Causality in Game Theory
In a previous piece, I talked about causality as being the ultimate tool in intelligence. I wanted to revisit this in the context of multiple intelligences competing to reach some end goal. Financial markets are prime examples of this. Here I want to talk about the branching factor within the game as a dilution parameter in the utility and hence longevity of “obvious” causality.
A superior intelligence will see the obvious phenomena apparent to inferior intelligences but the opposite is not true. The asymmetry here is usually called the edge or alpha. We now have to add in a “blind-spot” factor to the analysis — we assume that as long as a superior intelligence is not omniscient, it will not be able to predict the rise of new superior intelligences and will itself fall prey to the new kids on the block. I would say that in all dynamic systems from finance to geopolitics this should roughly hold.
The key to understanding the size of a given intelligence’s blind-spot is to look at the branching factor of the game that intelligence is playing. Tic-Tac-Toe, for example, has a small branching factor compared to chess and we know that agents competing in Tic-Tac-Toe will hit a natural barrier to their evolution where games will start ending with draws forevermore. In chess, as the strategy starts being “solved” better and better, a higher portion of the games will also end in stalemates. This will represent the end of intelligence’s evolution in that arena.
At the end of evolution, all paths will lead to draws which tells us that the utility of causality in that game has been maxed out — the cause-effect linkages will lead to this predetermined end-state. If we invert the thinking here we can say that the harder the game and the larger the branching factor then the end of evolution is not close by. In these situations, the utility of causality is far from being maxed out and strictly following what one believes is causal will typically not lead to certain victory.
In “hard” games, competing intelligences are changing the landscape of the game all the time to disrupt causal effects that other intelligences rely on. At this point, I will make a distinction between the games of finance and “lived life”. Lived life has got agents competing but also cooperating as it is in their best interests to do so. The cooperation aspect can reduce the branching factor of decisions made in real life and I dare say that real life can be easier to comprehend than finance and causal concepts can stand the test of time. Financial markets, however, are pure competition and cooperation in financial markets is actively regulated away — inside information, cartel behaviour etc are not acceptable in the game of finance.
Is focusing on causality in the markets and other hard games futile then? Of course not! However, one must understand the limits of causality in one’s game. Accepting past observations as facts without attaching the relevant probabilities and tail risk to them is simply overfitting. Instead, the agents should channel the effort in mastering more space and time. Space is for information — alternative data that no one else was looking at. Time is for computational ability — not only apparatus but the analytical methods themselves.
For people doing time-series analysis, this is why the evolution has gone from time-agnostic methods such as regressions to historical-context aware ones with recurrent components. This is an example of the evolution of intelligence to increase mastery of the temporal dimension. Gathering more data from, say, satellite imagery and social media helps increase the mastery of the spatial dimension.
As intelligence gets more clued up, here is to hoping that the game is still nowhere close to being solved!