## 3 The Bike-Share Case
### Insights and Implications  
A notable insight from the overview--evident in Figure 15, where the block of scenarios with the highest risk perception delay (risk delay for short) value has few highlighted cells--is the sharp decline in scenarios where crowdsourced inventory balancing through incentives outperforms the baseline (scenarios without incentives). When the risk perception delay is set to 3 and 6, 89 and 81 scenarios outperform the baseline, respectively, but this number drops significantly to 19 when the delay reaches 12. This delay parameter is part of the anchor-and-adjust heuristic that updates risk perception. A longer delay implies a slower assimilation of the current PeBAF. The steep drop at the highest delay value suggests that the wait-and-see approach, which anchors the decision maker's risk perception to prior beliefs, results in missed intervention opportunities when availability shifts away from the desired bandwidth. A closer inspection of scenarios with a utilisation sweet spot between 30% and 70% (risk buffer = 0.3) reveals a surprising behaviour: the number of scenarios showing improvement over the baseline slightly increases as the delay rises from 3 to 6. We analyse  
Figure 15: Performance results from simulation runs across 432 policy scenarios with decision parameters varied. the underlying stocks and flows driving this behaviour to understand this. The following graphs in Figure 16 illustrate two specific scenarios on a chosen day, comparing key stock and flow variables while holding all parameters constant except for the risk delay, set at three and six, respectively. When the risk delay is set to six timesteps (or 60 min), this medium delay causes lower responsiveness to PeBAF, allowing the memory of historical risk to persist longer than with a low delay of three timesteps. Early in the day, this results in the risk of bike outages at yang remaining above the incentive threshold (indicated by the horizontal dotted line) for an extended period, prompting incentives that encourage users to return bikes to yang over yin. Later in the day, this rerouting causes yin to reach a critical stock level sooner, triggering incentives that bring in additional returns just in time to prevent most stockouts--an advantage not achieved in the low-delay scenario. The analysis highlights how endogenous decision variables mediate the impact of exogenous temporal demand dynamics at the stations (which influence projected stock) on performance. Specifically, the inventory buffer at yin builds up faster than at yang earlier in the day. The longer delay creates a broader window for incentivisation at yang, setting off the downstream behaviours described earlier and ultimately leading to better performance under a longer delay in perceiving risk changes. While faster responsiveness to risk is generally beneficial, this example shows that uncertainty can simultaneously cause both clusters to experience high risk. In such cases, the system may defy typical assumptions about how decision variables affect performance, as recovery depends on exogenous factors. After risk delay, the delay in assimilating real-time availability information into perception (availability delay) has the next most significant impact on performance. While this generally holds, performance varies considerably across different availability delay  
Figure 16: Analysis of key stock and flow variables influencing performance at two different risk perception delay values (orange for the yin cluster, grey for the yang cluster). values between days. For instance, the coefficient of variation in improvement over baseline (defined as the standard deviation over the mean of the improvement metric) is lowest on the 24 th, at 0.85, and highest on the 23 rd, at 2.92. Analysing the lowest and highest availability delays for a given set of parameters further clarifies the underlying dynamics (see Figure 17).