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