However, the optimal actions remain the same, *low* (solid green) for healthy agents, *high* (dashed magenta) for infected agents, as shown in the left plot in \[fig: marl\](b). The trends of the Q curves also remain the same: the Q values do not depend on $m_k$ for infected agents and for healthy agents whose activity levels are zero. However, as shown in the right plot in \[fig: marl\](b), the agents learned to flatten the curve faster than in case 1, mainly because healthy agents are more cautious (converge faster to low activity levels) when they start to consider cumulative costs.

-   Case 3: discount $\gamma = 0.5$ with shaped runtime cost $\tilde l_{i,k}$ in .

    The shaped cost changes the optimal actions for all agents as well as the resulting Q values. As shown in the left plot in \[fig: marl\](c), the optimal action for an infected agent is *low* (dashed green), while that for a healthy agent is *high* (solid magenta) when $m_k$ is small and *low* (solid green) when $m_k$ is big. Note that when $m_k$ is high, the healthy agents still prefer low activity level, though the optimal actions for infected agents are low. That is because: 