4. Game theory formulation
In Section 3 we defined the request rate for ISPs (Θi, i = 1, . . . , k) that depends on several factors, e.g., algorithms for
overlay network management, number of peers in ISPs, video bit rate, server upload capacity. Rational ISPs aim at reducing
the bandwidth costs by possibly limiting the offered bandwidth Φi (e.g., Φi = 0). Clearly this free-rider behavior of ISPs
would cause the P2P streaming system to work inefficiently.
The main goal of the game theory framework we propose in this section is to avoid this ISP selfish behavior. Here we
introduce a game theory model where the players are ISPs. Finally, in Section 5 we propose an analysis of the ISP game using
the Evolutionary Game Theory, that allows us to devise a practical algorithm to optimize the interactions among ISPs.
The model is based on the following general utility function