*4.1. Soft-Collision Constraint on Common Resources*

Inspired by real-world scenarios, we introduce the recourse-related soft-collision property to the model of an agent. We define that all the agents have the following properties: (1) a collision among agents is *soft*, quantified using some *collision scores*; and (2) different agents have different collision scores, according to their individual experiences through the paths. We suppose that each agent cares about a set of resources *A* = {*A*1, ... , *AL*}. To obtain the properties, we introduce to each agent an additional attribute called *resource experience* (for each resource) and use the resource experience to calculate the *collision score*.

In doing so, this section first uses the *resource experience* (as defined in Section 4.1.1 Definition 1) to quantify how dissatisfying the agent is about the resource allocated to it. Then, we combine this information of all the resources into a *collision score* (as defined in Section 4.1.2 Definition 2) that indicates the probability of the agent announcing a collision given its resource experience. *Threshold of collision* is used to limit the collision score, implying to what degree of unpleasantness we want to pursue the solution. The agent, of which the collision score exceeds the threshold, will be placed into a soft-collision set via the *soft-collision function* for sub-dimensional expansion (as defined in Section 4.1.3 Definition 3).
