Noether's theorem tells us that (for a non dissipative system) evidence of a symmetry is proof of a conservation law or conserved property.
The Mahabharata displays two systems of symmetries in a remarkably systematic and well thought out manner. People like Buitenen and Lal had noticed the 'two trees' motif- the duality- the fact that everything happens twice, each character has a dual, every episode ties up with or reflects some other episode- it is as though the bards were continually employed in a type of double entry book-keeping.
Nothing is accidental, or a matter of chance, in the Mbh.
The two conserved principles, so to speak, in Mbh are karma and dharma. Karma, operating across life-spans, gives coherence and meaning to everything that is experienced. Dharma- operating across the social space- makes social life meaningful and socially defined entitlements and obligations a proper subject of study.
How does this relate to game theory? Well, we notice that Yudhishtra, to become a just King, must learn probability and tactics. He comes to see that virtue and morality is actually a vector, not a scalar. We are getting to a notion similar to the notion of Evolutionary Stable Strategies- i.e. a range of ethical choices all equally valid. Balaram is not condemned as a drunkard for refusing to fight. Krishna is not condemned as being partial to Arjuna for assisting him.
Yet the outcome of Mbh is not perfectly symmetrical. Though the Pandavas win, it is a tragic outcome.
The symbiotic nature of the Kaurava Pandava dichotomy had been pointed out early on by Sanathkumara who employed an ecological analogy- 'without the forest, the tiger dies. Without the tigers, the forest disappears. Your sons (Kauravas) and the Pandavas are like the forest and the tigers.'
Yuddhishtra can understand this. Dhritarshtra can't. When Yuddhishtra offers to fight Dhritrashtra himself he recognizes that the Kaurava principle of Power politics had as much validity- indeed, it is the starting point for- his own. The optimal solution lay in a meta-game.
The relationship of the Gita to game-theory arises from the fact that 'meaning is being gamed'. This fulfills the condition of apoorvata such that on each reading, or each hearing, there is something new and therefore the condition for Gita to be considered Shruti is fulfilled. This is nothing to do with rituals. Gita can be heard in any language where the author was properly inspired rather than just a translator.
In what manner is 'meaning being gamed'? Well, Krishna is arguing for a purpose not just showing off. Initially it looks like the Lord- out of love for his friend- has made a mistake. To spur on Arjun's martial spirit- while at the same time showing him the need to be cautious and plan things out- Krishna straight away takes him to see the two chiranjivis (immortal, unvanquishables) on the other side. This should stir up Arjun as well get him to think carefully. But, Arjun (unlike Dhrtrashtra) is so confident he starts thinking his foes are already dead! (Alternatively, we may note that a Gandharva had gifted Arjuna with cakshushi vidya- a sort of second sight. This parallels Krishna's own gift- mentioned in Chandogya. However, notice that whereas the Gandharva's caksuci yields only Vishada (depression) Krishna's gift is of another order.)
Arjuna blames himself- how could he have killed his own Guru and his beloved Grandsire- not to mention so many cousins and friends! Of course, there is a simple answer. Fight so well, that the other side loses morale and sues for peace! But, we know that those assembled, having forgotten they were desecrating a holy spot, were ripe for a vishodhana- a ritual type of cleansing. In any case, Sociologically speaking, the feudal code was untenable and the aristocracy had to die.
From the theistic point of view, if the Lord is depicted as twisting and turning to help his friend (that is devotee) there is a noble purpose here- viz. to illumine the psychological truth that at every moment, taking on every form- (rupam rupam pratirupo babhoova etc)- the Lord is struggling to come to us and to win us away from anxiety and depression.
However, we notice that Krishna's every philosophical excursion ends in aporia- more notably, from the point of view of ordinary people (for whom the work was intended) these philosophies are immediately shown to be false because they lead to social injustice. I don't need to know Philosophy to know that any Philosophy is wrong which arrives at the conclusion that I should be the slave of its practitioners.
From Theism's point of view, it is important that even Krishna should not be able to show any philosophical system or approach to be other than silly. It's like Douglas Adams's story about the philosopher who provides a valid proof of God's existence. Even God is impressed. But, the philosopher points out, there is no longer any need for Faith. But there is no God without Faith. God is convinced and immediately ceases to exist.
Still, the Gita is quoted as supporting misogyny, casteism, the morality of slaughtering millions of people coz you're miffed that your cousins get to rule rather than you- and so on and so forth.
The point is that though ad captum vulgi arguments can be adduced for all of the above- they, nevertheless are complete shit. The Gita does have a message- it's the same as Buddhism, Jainism... urm common sense actually which is that we are all radically interdependent. Mutually supportive co-existence must be the rule. Pluralism is necessary for Life is about Symbiosis not Extermination. As Jefferson said, in matters of Religion, divided we stand, united we fall. There are delicious ironies in the casteist and misogynistic portions of the Gita. The whole thing is like one of those sit coms where, if at the beginning of a scene, an actor states some principle, then he or she will be shown to behave in the opposite way by the end. Thus, there is nothing casteist about a work which shows the destruction of the fucking aristocrats- no matter how splendid their attributes and achievements.
The reason that the Mbh exhibits a lot of mathematical structure is that, if not its conception, then certainly its transmission depended on heuristics. But heuristics- including rules of thumb- are just special cases of a more general law. Since Mbh is trying to show karma and dharma as being logically consistent, there is obviously going to be a lot of symmetry.
Thus if the question is raised 'what did this guy do this at this time?' we can reconstruct it by figuring out who his dual is and what episode elsewhere is the dual of this episode and so on. Of course, this method of comparison also gives a lot of scope for clarifying matters. It is like you have two parallel cases to which the same rule applies in which the decision was different.
If Krishna has one way of discharging his duty as a charioteer, Shalya has another. Actually, Shalya's is pretty effective. Insults get a guys dander up. He fights harder.
On the other hand, we say the parallelism here is imperfect. Krishna is a pal and relative of Arjuna. Shalya is a relative of the Ashvins (he is their maternal uncle). BUT, if Karna revealed his true birth to Shalya the latter would have been obliged to inform his nephews (so as to prevent them from falling into the sin of filial impiety) in which case the Kauravas get a walkover! Thus the symmetry here is- Krishna reveals his true form to Arjuna, Karna conceals his true birth from his charioteer. This is subtle, not mechanistic.
No wonder people write crap about Mbh.