depending on the details of the system. However through the use of "effect sets" COINs can account even for such delayed side-effects 2 .

## 2.3 Braess' Paradox

Let us conclude this section with an illustration of Braess' paradox (Bass, 1992; Cohen & Kelly, 1990; Cohen & Jeffries, 1997; Glance & Hogg, 1995; Hogg, 1995; Korilis, Lazar, & Orda, 1997b; Korilis et al., 1999), a phenomenon that dramatically underscores the inefficiency of the ISPA. This apparent "paradox" is perhaps best illustrated through a highway traffic example first given by Bass (Bass, 1992).  There are two highways connecting towns S and D. The cost associated with traversing either highway (either in terms of tolls, or delays) is V 1 + V 2 , as illustrated in Net A of Figure 2. So when x = 1 (a single traveler) for either path, total accrued cost is 61 units. If on the other hand, six travelers are split equally among the two paths, they will each incur a cost of 83 units to get to their destinations. Now, suppose a new highway is built connecting the two branes, as shown in Net B in Figure 2.

Further, note that the cost associated with taking this highway is not particularly high (in fact for any load higher than 1, this highway has a lower cost than any other highway in the stem). The benefit of this highway is illustrated by the dramatically reduced cost incurred by the single traveler: by taking the short-cut, one traveler can traverse the network at a cst of 31 units (2 V 1 + V 3 ). Adding a new road has seemingly reduced the traversal cost dramatically.

![0_image_0.png](0_image_0.png)

However consider what happens when six travelers are on the highways in net B. If each agent uses an ISPA, then at equilibrium each of the three possible paths contains two travelers. 3 Due to overlaps in the paths however, this results in each traveler incurring a ccccll of 92 units, which is higher than than what they incurred before the new highway was built. The net effect of adding a new road is to increase the cost incurred by every traveler.

This phenomenon is known as Braess' paradox.