Toward the Game Theory of Everything

On July 22nd Business Insider published an article titled “They Finally Tested The ‘Prisoner’s Dilemma’ On Actual Prisoners — And The Results Were Not What You Would Expect“.

There are few different variations of the dilemma. The study uses this one: “Two criminals are arrested, but police can’t convict either on the primary charge, so they plan to sentence them to a year in jail on a lesser charge. Each of the prisoners, who can’t communicate with each other, are given the option of testifying against their partner. If they testify, and their partner remains silent, the partner gets 3 years and they go free. If they both testify, both get two. If both remain silent, they each get one.”

The article claims that as per the game theory betraying the partner should be the dominant strategy even if mutual co-operation would be the best outcome for the both player. (This interpretation and analysis of the dilemma is a bit too straightforward to my taste. See Stanford Encyclopedia of Philosophy’s article on the prisoner’s dilemma for more complete analysis.) For me it wasn’t a surprise that humans are more cooperative than the purely rational models used traditionally in economics predicts. Applying the game theory to social reality is a tricky thing to do right.

Then again, the game theory could work, but… That’s the subject of this blog entry.

Evidence against the game theory?

Among my social network the most common interpretation was that the study is a counter-evidence against the games theory. Prisoner’s dilemma in overall can be seen as a counterexample against the game theory.

I’m unwilling to do such a hasty conclusion. It might be an evidence against the self-interested, calculative and rational behavior suggested by the game theory. On the other hand, the study may as well just show that our conception of what is beneficial or desirable for an individual is too limited, or that the used interpretation of rationality is too narrow.

A rational agent

A problem in the game theoretical models is that every now and then even intelligent and well-informed persons behave differently than the model predicts for reasons that are intuitively clear and understandable for other. To be useful a model need to be complete and errorless, but if it gives false predictions that are in addition counter-intuitive there something wrong in the model. In my opinion the problem is not in the game theoretical approach per se but in the preferences the models (arbitrarily) expects the rational agents to have or to not have.

Since I don’t want to take preferences for granted, I start by defining a rational agent slightly differently than normally: A rational agent always tries to attain the most beneficial overall outcome for itself in a systematic and consistent way. A rational agent can be a person, organization, machine or software. The most beneficial outcome for an agent is defined directly or indirectly by its needs (e.g. it is rational to seek food if you are hungry).

By ‘need’, I refer a mechanism that makes an agent to prefer one alternative over another, rather than to prefer nothing. In case of organizations ‘demand of something’ is a need. In case of machines, the need is a preprogrammed “state of satisfaction”. E.g. think of an intelligent painting robot. It have a ‘need’ to paint ever point of surface with minimum amount of paint and within minimum amount of time. That state of satisfaction defines and determines its decision making and learning everywhere. In case of human, ‘need’ means pretty much what you expect it to. We have a basic need for nutrition, and not-so-basic need for financial prosperity. Our ability to evaluate benefits of different outcomes is derived from the needs. We are able to evaluate financial value of an object (most likely) because we have a need for financial prosperity, otherwise we would find such an evaluation irrelevant and obscure.

Within this definition an agent is irrational only in two cases:

  1. if an agent does an error in deduction. I call this ‘unintentional irrationality’.
  2. if we have a bounded context for rationality in which we ignored intentionally some of the de facto needs an agent have and the agent’s decision was based on an ignored need. I call this ‘contextual irrationality’.

My position here is naturalistic: I don’t take preferences, goals or expected value of an outcome for granted or as objective facts. There is no god-like point of reference or a platonic world or ideas that would make an outcome valuable or preferable. There is only a system (or a machine – organic, abstract, electronic etc.) that produces the preferences and the evaluation functions from the needs and the information the system have or can achieve. In case your backgrounds are in the continental philosophical tradition, I believe that the ‘needs’ are more or less equivalent to Deleuze and Guattari’s ‘desire machines’. Yet, I’m not completely sure on that.

The question on self-interest

Back to the prisoner’s dilemma.

According SCARF model (see David Rock’s article on SCARF form NeuroLeadership Journal: autonomy – control over one’s environment; a sensation of having choices – is just one of five primitive needs we have. There are at least two others that are relevant in the case of prisoner’s dilemma: social relatedness and fairness. According SCARF model relatedness and fairness are as strong needs as autonomy and may even be as strong as Maslow’s basic needs (e.g. food and physical safety).

If SCARF model is true, a person who have a strong need for fairness and who acts systematically and consistently to make the world around fairer, is not only rational, but also behave in self-interested and calculative way.

You cannot claim that ‘minimizing the expected time in prison’ is necessarily more rational, beneficial and self-interested goal than fairness toward the other prisoner – for some actor it is, for another it’s not. At least, you need one more premise to make such a conclusion: “For agent X objective to ‘minimize the expected time in prison’ base on presently stronger needs, and thus is presently more desirable for him, than the objective to do a maximally fair and mutually optimal decision.”

If the needs of an agent did not define what is self-interested behavior, what would? The theories of rationality are often biased by an idealistic conception of self-interested behavior. The contradiction between altruism and self-interested behavior is often delusive, but still possible in certain situations.

Simplistic game theory

In order to fulfil needs and desires alike fairness or relatedness, a rational agent needs to do such calculations for which classical game theory is a bit simplistic and naive.

The game theory is not simplistic because it seems to ignore psychological facts about human nature; because it presuppose that all actors are rational but in real world we sometimes seems to act irrationally. Psychology is here somewhat irrelevant. You can see the game theory as a purely mathematical theory that – obviously – is poorly adapted into psychology and sociology.

A game theorist can always claim that our mathematical model of the psychological reality is incomplete (within the bounded context we are interested in). If it was complete and sufficient within the context, the game theory would be fully applicable. A game theoretical model could take (for instance) emotions into account; it could mathematically model them within sufficient extend –not completely but extensively enough. If a practical application of the game theory doesn’t do that even if it should, it does not prove anything about the mathematical core of the game theory.

Rather, the concurrent game theory is simplistic, because it focuses almost solely on the first order desirable outcomes and needs and ignores almost completely the second and third order desirable outcomes and needs. Because of that, you can use it only in limited contexts. Often the limitations are a bit too strong and a game theoretical model becomes rather only a theoretical model than a practical one.

Winning strategy vs. heuristic strategy

The second order preferable outcomes and needs relates to the properties of the structure of reality. Fairness and certainty are examples of such properties. (For sake of clarity, I ignore “non-living machines” for now on, as we don’t have machines that do decisions on this level.)

While the first order outcomes are immediately attainable factual things or states of things (e.g. freedom or two years in prison), the second order outcomes are something people want to maintain, improve or change, but they cannot have or attain them. That is, people cannot achieve fairness as a factual thing, but they can make the world around more fair.

Achieving a second order desirable outcome requires a heuristic strategy rather than a winning strategy: “What it is means to be fair and to be treaded in a fair way?” before “how to ensure fairness regardless of what ‘moves’ the other agents do?” A rational agent cannot know in advance what would be the optimal, because the optimal state is not a state the actual world but of the all relevant possible worlds. The meaning of fairness depends upon what an agent is able to expect from the others in any actual and counterfactual situation. The heuristic strategy is about finding the relevant possible worlds. It is noteworthy that ‘possible world’ is already a concept of the game theory. It is needed for to understand probabilities. Then again, possible world are more than just probabilities and the game theory seems to ignore many aspects of this concepts.

Winning strategy vs. reflective strategy

The third order desirable outcomes and needs relates to generative patterns of observed social, physical and internal reality. They are building blocks of the subjective reality. The needs for creativeness and relatedness are examples of them.

Often, the theories of rationality faces serious problems with the third order outcomes and needs. Why an artist wants to be an artist even if the society sees him as an obsessed outcast and he has barely enough money to food and shelter? Why a soldier was ready to do die (and also died) in order to protect his family and countrymen? For a theory of rationality, it’s problematic if you need to explain some systematic and consistent decision making paradigms – like artist’s passion to do art or soldier’s patriotic self-sacrification – as insanity and irrationality even in those cases we emphatically understand the reasons behind the decisions of an agents and they are not insane or irrational. I’m saying that dying for others – for instance, can be completely rational and self-interested action. Its rationality depends upon how you define yourself and your relation to everything else.

Now, consider creativeness and a need for creative insights. There is no heuristic map nor winning strategy toward creative insight. Creativeness is not attainable state of things in actual or possible worlds, nor is it about understanding what it is all about. Yet, it is not random, arbitrary thing either. You can have a strategy toward a state in which your need for creativity is temporarily fulfilled: a reflective strategy. The reflective strategy is “pattern matching with your life and identity”. The both examples illustrates that suddenly the question “who is the subject called ‘me’ whom an outcome is more beneficial than another one?” always precedes the question “what actions are maximally beneficial for me in this situation?” Re-identification and re-initiation of the agent itself is a rational strategy toward ‘a better real’.

This is rather far from the classical theory of the rational agent and the concurrent game theory. Nonetheless, the idea is simple, an agent is a system that can affect surrounding reality that is also a system. The system of self is not separate from the system of the surrounding‘. Thus, a change in the system of self is always a change is the system of surrounding reality (including both the actual world and the possible worlds). This is the reason why changing your perspective to a hard problem is a very efficient problem solving method. That is, a change of self is obviously rational action, but it’s hard to explain why exactly this change was rational – why I chose this change of self rather than that? Even in case of problem solving this is far from obvious; social situations requires are far more complex rational changes of self.

Perhaps, a game theorist could claim that the second and third order goods and needs can be reduced into first order desirable outcomes, preferences and needs. I find such a claim poorly justified. I personally think that the need for creativity or fairness for instance are irreducible to first order needs like physical pleasure, status (or observed appreciation), satisfaction and safety. There are games that can be understood fully via a winning strategy of the traditional game theory (e.g. chess). Social reality, for instance, is not such a game. In order to attain the most beneficial outcomes for us in the game of social real, we need also heuristic and reflective strategies. After all winning is irrelevant, if we win things that does not matter.


The study mentioned above is not necessary an evidence against the game theoretical approach to human behavior. It just clarifies the boundaries within which the concurrent game theory can be applied. Despite of this study, the game theory can still be applied within certain, rather strict constraints without any problems. Actually, the study – as presented in the article – is about internal logic of a rational agent rather than the game theory. Perhaps in future we have the game theory of everything that would apply in any situation. Actually, I hope we do, since the game theory is pretty cool thing. 😉

However, in order to have the game theory of everything we must understand better the internal logic of rational agents and the ways an agent interacts with the surrounding reality. We also have to answer more accurately to the question “in which sense rational”. And at last, we have to pay more attention in the modalities and the semantics of possible worlds.