| Abstract: |
| Equilibria in nonatomic congestion games model how traffic distributes across resources when independent agents seek to minimize their own delays. While one might expect increased demand to uniformly increase resource usage, paradoxical non-monotone behavior is a well-documented phenomenon. In this talk, we investigate the monotonicity of equilibrium loads and costs as functions of total demand.
In the classic case of single-commodity routing, it is known that network topology alone dictates these paradoxes. However, with multiple commodities, the combinatorial structure of strategy sets also plays an important role. We first demonstrate that singleton congestion games maintain monotone equilibrium loads with respect to any demand. We then extend this result to a broader class of multi-commodity games, which we define as Constrained Series-Parallel (CSP) games. Finally, we show that CSP games can be represented as variant of multi-commodity routing games on series-parallel networks, bridging the gap between abstract strategy sets and physical network topology. |
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