Prestige Simulations

Trust, but verify: simulations of Prestige under different stress factors

Here we share a set of simulations taking into account the highest value for each parameter and normalizing them accordingly.

We also use different default archetype to determine the different weight distributions for each Hub based on their community type - the leading parameter of choice - and we analyze how this influences the evolution of $\mathfrak {P}$.

⚠️ *It’s important to notice that neither the results or the weight allocations are influenced by the parameter/type itself. Rather, the Prestige framework is designed to be infinitely expandable, and we expect hundreds of Hub Types in the near future. The only requirement - as we specified in prior docs and publications - is for each newly-added parameter to be measurable, and combine existing or mathematically provable strategies and Archetypes.*

1. Stress Factors

1. Hub A (Archetype: Size):

   • High and increasing TCM

   • Consistent high performance ($\overrightarrow{P}$)

   • Emphasis on Size ( $w_{\tiny \overlinesegment S}$) with 60% weight

2. Hub B (Archetype: Performance):

   • Fluctuating and declining TCM

   • Consistently low and declining performance ( $\overrightarrow{P}$)

   • Negative growth ( $\check{G}$)

   • Emphasis on Performance ( $w_{\tiny \overrightarrow{P}}$) with 60% weight

3. Hub C (Archetype: Conviction):

   • Moderate growth in TCM

   • Consistently high Conviction ( $\overline{iCL}$)

   • Emphasis on Conviction ( $w_{\tiny \overline{iCL}}$) with 60% weight

2. Fixed Values

• Initial Prestige ( $\mathfrak{P}_{\tiny 0}$) for all Hubs: 100
• Constraint factor ( c ): 1.4

• Penalty factor ( $p_{\tiny \ominus}$): 0.4

3. Normalization & Simplifications

• TCM: Divided by the highest TCM value (3000) across all periods and Hubs.

• $\overline{PS} \text{, } \overline{iCL} \text{, } \overrightarrow{P}$: Divided by the highest value (1.00) across all periods and Hubs
• $\check{G}$: Calculated as the percentage change in TCM from the previous period
• For simplicity, in this simulation we considered a “flat sum” of K and $\Delta K$, to include the linear change between a period and the other, while also skipping the individual, constant change in each of the parameters p.

4. Results

Tab. 1 shows the results for the simulations described - demonstrating how Prestige maintains stability disregarding different inputs and stress factors.

In this simulation, Hub B sets the Performance archetype but consistently fails to meet expectations, with low and declining performance ( $\overrightarrow{P}$) throughout the periods.

Because of that, Hub B's Prestige has a significant decline, falling from 100 to 29.17 by the end of the simulation.

Meanwhile, Hub A (Size archetype) and Hub C (Conviction archetype) maintain a strong performance in their respective KPIs, translating into stable growth in their Prestige scores.

Conclusions

This simulation demonstrates how the Prestige framework effectively captures the impact of consistent underperformance in a Hub's primary focus area, resulting in a significant decline in its overall Prestige score. It also highlights the importance of aligning a Hub's performance with its chosen archetype to maintain and grow its Prestige within the ecosystem.

This revised simulation better captures the dynamics of the Prestige framework under stress conditions and highlights the importance of parameter normalization for accurate comparisons between Hubs.