No equilibrium theorem

1. in the classic "How markets slowly digest", Bouchaud et. al (B): "Then begins a kind of hide and seek game, where each side attempts to guess the available liquidity on the other side. A 'tit-for-tat' process then starts, whereby market orders trigger limit orders and limit orders attracts market orders ", 6.5.4
2. Incidentally, tit-for-tat (TT) refers to a strategy of the iterated PD (prisoner dilemma)
3. what can be the meaning of the looming of game theory GT within a paper at distance of Rational Equilibrium approach and critic of K85?
4. We can argue a methodological isomorphism between theoretical physics TP (Physics and learning) and GT
\begin{array}{r c l}
\  TP & \leftrightarrow & GT \\
 (SO (3) / local / etc) \quad symmetries & \rightarrow & (infinite) \quad  strategic \quad regress \\
\end{array}
5. See, for example, 'Rational interaction', 'game theory, symmetry, and scientific discovery', HW Brock
6. We would be tempted to conclude that B "fail to learn": he does not recognize the natural (theoretical) space of the domain he is studying, i.e. the symmetries of the domain
But GT suggests that "physical" dynamics have a good chance of lapsing in finance
7. In physics the causality \( F ^ i = m * a ^ i \) (or even the equations of the field in RG) establishes the causal link between force and acceleration
8. K is still in this paradigm: \( imb = 1 / λ * δp \) CF 'mm second law'
9. As is often the case with this type of article, equilibrium is obtained conditionally only by assumptions of implicit coordination that are not realistic (K explicitly excludes any form of manipulation, insider and mm assume the optimal strategy of other agents)
10. A natural framework is rather the PD: in a game of sharing P&L (= long term equilibrium), the two agents can play cooperation, ie a kind of à la Kyle equilibrium corresponding to a kind of average historical behavior of these Agents), or deviate significantly from them, fooling other expectations
11. More precisely, in K, the fundamental symmetry is written simply
\begin{array}{r c l}
\ & K & \\
 mm & \rightarrow & insider \\
\end{array}
Mm and insider know all about one another, the reasoning rules are CK (common knowledge). They could reverse their respective roles, but they do not, symmetry is only valid in K(nowledge) and not in A(ct)
12. The literature on PD is considerable (and for good reason), but in iterated strategies such as TT or win-stay lose-switch appear not only theoretically (including in an evolutionary framework) but empirically observed (CF Axelrod 84, 'Evolutionary dynamics', Nowak)
13. Note that this takes place in a framework of payoff without any uncertainty: the matrix of the payoffs is perfectly known.
There is therefore no stake in learning a representation of the world
14. Projected in the framework of K, this amounts to saying that the representation (imb) is not an issue
On the other hand, \( \lambda \) can not be stable
And this non-stationarity is fundamental, in the sense that it results from the space symmetry of space (GT) space (finance)
In a GT frame, we now have a substitution in Act between mm and insider:
\begin{array}{r c l}
\ & K, A & \\
 mm & \rightarrow & insider \\
\end{array}
The mm can mimic the insider, and reciprocally