## 5 Experiments and Results
### Positional Attention Analysis  
In this section, we discuss the contribution of positional attention to the performance difference between the two observation methods and the effects of observation methods on cooperative behaviors as the attention heatmaps indicate the underlying strategy where they focus their attention acquired during learning. We present three types of heatmaps for eDA3-IQN agent \(i\) (\(\in\{0,1,2,3\}\)) in Figures 5 and 6: the positional attention heatmap (top), the heatmap of agent \(i\)'s trajectory indicating where \(i\) visited through 1000 episodes (middle), and the heatmap indicating where agent \(i\) collected objects through 1000 episodes (bottom). For this analysis, we removed the constraints of designated areas of object collection to evaluate the agents' ability to learn their areas of responsibility correctly; in other words, we replaced all green and red regions to beige regions in Figure 1a. Thus, agents were allowed to collect objects anywhere in the environment \(\mathcal{E}\). The heatmaps of _agent_\(4\) and _agent_\(5\) were omitted as they were roaming agents. Notably, the positional attention heatmaps of local views are \(7\times 7\) in Figure 5, whereas those of relative views are \(5\times 5\), as shown in Figure 6. This difference is because the environment size is \(G_{\mathrm{X}}\times G_{\mathrm{Y}}=25\times 25\), and the patch size is \(P=5\) for the relative view method. Thus, each attention weight at each segment of the attention heatmaps in Figure 6 corresponds to a \(5\times 5\) area of the environment. The attention heatmaps depicted in Figure 5 reveal that eDA3-IQN agents typically focus on their adjacent cells. Notably, the region of attention varies for each agent; for example, the positional attentions of _agent_\(0\), _agent_\(1\), and _agent_\(3\) are mainly directed towards the neighboring and boundary cells (Figure 5a,b,d) whilst that of _agent_\(2\) indicates high attention on the neighboring cells only (Figure 5c). The heatmaps of object collection indicate that the agents roughly divide the environment for exploration. Each agent is responsible for the region around a particular corner. However, the trajectory heatmaps in Figure 5 indicate that agents move in the same regions; for instance, _agent_\(1\) sometimes explored the upper region where _agent_\(2\) and _agent_\(3\) were collecting objects. Similarly, _agent_\(2\) also covered the areas partly overlapped with _agent_\(0\) and _agent_\(1\). In other words, agents sometimes move into another agent's region to collect objects whilst the other agent is distant from it. We interpret this behavior as a combination of two strategies:(1) segmenting the area per agent and (2) moving in the same direction collecting objects. As a result of following two strategies, agents with the local view method obtain such a vague allocation of regions that leads to lower performance compared to agents with the relative view method. The relative view method leads to a nearly equal distribution of the environment among agents, as illustrated in Figure 6. The positional attention heatmaps of each agent  
Figure 5: Positional attention analysis with local view. Each row shows positional attention heatmap in \(7\times 7\) (**top**), heatmap of agent \(i\)’s trajectory (**middle**), and heatmap of collected objects by agent \(i\) (**bottom**). Figure 6: Positional attention analysis with relative view. Each row shows positional attention heatmap in \(5\times 5\) (**top**), heatmap of agent \(i\)’s trajectory (**middle**), and heatmap of collected objects by agent \(i\) (**bottom**). highlight the same region that they mostly explore because of the rough (\(P=5\)) global positions. For instance, _agent_ 0's attention is mainly focused on the upper-left region of its heatmap, which corresponds to its areas of exploration and object collection, as depicted in Figure 6a. Other agents also assume responsibility for specific regions of the environment and rarely interfere with one another.