By Philip Pilkington, a journalist and writer living in Dublin, Ireland
I prefer the company of peasants because they have not been educated sufficiently to reason incorrectly.
– Michel de Montaigne
The so-called ‘games’ depicted in game theory include some particularly disingenuous and evasive intellectual constructions. In times past people devised rationalisations in the most fantastic of ways, summoning up imaginary demons, angels, witches and warlocks to contextualise their psychological and existential difficulties. Today, some turn instead to mathematical games.
Long ago our ancestors constructed mythological systems wherein the world was a place inhabited by mystical and animistic forces. Those who summoned these forces generally lived in close proximity, giving immediate presence to magic and intrigue. Religious systems came later. These were more abstract and impersonal; the leader-figure no longer lived nearby and miracles became increasingly rare and valued.
After some time the more “civilised” and organised societies began to create more rational theologies. By fusing the key structural aspects of the religions with certain metaphysical principles, great systems were constructed that vied with one another for authority.
It was all imagination of course. All of these systems were just ways that men made sense of the world around them. These great mythic, religious and theological systems were just rationalisations used to organise and lend authority to otherwise arbitrary social institutions. The most important and probably most primal among these institutions was marriage, which we will have ample occasion to return to in what follows.
The Age of Enlightenment came next and with it the more fantastic products of the human imagination were dissolved into the bland homogeneity of Reason. The Enlightenment philosophers described social relations primarily in terms of equality – an obvious value judgment on their part. The world was not an equal or a harmonious place, but the Enlightenment philosophers pretended as if it were and concocted their ideological systems accordingly. To look back on the crass oversimplifications these men came up with – many of which continue to haunt us today – is an exercise in both entertainment and caution.
Those that did raise issues of conflict and change – like Hegel and Marx – quickly veneered over them with vast metaphysical and teleological systems that assured us all that society was moving from point X to point Y. The imbalances, they both thought, would be levelled by History – an unstoppable moving force that would reduce all to complete equality and homogeneity.
Today the great leveller is ‘The Market’. And neoclassical economics is the great metaphysical system that supports it. The Market, we are assured, is moving to a state of harmony and equilibrium – an equality in the sense that everybody will be content, of course (they will have their ‘utility maximised’).
What characterised the later metaphysical systems however – modern economics included – was that they banished the relations they were trying to describe to the margin, only to take them up by applying to them pre-constructed systems of reasoning. While marriage – which we take again because it is, as the anthropologists well know, the primal social institution – is absolutely central to social organisation it is completely ignored in the latter day systems. Whereas it occupied a central role in the older systems, it is only dealt with by the later systems by applying pre-established principles (marriage is a utility-maximisation operation; marriage will be unnecessary under Communism etc.).
But every now and then these more primal social relationships bubble up in the new doctrines. And when they do the effort to force fit them into the new construct is far from convincing.
Back to game theory. Why do we claim that it is so evasive? Because it nakedly displays the nature of the material it deals with and then denies that it is indeed this material that it is dealing with. Game theory sets up ‘games’ between certain personalities and then claims that the players have no personalities.
The ‘Battle of the Sexes’ game is perhaps the most outlandish example of this. The game, as we will see, is blatantly a psychological construction set up to assuage the theorist that he has a perfectly rational means with which to understand his/her interpersonal relationships. The theorist sets up a game that deals with a difficult interpersonal marital issue and then tries to solve it with various mathematical formulas. When this psychological dimension is pointed out to the game theorist they vigorously deny it, claiming that it is only a ‘pure’ mathematical game and says nothing about his or her conception of their own interpersonal relationships; this even though they have explicitly labelled this game ‘the battle of the sexes’ and allowed the participants’ relationship to be that of an intimate couple.
Here’s how the game works. We have a man and a woman. We assume that they are in a long-term relationship, most likely married. The man wants to go to a football game and the woman wants to go to the opera. They both want to go somewhere together, so they will not simply go their separate ways to their desired event.
Game theorists see two so-called equilibrium points. One is that the couple go to the football game; the other is that they go to the opera. The game theorists then tie themselves in knots trying to figure out probabilities and equitable solutions. They torture themselves when they find that in order for equilibrium to be obtained one ‘player’ has to lose. They introduce bizarre tropes to equalise this, one being a ‘randomising element’ – in other words the couple agree to flip a coin to see which event they will attend.
What a pile of garbage!
Let’s say I’m writing a script or a story wherein such a circumstance arises. Do I break out my game theory book and do some calculations in order to decide how to move the plot forward? Of course not. Instinctively – based largely on empirical experience and common sense – I would argue that there are only two probable outcomes to this so-called ‘game’:
(1) The person assuming the masculine role submits and the couple attend the opera.
(2) The person assuming the masculine role remains recalcitrant, the ‘game’ breaks down and the couple go home.
Yes, there is a certain amount of stereotyping undertaken here. Yes, some people negotiate their relationships differently. And the answer in real life probably depends in particular how extreme one partner’s aversion is to the other’s choice.
But when dealing with this sort of material we’re always dealing with stereotypes and ‘averages.’ Anyway, they can be modified later if we wish. For now, let us just try to tease out some of the underlying structure.
The ‘game’ will not stop there. Two new ‘scenes’ arise organically from both these outcomes:
(1) After the opera the couple return home and have an, erm, romantic evening.
(2) The couple have a temporary falling out. The person assuming the masculine role then make amends and possibly gives the person in the feminine role a gift.
Again, these do not follow from each other in some quasi-mathematical or pre-determined manner, but they form a coherent narrative. They are realistic and convincing representations of the so-called ‘game’.
Before moving on to the implicit rules structuring this so-called ‘game’ let us note a few things:
(1) As we will see, the ‘game’ is not based on a relationship of strict equality. We cannot interchange the two ‘players’ with one another without changing the outcome (for a given ‘player’). Their position vis-à-vis one another determines the potential outcomes of the ‘game’. Their positions are thus not static, but relational.
(2) The relational positions of the two players are implicitly structured by ‘external’ rules that must be taken into account before establishing how the ‘game’ will be ‘played’.
(3) The ‘game’ does not have to result in so-called ‘equilibrium’. It can easily break down. We can assume that an infinite and unknowable amount of variables ‘plug in’ to the ‘game’ in order to determine the outcome. Everything from the mood of the two ‘players’ to the nature of the events that they may attend must be taken into account. These elements are 100% unknowable prior to being empirically established and even then they are probably impossible to pin down.
Let us now move onto the implicit rules structuring the so-called ‘game’. Again, we will have to engage in some pretty heavy stereotyping here but such is the nature of the material. Different ‘games’ could easily be constructed taking into account different personal or cultural ‘rules’. Our exposition is merely to try to provide a deeper understanding of what really determines the outcome of such ‘games’ and why game theory is a pointless and absurd device for even trying to approach this sort of thing.
Rules of the Game
So, let’s say that our little narrative appears convincing. Yes, it is almost crassly stereotypical and would not apply to every couple under the sun, but let’s accept it as a ‘model case’ of sorts. What are the structuring principles that lead to the outcome of our so-called game?
When boiled right down this is implicitly an issue of debt. The key rule structuring the ‘game’ is that the player assuming the masculine role is always already in debt to the player assuming the feminine role. There is no need for us here to try to understand why this is the case, we will merely hint that it probably has to do with certain marital/sexual institutions and norms in Western culture (again, and we must stress this: these are not universal).
This ‘indebtedness’ is the key element that leads to the possible outcomes of the game. Either the player in the masculine position plays ‘by the rules’ or the game breaks down. This means that the ‘game’ starts out from a position of inequality rather than equality. Indeed, the implicit argument here is that any ‘game’ that is set up will always start out from a position of inequality and the very idea of a ‘game’ that begins from a position of equality is a mere fantasy. It is the dimension of debt – a burden of debt, as it were – that enforces this inequality at a structural or institutional level.
The ‘game’ thus has no ‘equilibrium’ position. Instead it should be seen as a relationship of force based upon given rules. The rules allow the game to potentially have a sociable but not immediately equitable outcome. Without the rules the ‘game’ would merely break down into bickering. Of course, if force is pursued outside the rules by the player in the masculine position the game will fall apart anyway. So, while the rules give the game a path through which it can be resolved in a fairly sociably acceptable way they do not pre-determine the outcome of the game.
Does this make the game a zero-sum game plain and simple? Does this mean that the player in the masculine position always ‘loses’? No. Recall that we have already alluded to what other outcomes the game would likely have in the medium-run. By reaching a socially equitable compromise – albeit one that they are not particularly pleased with – the player in the masculine position will likely get a ‘payoff’ eventually. It is also likely that said player is quite consciously aware of this.
Because the outcomes of the game run throughout time and are the basis of a relationship that cannot be said to be constantly ‘in balance’, it should not be thought of in terms of equilibrium. There is no static equilibrium. There are simply relations of force structured within social rules or norms. Again, this is not to imply that this is an institutional structure that is completely unstable. Instead it should be seen as an institutional structure that, being constantly out of balance, requires that the participant constantly negotiate various forces that threaten to destabilise the entire structure.
Of course, when you strip away all the fancy language the point being made is rather simple: relationships – all human relationships – never tend toward some sort of fantasy ‘equilibrium’ position. Rather, they are inherently mired in power-imbalances and compromise formations or rules that allow these imbalances to be navigated. Most of the time the compromise formations (or: rules) hold; but sometimes when the power-imbalances become too pronounced and the entire structure of the relationship breaks down.
Arrested at a very primitive level of psychological development game theory cannot even begin to approach this. Indeed, one would be better trying to derive lessons about the real world from a consultation with a fortune-teller or a shaman – they tend to be more subtle psychologists.
Game theorists will, of course, tell me that I have cheated and misrepresented them. “We only play ‘pure’ games,” they will protest. “These are not supposed to be applied to real people with real psychologies in real institutional settings.” If the reader cares to look over the series of ‘games’ that the theorists set up – replete as they are with characters ranging from star-struck lovers to nefarious crooks – and finds the game theorists’ defence to be a credible one then they can happily discount my argument.
For my part, I don’t believe this defence for a second. It is quite obvious what the game theorists seek to do, constructing their little islands of Reason amidst the great sea of indeterminacy and change in which we all exist. Perhaps, indeed, we all need something to hold on to amidst such chaos and tumult. But surely we can do a little better than this crude child’s play that the game theorists have concocted.