. It’s much more likely that the proposal would insult Maurice. After all, Maurice isn’t such an extreme rationalist. He has human feelings – known as anger, cravings for decency, schadenfreude, jealousy, a sense of justice. Knowing that, what do you think Boris should offer to make the entire deal happen?
Maybe, instead of maximising his personal gain, Boris should go for the simple just solution and simply equally split the sum.
I have always found this game irresistibly appealing and have made several experiments with it. As in many real-life situations, I’ve seen people turn down insulting offers, many refusing to accept, for example, less than 25% of the total (naturally, the 25% barrier applies only when the game is played for relatively small sums).
In Israel I saw people who were displeased when offered 200 shekels out of 500: deciding between 200 and 0, they chose zero! This seems like a great moment to reveal a recent major discovery in mathematics: 200 is more than 0.
This being the case, why do people make such choices? The responder knows that the proposer keeps 300 and will not accept the situation, believing it to be unfair and insulting. Zero is better for their nerves. In the past, mathematicians didn’t pay enough respect to people’s sense of justice. They do now.
From a sociological standpoint, the ultimatum game is fascinating because it illustrates the human unwillingness to accept injustice, as well as highlighting the significance of honour.
The unwillingness to accept injustice is found in children and chimpanzees. Sarah Brosnan and Frans de Waal of the Yerkes National Primate Research Center in Atlanta discovered that monkeys don’t like being subjected to treatment they deem unjust (their famous ‘cucumber versus grape’ experiment is one of the most watched clips on YouTube – and you can check that out for yourself below). This discovery points to a genetic basis in our injustice aversion.
The psychologist and anthropologist Francisco Gil-White from the University of Pennsylvania found that in small-scale societies in Mongolia, the proposers tended to offer even splits regardless of knowing that unequal splits are almost always accepted. Maybe a good reputation is more valuable than economic reward? People are not Homo economicus; we are much more complicated than this…
Haim Shapira is a mathematician and author. His book Gladiators, Pirates and Games of Trust explores how game theory influences decision-making
Primate injustice abounds in this scientific experiment…
This article was taken from the March 2017 issue of The Treasurer magazine. For more great insights, log in to view the full issue or sign up for eAffiliate membership