Token Model Simulation #1 Fools’ Agreement Part 2
Tags: Token Economy, Agent Based Modeling, Simulation, Reinforcement Learning, Blockchain

Why doesn’t the lower 80% conduct research? The research rate graph per timestep shows a reversed U shape that slightly inclines at first but continues to decline. Because the research rate drops instead of steadily incresaing, it becomes saturated. The reason why such a graph is formed is because the token inequality aggravates rapidly. At first, the whales and private investors all realize the value of researching and actively study. Whales who hold a substantial amount of tokens reap most of the rewards when their vote wins.

The severity of token inequality only worsens from this point on. This is depicted on the Whale Index graph on the upper right. The Whale Index indicates the share of tokens that the voter holding the largest amount (whale) among the votes of the winning side. Taking a closer look, you can see that the Whale Index reaches almost 50% around timesteps 20~25, showing severely aggravated inequality.

Since private investors would receive a small amount of reward tokens, they would start to feel that researching ahead of votes is not worth their time. The simulation data analysis shows that the lower 20% and 10% of the winning voters receive minus rewards from timestep 15 even though they voted successfully by doing their research. Also, once the whales obtain enough shares to dictate the vote results, private investors will lose all incentives to study since they would have no effect on the vote results.

In summary, the reason why the research rate does not grow is because as the vote proceeds, the whales gain more influence and take more of the reward pie, which eliminates the motivation for other voters to vote. The inequality of wealth rendered by the whales gradually obtain more tokens by doing their research diminishes the research rate.

The problem is that whales actively conducting research is not something negative. Moreover, implementing artificial measures hindering the whales from conducting research or stripping their voting rights is inappropriate, let alone infeasible.

Then, what should be done to solve this problem? We established a hypothesis that we could increase the voters’ research rate by bestowing appropriate research incentives and effectively utilizing mechanisms to alleviate inequality, and used simulation to verify this hypothesis.

Hypothesis to Increase Research Rate

In each game, there are four possible situations that the voters could face: winning the vote after doing research, losing the vote despite doing research, winning the vote without research, or losing the vote without research. This can be depicted into a 2x2 matrix as follows. From here, we will use the matrix below to elucidate our analysis.

A proper mechanism would give positive (+) incentive to the voters (R) in order to enhance the research rate. The issue is that due to the asymmetry of information, it is impossible to know whether or not certain voters actually conducted research. The game results will only show whether the voter won or lost and cannot distinguish whether the voter won with or without research. It becomes hard to design a mechanism that only rewards the people who conducted research.

To solve this problem, we established a hypothesis that agents who have won four or more votes out of the five games. An agent could win without research once or twice thanks to luck, but winning four times or more seems to be the result of research.

Mechanism 2(M2) Hypothesis : The Rescue Mechanism

Mechanism 2 aims to alleviate the penalty on the above matrix (R, L). A portion of the tokens rewarded to the voters who won the vote would be given back to the voters who lost. Here what is noteworthy is that tokens are given back to those who have won four or more times out of the past five games.

The core idea of M2 is to lessen the blow for voters who have diligently conducted research but were unlucky. Because there is always the possibility of losing a vote even though a voter studied, levying a harsh penalty on one unfortunate loss would discourage voters to research. Whales who have gathered sufficient shares to manipulate the vote results could lead the majority vote to select the wrong option because of bad judgment. It is cruel to have voters be penalized for the misjudgment of whales just because they have low shares.

Mechanism 3(M3) Hypothesis : Emerson Mechanism

“Shallow men believe in luck. Strong men believe in cause and effect.” — Ralph Waldo Emerson

Mechanism 3 reinforces the (W, R) reward and weakens the (W, N) reward. M3 does not compensate all winning voters but only to those who have shown good progress. Specifically, the rewards are only given to voters who have won four or more times out of five.

The key idea for M3 is that instead of rewarding winners who simply got lucky and did not do research, it aims to score high research rates by giving rewards to those who have been diligent. In order to solve the problem of not being able to distinguish those who have won with research and those who have won without research, M3 perceives a voter’s 4/5 record as a type of signal.

Mechanism 4(M4) Hypothesis : High Controversity Mechanism

The high controversity mechanism is based on a slightly different premise than the aforementioned mechanisms. Here, the reward and penalty are adjusted in accordance with how controversial the vote was. Before moving forward, we will explain what ‘controversity’ means. We defined controversity as:

Controversity = H(the ratio of tokens deposited on True and False)

H(X) represents the uncertainty that a possibility variable holds in the concept of entropy. Generally, entropy if the possibility value is concentrated, there is lower entropy while an even distribution creates higher entropy. Let’s look at an example dealing with uncertainty. If the vote result shows 100:0, then we can have full confidence on the result. However, if the vote result is 51:49, we cannot be sure whether the result is right. We correlated this uncertainty with the controversity of the vote result. We calculated the entropy of the vote ratio and used it as the value of controversity.

As you can see in the results of the vanilla mechanism, 75–80% of agents vote after doing research. In real-life services, we can predict that most users, excluding a few malevolent users, will honestly vote on the right answer. Therefore, when the vote result was False, we believed that a portion of the voters chose False, deviating from the majority, which made False become the winning choice with a narrow margin. If the vote result was True, we believed that there was a high probability that the absolute majority voted correctly and rendered a dominant True vote.