Video Game Lootcrate Keys: Part 2 – Power Law
This is a follow-up post to Bingsong Li’s post about the Applecraft economy.
Part 2: Power Law Phenomena and Inequality in Applecraft
Greetings, fellow Adventurers of Applecraft!
Today, let’s embark on an exploration into the heart of our economy and uncover the reasons why selling keys instead of opening them leads to a power law distribution in the game among the fraction of players possessing rare items.
Power Law Distribution:
The decision to sell keys instead of opening them for poor players ensures a safer, albeit less potentially rewarding, path. This risk-averse strategy results in a power law distribution among players based on the number of rare items they possess. The power law equation for the fraction of people having k very rare items is often expressed as:
where:
- P(k) is the fraction of players who own k very rare items.
- α is the exponent determining the shape of the power law distribution. This depends on how often players sell their keys to wealthier players as well as the probability of winning a good item.
Understanding the Impact:
Using the above observation about the power law in our community let us observe how this phenomena further affects our experience of the game!
- Inequality among Players: This strategy perpetuates inequality among players. Those who sell their keys avoid the risk of losing value but miss out on the opportunity to obtain rare items. Consequently, a small fraction of the player base accumulates a disproportionate number of rare items due to their willingness to take risks, spend more, and exploit the variability inherent in opening crates.
- Concentration of Wealth: As a consequence, a select few become significantly wealthier in the game compared to the majority. They hold a higher number of rare items, often the most valuable, increasing their in-game wealth and status. This concentration of rare items among a small fraction of players mirrors real-world wealth concentration dynamics.
- Reinforcement of Inequality: The cycle perpetuates as the rich get richer. With more resources (in-game currency or wealth), players can afford to take risks repeatedly, increasing their chances of acquiring rare items. This ongoing cycle of risk and reward contributes to a widening gap between the rich and poor within the game.
These are some of the reasons that lead games to become obsolete. The richer players get reacher and the new players joining the game are incentivized when seeing the immense discrepancy between these top players and themselves.
- Improving the game system: With all that said, a way of improving the crate system and mitigating the power law the game makers could make a system where a user with less in-game wealth is more likely to win a good item than a person with more in-game wealth as well as decrease the probability of winning a rare item when paying real money to buy keys. This would however disincentivse people from spending money on the game, which could again be undesirable.
Conclusion:
The power law phenomena resulting from the optimal strategy of selling keys for poor players and the subsequent concentration of rare items exacerbate inequality among players. This trend, while reflective of individual player strategies, underscores the broader impact on the game’s economy and the disparities among its participants.
As a final thought, I believe that to counter the effect of power law and the subsequent inequality of wealth in the games you, the adventurer, should ultimately prioritize your enjoyment and satisfaction within the game. Some players find pleasure in the thrill of opening crates, while others prefer the stability of selling keys.
With all this said, farewell adventurer!