We develop models for Internet Service Provider (ISP) peering when ISPs charge each other for carrying traffic. We study linear pricing schemes in a simple ISP peering model using a two stage sequential Nash game in which self interested providers first set linear prices for carrying peers' traffic and then choose to route their traffic according to the prices set and costs incurred by carrying traffic on their links. Under reasonable cost models, we show that rational ISPs will participate in this game. Moreover, we show that the ISP with the lower marginal cost in the absence of peering has no incentive to send traffic in a hot-potato fashion and effectively acts as a monopolist. The other provider strategically routes traffic, splitting between hot-potato and cold-potato routing. We also show that though this outcome is inefficient, both ISPs are strictly better off when compared to not peering at all. Finally, we consider appropriate cost models that make the notion of capacity explicit. Under certain conditions we show not only that the monopolist has an incentive to upgrade the capacity of its links but also that this incentive is higher when the monopolist is in a peering relationship.
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