The figure above depicts the relationship between the size of the cycle created by strategies (for example, in the case of rock-paper-scissors, the size is counted as “3”) (horizontal axis) and the (average) skill of groups of players (vertical axis) in games with cyclic strategy advantages and disadvantages, such as “goo-choke-par” in rock-paper-scissors. (Source: “Real World Games Look Like Spinning Tops”).
The higher you go along the vertical axis, the higher the skill of the player in the game; the top (Nash of the game) is when the players are “able to calculate optimal strategies like gods”; the bottom is when the players are “so unskilled that they can only take meaningless actions like losing on purpose”; and the middle represents “ a population of players whose skill average gradually increases.”
Meanwhile, the spread on the horizontal axis expresses the size of the strategy cycle existing in the population of that skill level, as described earlier.
First, if no one has any skill (as everyone loses quickly), no strategy cycle is possible (bottom, “Agents trying to lose”).
As we move up along the vertical axis, we come to a stage (“Extremely non-transitive”) where everyone starts to have some skill, the diversity of strategies increases, and large cycles between strategies form. Then, in a “ well-established game” such as Go, for example, there comes a phase where only short cycles between small numbers of sophisticated strategies are maintained (“Non-transitivity gradually disappears”).
In the context of this paper, the emergence of small groups of strategies with high skill levels beyond the broad set of strategies is more desirable (higher quality game) than the formation of huge cycles with diverse strategies. The reasons for this are discussed as follows. In many “interesting” games, in the early stages, when player skill is generally low, there are many different “surprise strategies” emerging. Eventually, however, the players accumulate a set of formulas for dealing with such tricky strategies, and the strategies are eliminated. After that, advanced tactics emerge among the remaining strategies. The first stage may seem diverse, but in reality, it is essentially meaningless since experts can counter-strategies with established strategies at once. From this point of view, it is not desirable to have “ just a diversity.
Essentially, the paper is based on the elitist view that games where “everyone is just doing crazy things in different ways” are “uninteresting” or “lacking in-depth,” a view Thomas Pynchon might criticize. If we dare to caricaturally refer to DeepMind, the paper’s author, as “Google,” the Google vs. Pynchon-like composition is hidden in evaluating this figure.
In contrast, if we think of the relationship between control and controlled (between layers) as win-lose (in-game strategy), our article takes the existence of cycles between strategies as a positive sign of separation, where power is not concentrated in one layer.
“ Diversity is important” is often pointed out. However, what type of diversity is desirable in a society becomes a delicate issue when the concept of ability differences such as “skill level” is included.
Our article discussed not an “optimal solution in an idealized laboratory situation,” but rather a very elementary consideration for designing mechanisms aiming to “maintain a certain level of diversity and range of cycle sizes” in noisy environments.
For example, a population with huge dependency and diversity, such as a rainforest, can possibly be interpreted as “extremely wide in width” in the above diagram, while a small number of carefully selected institutions restraining each other can be understood as “narrow in width,” and our discussion of layer cycles mainly deals with the latter.
However, unlike board games such as Go, the layer cycle targets the operation of “open rules (where the set of rules is not clearly defined, and many accidental factors are involved in the progress of the game)” through “ a layer where anything can enter,” such as “the world. The question is whether the number of layers will be refined or reduced in that case. Further discussion is still needed on this issue.
Credits: Original idea by Asaki NISHIKAWA, Draft written by Asaki NISHIKAWA, Drawing by Yoshimi KIKUYA, Simultaneous editing by VECTION