Race, Gender , and Class

[waffle]

Waffle, Poetix:

These are very superficial understanding of game theory, derived from watching a TV program!

And that's a 'superficial understanding' of our understanding ...

From the section (pp. 335-49) in Philip Mirowski's Machine Dreams on "what has come in retrospect to be regarded the signal mathematical development in game theory in the 1950s, the event most consequential for the subsequent history of *economics*, the invention of the 'Nash equilibrium' concept." p. 331

"The Nash equilibrium is the embodiment of the idea that the economic agents are rational; that they simultaneously act to maximize their utility; Nash equilibrium embodies the most important and fundamental idea in economics" (Robert Aumann, quoted by Mirowski on p. 343)

"Although it far outstrips our capacity, or even interest, to engage in psychological theorizing, a very stimulating comparison can be found between paranoia and the cognitive style of the masculine scientist in the work of Evelyn Fox Keller (1985). We quote some of her analysis, not so much to endorse it as to evoke some parallels with the Nash solution concept.

'The cognitive style of the paranoid ... [is] grounded in the fear of being controlled by others rather than in apprehension about lack of self-control, in the fear of giving in to others rather than one's own unwelcome impulses, the attention of the paranoid is rigid, but it is not narrowly focused. Rather than ignore what does not fit, he or she must be alert to every possible clue. Nothing - no detail, however minor - eludes scrutiny. Everything *must* fit. The paranoid delusion suffers not from a lack of logic but from unreality. Indeed, its distortion derives, at least in part, from the very effort to make all the clues fit into a single interpretation. ... For the paranoid, interpretation is determined primarily by subjective need - in particular, by the need to defend against the pervasive sense of threat to one's own autonomy. ... the very fact of such vigilance - even while it sharpens some forms of perception and may be extremely useful for many kinds of scientific work - also works against all those affective and cognitive experiences that require receptivity, reciprocity, or simply a relaxed state of mind. The world of objects that emerges is a world that may be defined with extraordinary accuracy in many respects, but is one whose parameters are determined principally by the needs of the observer. (pp. 121-22)’

"This mortal fear of abject capitulation to others is the moral center of gravity of the Nash equilibrium, and its implacable commitment to the solitary self-sufficiency of the ego is the marginal supplement that renders the otherwise quite confused and contradictory textbook justifications of the Nash equilibria comprehensible. It is also the key to linking the Nash equilibrium to the Cold War. The Nash equilibrium stands as the mathematical expression of the very essence of the closed-world mentality of impervious rationality: 'paranoids exhibit remarkable consistent and coherence in their belief systems. However, it is extremely difficult to convince such people that they have made errors in reasoning' (Einhorn in Cohen, 1981)." pp. 341-2

"the Nash solution is best glossed as the rationality of the paranoid. Nash appropriated the notion of a strategy as an algorithmic program and pushed it to the nth degree. In the grips of paranoia, the only way to elude the control of others is unwavering eternal vigilance and hyperactive simulation of the thought processes of the Other (Pierides, 1998). Not only must one monitor the relative 'dominance' of one's own strategies, but vigilance demands the complete and total reconstruction of the thought processes of the Other - *without* communication, *without* interaction, *without* cooperation - so that one could internally reproduce (or *simulate*) the very intentionality of the opponent as a precondition for choosing the best response. An equilibrium point is attained when the solitary thinker has convinced himself that the infinite regress of simulation, dissimulation, and countersimulation has reached a fixed point, a situation where his simulation of the response of the Other coincides with the other's own understanding of his optimal choice. Everything must fit into a single interpretation, come hell or high water.

"There may be multiplicity of such possible interpretations, but that is no cause for undue alarm; all that really counts is that one such comprehensive account exists, that it can be demonstrated to the player's satisfaction that it is *consistent*. (When others resist the paranoid's construction of events, usually it only serves to reinforce his paranoia.) Patently, the fact that this happens within the confines of a single isolated consciousness suspends the maximization calculation outside the conventional bounds of time and space: instead it occurs within the closed world of closely scripted apocalyptic conflicts. Equilibration is not a process, isn't learned, and it is most assuredly asocial. The fact that the mere choice of strategies could itself be construed as an act of 'communication' is irrelevant in this context; all play is unremittingly virtual. Appeals to learning or signalling or shared 'common knowledge' would be most emphatically beside the point, because the other has been rendered irrelevant." pp. 343-4

"Nash invented a distinction ... between cooperative and noncooperative games. Questions of the actual numbers of opponents (they're everywhere!) and the extent of their hostility (as expressed in conservation principles of joint valuation) are not matters of import for the paranoid mind-set. Rather, in Nash's scheme, von Neumann's minimax-cum-imputation values were to be relegated to the narrow cooperative category, as a prelude to being swallowed up by the 'more general' noncooperative approach. This mantra became the hallmark of the Nash program: 'One proceeds by constructing a model of the pre-play negotiation so that the steps of the negotiation become moves in a larger non-cooperative game [which will have an infinity of pure strategies] describing the total situation' (Nash, 1996, p. 31). The 'game' would therefore need to expand exponentially to encompass everything that would potentially bear any possible relevance to strategic play in any conceivable scenario; it would be hard to discern where the game stopped and life took up the slack. But paranoia is marked by the belief that one can defend oneself against *every possible contingency*." p. 346

"For Nash ... the act of axiomatization was the paradigm of making everything 'fit' the scheme of rationality (1996, p. 42); consistency would invariably trump tractability and practicality. Here, of course, resides the paranoid core of the Cold War fascination with formal axiomatics that so pervaded the social sciences in the postwar period." p. 347

 

[poetix]

I got my game theory from Dennett and Dawkins mainly (Curtis is entertainment), where the emphasis is precisely on the emergence of "altruistic" or non-antagonistic behaviour from a grid of competitive strategic interactions. It doesn't predict universal antagonism as an outcome, but assumes it as a premise - in a situation where I can get my first-choice optimal outcome and you can get yours (that is, a situation without scarcity) there's no "game" as such to be had.

Co-operation in game theory means all parties settling for less than their best, in order to avoid the negative consequences of competing aggressively for a prize that can't be shared (as when participants in civilised debate agree to differ instead of escalating their disagreements in the hope of ultimate victory - since the likelihood is rather that the outcome of such an escalation will be everyone's making an ass of himself). So far as I'm aware, the possibility that co-operative behaviour might eliminate scarcity, removing the strategic rationale altogether, is beyond the scope of the theory.

 

[nomadthethird]

I got my game theory from Dennett and Dawkins mainly (Curtis is entertainment), where the emphasis is precisely on the emergence of "altruistic" or non-antagonistic behaviour from a grid of competitive strategic interactions. It doesn't predict universal antagonism as an outcome, but assumes it as a premise - in a situation where I can get my first-choice optimal outcome and you can get yours (that is, a situation without scarcity) there's no "game" as such to be had.

Co-operation in game theory means all parties settling for less than their best, in order to avoid the negative consequences of competing aggressively for a prize that can't be shared (as when participants in civilised debate agree to differ instead of escalating their disagreements in the hope of ultimate victory - since the likelihood is rather that the outcome of such an escalation will be everyone's making an ass of himself). So far as I'm aware, the possibility that co-operative behaviour might eliminate scarcity, removing the strategic rationale altogether, is beyond the scope of the theory.

What exactly would "victory" in an exchange of words mean, anyway, I wonder...

One person still thinks their arguments are better and they have "won", while others still disagree and believe that they themselves have "won."

Victory isn't the "prize" in a dialogue, the thing itself is its own reward.

 

[nomadthethird]

When it comes to all of this game theory stuff, it seems to me that it's a little too in love with its own precious reduction of humans to machines-cum-computers and human behavior to a computation of various risks versus potential rewards [cost-benefit analysis?] a la some sad shareware Minefield game from 1990 [or free market fundamentalism].

I'm all for understanding humans as machines, but,

The ontological problem here is obvious: if technology is an "extension of man" (and so it would seem, would it not?--I've never bought the "technology is alienation/alienating" bit), it is computers that are created in man's image, not man in the image of the computer. Computers are machines that work according to a model that is a reduction, perhaps a refinement, of human cognition, one that mirrors the way a brain or mind works, but one that never fully replicates the human brain's biological mechanisms (only sometimes similar "outputs").

When it comes to human cognition, it's absurd (imo) to overlook biological machinery in favor of some sort of easily computable "if X then Y" code-based model. More interesting maybe would be to understand how and to what extent biological processes operate in a way that can be understood according to computational models before just assuming that minds work like computers, and therefore bodies do as well.

I've talked about this quite a bit with a friend who is a post-doc studying AI, and from what I understand, even within the field it is recognized that "cognition is not [merely] algorithmic" (my words not his, but he agrees)...

 

[nomadthethird]

I would be very interested in concrete criticism, if you had a specific instance of power, that you think cannot be phrased in terms of my definition.

How about the power a past trauma has over a person whose life is at the moment otherwise uncluttered with obstacles? Maybe this is not an "interaction" example.

How about a person who is in the grips of severe dementia or Alzheimer's? They cannot properly "interact" with other bodies/subjects because they very frequently have no idea who they are/where they are/etc. They talk but it's mostly meaningless and without regard to tasks at hand. They eat when they are hungry but often fail to have a formal "meal" at the standard mealtimes.

How would their daily interactions be mapped out according to the risk analysis sort of model? Someone like the Alzheimer's patient who is often incampable of calculating risk, I mean.

 

[poetix]

it is computers that are created in man's image, not man in the image of the computer

I don't think either is true; at least, I don't think the original/copy (God/Man) dyad is a useful way of thinking about the relationship, in either direction. Computers aren't further down (or up) the Great Chain of Being than human beings; they're just another kind of Thing, one which we happen to have stumbled across during our ramble through the design space of humanly conceivable and utilisable technology, and which happens to be quite disruptive in terms of the paradigms it suggests / supports. Something else may well come along later - I don't think we've quite got our heads round the implications of quantum computation, for example...

 

[josef k.]

How about the power a past trauma has over a person whose life is at the moment otherwise uncluttered with obstacles? Maybe this is not an "interaction" example.

I think this is a great example, which it is possible to model in game theoretical terms. The question here would be how the power of this trauma was being repeatedly instantiated and maintained in the form of a repeated series of games - habitual, linguistic, symptomatic - and then the operation against it would consist of an attempt to intervene into those games. Which is what psychoanalysis does.

One can be in game theoretical situations with non-human actors, such as fantasies, and so on...

 

[poetix]

I believe I mentioned Games People Play.

 

[waffle]

I think this is a great example, which it is possible to model in game theoretical terms. The question here would be how the power of this trauma was being repeatedly instantiated and maintained in the form of a repeated series of games - habitual, linguistic, symptomatic - and then the operation against it would consist of an attempt to intervene into those games. Which is what psychoanalysis does.

One can be in game theoretical situations with non-human actors, such as fantasies, and so on...

Lacan's Graphs of Sexuation.

Lacan examined game theory decades ago, but unlike the ego-based positivist assumptions of game theory (including transactional analysis), he was attempting to mathematically formalize some parts of ordinary language while including in this formalization the unconscious “structured as a language.” Any approach that excludes the unconscious is effectively abandoning psychoanalysis altogether, which, of course, is why the psychoanalytic cure has gone into decline, as Lacan predicted, being replaced everywhere by pomo ego-psychology/psychotherapy, etc: “When psychoanalysis has been vanquished by the growing impasses of our civilization (a discontent that Freud foresaw), the Écrits indications will be taken up by somebody”. Lacan had created a new discipline that rigorously takes into account the symbolic effects of language on human beings.

"Lacan strove to transmit his theory unencumbered by the interferences that always appear in human linguistic communication. That is why he devoted himself to a mathematical formalization of his concepts, since, in an algorithm, everything is transmissible and not subject to the loss that occurs in ordinary language. At stake is a map of the psyche that connects the agencies (symbolic, imaginary, and real) and that dispenses with Freud’s unusable diagram of the psyche published in The Ego and the Id (1923). Lacan’s first attempt, based on vector analysis, is schema L’, published in 1956 (Écrits, p. 53). The last formalization is grounded in topology and knot theory; Lacan uses the Borromean knot and the Möbius strip as his models."

"In this light, Lacan's important recourse to game theory also becomes explicable. For game theory involves precisely the attempt to formalise the possibilities available to individuals in situations where their decisions concerning their wants can in principle both affect and be affected by the decisions of others. As Lacan's article in the Ecrits on the "Direction of the Treatment" spells out, he takes it that the analytic situation, as theorised by Freud around the notion of transference, is precisely such a situation. In that essay, Lacan focuses on the dream of the butcher's wife in Freud's Interpretation of Dreams. The said 'butcher’s wife’ thought that she had had a dream which was proof of the invalidity of Freud's theory that dreams are always encoded wish-fulfilments. As Freud comments, however, this dream becomes explicable when one considers how, after a patient has entered into analysis, her wishes are constructed (at least in part) in relation to the perceived wishes of the analyst. In this case, at least one of the wishes expressed by the dream was the woman's wish that Freud’s desire (for his theory to be correct) be thwarted. In the same way, Lacan details how the deeper unconscious wish expressed in the manifest content of the dream (which featured the woman attempting to stage a dinner party with only one piece of smoked salmon) can only be comprehended as the coded fulfilment of a desire that her husband would not fulfil her every wish, and leave her with an unsatisfied desire."

 

[nomadthethird]

I don't think either is true; at least, I don't think the original/copy (God/Man) dyad is a useful way of thinking about the relationship, in either direction. Computers aren't further down (or up) the Great Chain of Being than human beings; they're just another kind of Thing, one which we happen to have stumbled across during our ramble through the design space of humanly conceivable and utilisable technology, and which happens to be quite disruptive in terms of the paradigms it suggests / supports. Something else may well come along later - I don't think we've quite got our heads round the implications of quantum computation, for example...

Good point, I suppose using the original/copy language was a poor way of stating what I meant.

 

[3 Body No Problem]

My answer will use the name "interaction theory" to stand for the various theory strands that seek to theorise interaction, including what it traditionally known as game theory.

Game theory developed out of the instrumentalist utilitarianism of rational choice theory (which considers only rational actions performed because they are assumed to be 'rational'), and this is why all of its early applications were in mainstream
bourgeoise economics, as attested to by the title of the first text on the subject, John von Neumann and Oskar Morgenstern's 1944 Theory of Games and Economic Behavior.

It is true that a lot of work in interaction theory was done by with a view towards economics. But that far from exhausts the subject, and, as I have pointed out before. Moreover, von Neumann and Morgenstern point out the provisional nature of their assumptions about rationality, but argue that one has to start somewhere with simple assumptions about human behaviour, to be refined later.

I would imagine that the right way to criticise a scientific work is to come up with something better.

Game theory developed out of the instrumentalist utilitarianism of rational choice theory (which considers only rational actions performed because they are assumed to be 'rational'), and this is why all of its early applications were in mainstream

No, RCT theory was developed after interaction theory. While it is true that economists of a market-friendly variety have done much work using a specific special case of interaction theory, this is just one application, not the whole thing.

By defining the political field as simply a game it serves ideology: game theory becomes an effective strategy for disavowing the political altogether,

No, this is wrong, politics is clearly an instance of interaction theory, and my own analysis of power grew out of an interest in politics and social theory. I think that e.g. Marx work on class formation can easily be seen as a special case of my analysis.

Incidentally, in his General Theory of Exploitation and Class, Canadian Marxist John Roemer used rational choice and interaction theory in order to demonstrate how exploitation and class relations may arise in the development of a market for labour. Another Marxist, Adam Przeworski, in his Capitalism and Social Democracy used rational choice theory and interaction theory to theorise the process of revolution.

substituting a post-political realm of managerialism, strategy and 'expert' administration, so seemingly shutting down all social antagonisms and real choices (but in fact relying on a politics of fear: it is hardly coincidental that game theory became popular during the Cold War).

No, interaction theory is a convenient basis for theorising social antagonisms, in fact better than all known alternatives.

What's interesting from the game example above between AA and BB is that it conceives of rational decision-making

No, this is wrong, my definition consciously avoids using any assumptions about rationality.

that it conceives of [...] pre-determined structure devoid of all agency:

No, this is wrong, my definition explicitly supposes actors as participants in the interaction, to quote myself: "Assume two actors AA and BB", and "AA thinks of him/herself as being able causally to bring about".

I suspect that you don't understand the concept of agency and actor.

in game-theoretic scenarios, free choice and predestination are strictly equivalent

No, this is wrong, interaction theory is explicitly and self-consciously a theory of actor choice, otherwise it would be pointless.

(AA has no real choice in the above game, for by failing to select the 'right' choice he is, according to the rules, irrational and therefore 'breaking the rules', which is disallowed.

No, this is wrong. By definition, AA has choices. Please read what I wrote: "AA thinks of him/herself as being able causally to bring about w or x". In reality, actors have more than two choices, but for didactic purposes, I have presented it with two choices only per actor. I assume that my readers will be able to generalise this to an arbitrary number of choices.

In particular you commit a category mistake by confusing the theortical analysis (meta-level) and "breaking the rules" w.r.t. to socially constructed rules that the actors might see in the society they are part of (object-level). For example a thief knows that stealing is breaking legal rules in his/her societies, but that can be modelled perfectly well in my setup, where breaking object-level social rules would be modelled as one of the available choices.

It's oppressively pre-rigged from the start, substituting faux choices for real ones.

No, that's wrong, interaction theory seeks to be a theory of the real choices the modelled actors have.

game theory assumes that at the limits of our ability to calculatively predict the conduct of other subjects, the only 'rational' thing to do is precisely to presume the pre-existence of fixed, dehistoricized, and impersonal social norms regulating our own conduct and that of others ie to assume that the Big Other exists.

No, interaction theory assumes no such thing. Interaction theory is explicitly and self-consciously historicising, which is why it is so interested in "history-sensitive" strategies. I would also like to reiterate that my own definition was explicitly historic, to quote myself again:

My definition of power is implicitly also temporalised (I should have stated that more clearly, but didn't want to complicate too much). It is based on preferences and expectations. But there's no reason to assume that preferences and expectations are temporally stable, and in fact, it's easy to give examples of changing preferences and expectations. With these changes, power changes. A typical example is the subjugation of women: as long as they were financially dependent on men, the latter had a lot of power over women. With the rise of female employment and financial independence, this has changed.

 

[3 Body No Problem]

The real essence and thrust of game theory lies in its materialism - the point is not that all games are unfriendly, but rather that the principle of "friendliness" is not metaphysical, but rather susceptible to analysis in game-theoretical terms. What are the benefits of maintaining a friendship? They may be economic, political, libidinal, intellectual... but the wager of game theory is that they can be understood calculatively. Is this not preferable to (bourgeois, liberal) sentimentalism?

I'm afraid, that's also not correct. The notion of calculability is very well investigated, and it is trivial to produce games that are provably not calculable.

In fact, the last couple of years have seen a revolution in game theory through the analysis of the complexity of computing equilibria/optimal strategies and the like. It turns out that computing equilibria/optimal strategies is very hard. And if that's how, we have no particular reason to assume that markets can find it. To paraphrase a deep thinker: "If your laptop can't find a Nash equilibrium, neither can the market".

See this wonderful book for details.

 

[3 Body No Problem]

So far as I'm aware, the possibility that co-operative behaviour might /eliminate/ scarcity, removing the strategic rationale altogether, is beyond the scope of the theory.

Not at all. You just need a more complicated game where co-operative behaviour to eliminate scarcity is one of the behavioural options. Game theory is very general. In principle GT is can be a theory of everything. The problem with GT (and any other theory) is that as soon as soon as you make the game complicated, it becomes quickly hard to analyse.

 

[3 Body No Problem]

More interesting maybe would be to understand how and to what extent biological processes operate in a way that can be understood according to computational models before just assuming that minds work like computers, and therefore bodies do as well.

Of course this is being done, see for example here. The reason for models that you deem too simple is not that the modellers are maliciuos or stupid, it's that more realistic/complicated models are hard to come by and to understand. It's easy to make fun of simplistic assumptions in economics or in computational models of mind. The real point is to come up with better models.

I've talked about this quite a bit with a friend who is a post-doc studying AI, and from what I understand, even within the field it is recognized that "cognition is not [merely] algorithmic" (my words not his, but he agrees)...

There is the more basic question of whether physics (e.g. as embodies in the laws of quantum mechanics) is computable. If physics is computable, then cognition is computable. As far as I'm aware, this question has not been fully resolved. Whether good, humanly usable models are computable in an easily appreciable way is another question.

My presonal belief is that so far we have not discovered anything that is in principle not amenable to a computable analysis/simulation, but it's just a heuristic, I'm happy to be convinced otherwise.

How about the power a past trauma has over a person whose life is at the moment otherwise uncluttered with obstacles? Maybe this is not an "interaction" example.

Interesting example. I'd concur with your not-an-"interaction" interpretation, but would like to add that metaphorically, and relying on the human propensity to anthropomorphise, we can think/speak of a trauma as an actor. Moreover, the trauma -- qua trauma -- would threaten the traumatised person with some form of dread that he/she is trying to avoid, hence the traumatised person conceives of alternatives: being subjected to the horrors of the trauma, and finding some kind of (possibly temporary) diversion that banishes the trauma. It seems that in this metaphorical sense, the
example fits quite well.

How about a person who is in the grips of severe dementia or Alzheimer's? They cannot properly "interact" with other bodies/subjects because they very frequently have no idea who they are/where they are/etc. They talk but it's mostly meaningless and without regard to tasks at hand. They eat when they are hungry but often fail to have a formal "meal" at the standard mealtimes. How would their daily interactions be mapped out according to the risk analysis sort of model? Someone like the Alzheimer's patient who is often incampable of calculating risk, I mean.

But what is the power here that we seek to analyse? Alzheimers?

 

[jambo]

Not at all. You just need a more complicated game where co-operative behaviour to eliminate scarcity is one of the behavioural options.

Precisely the sort of thing R. Buckminster Fuller was interested in, actually it's not even necessarily more complicated.

http://en.wikipedia.org/wiki/World_Game

 

[josef k.]

I'm afraid, that's also not correct. The notion of calculability is very well investigated, and it is trivial to produce games that are provably not calculable."

3BNP - Do you mean not rationally calculable from the perspective of the agent involved in the game, or not calculable at all, even from the perspective of an external analyst. And in either case, could you give an example?

 

[waffle]

My answer will use the name "interaction theory" to stand for the various theory strands that seek to theorise interaction, including what it traditionally known as game theory.

This is called moving the goal posts. I understand that game theory is still called game theory.

It is true that a lot of work in interaction theory was done by with a view towards economics.

Game theory originated from neoclassical economics and its long discredited assumptions about the world, dating from the 19th century: methodological individualism, methodological instrumentalism, and methodological equilibrium.

No, RCT theory was developed after interaction theory.

Again, rational choice theory originated with neoclassical economics, over a century before game theory.

No, this is wrong, politics is clearly an instance of interaction theory, and my own analysis of power grew out of an interest in politics and social theory. I think that e.g. Marx work on class formation can easily be seen as a special case of my analysis.

This is absurd. Nuts.

No, this is wrong, my definition consciously avoids using any assumptions about rationality.

Avoids articulating its faulty premises ("assumptions").

No, this is wrong, my definition explicitly supposes actors as participants in the interaction, to quote myself: "Assume two actors AA and BB", and "AA thinks of him/herself as being able causally to bring about".

More faulty premises. Fantasies of agency.

No, this is wrong, interaction theory is explicitly and self-consciously a theory of actor choice, otherwise it would be pointless.

You might want to review your assumptions about, and conception of, agency.

No, this is wrong. By definition, AA has choices. Please read what I wrote: "AA thinks of him/herself as being able causally to bring about w or x". In reality, actors have more than two choices, but for didactic purposes, I have presented it with two choices only per actor. I assume that my readers will be able to generalise this to an arbitrary number of choices.

There are ten brands of beans in my local supermarket. TEN!! And all with a variety of seductive 'carrot' ('buy one get one free', 'improves libido') and repressive 'stick' ('all other brands make you fat') inducements. AA doesn't like supermarkets.

 

[3 Body No Problem]

3BNP - Do you mean not rationally calculable from the perspective of the agent involved in the game, or not calculable at all, even from the perspective of an external analyst. And in either case, could you give an example?

An example of a game where we (as players) don't currently have winning strategies is chess: we know that chess must have a winning strategy, because it allows only a finite number of game sequences. But nobody knows what a winning strategy might be. That reflects our lacking understanding of the game and our lacking computational power, because we cannot currently build a machine that can simply iterate through all possible games of chess and compute a winning strategy.

A game that has a winning strategy that is not calculable (mechanically computable) at all would be the following, Goedel Game:

It has two players AA and BB and at each round in the game, we have a set Sn of mathematical formulae in the language of Peano arithmetic.

• In the 0th round that set S0 is empty
  
• In the n+1st round the player whose move it is (AA starts and from then on AA and BB alternate moves), can do either:
  • Show that the set Sn is formally inconsistent (i.e. the set of formulae allows to prove 0 = 1), in which case that player wins, or
  • Add a mathematical formula to Sn, creating the set S(n+1).
    
• If the game goes on forever, AA wins.
  

There cannot be a winning strategy for this game that is "calculable" in the sense of mechanically computable. However, there still is a winning for AA, namely whenever it's her turn, and Sn is formally inconsistent, then AA proves 0=1 from Sn, otherwise to add a harmless formula like 0 = 0.

It's not totally unreasonable to argue that a variant of the Goedel Game is being played, and it's known under the name "Mathematics".

 

[3 Body No Problem]

This is absurd. Nuts.

Thanks for your exceptionally well argued dismissal.

 

[3 Body No Problem]

There's a lot of misunderstanding and misapplication of the Oedipus complex in popular culture. It's not about literally wanting to have intercourse with your own parents,

I'm afraid the opposite is true. Freud has gone out of his way to emphasise that the OC is not symbolic, that children really want to be incestous with their father/mother. One of the reasons for breaking with former acclytes like Jung was that the latter declared the OC to be merely symbolic.