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A bandwidth-sharing game is a type of resource allocation game designed to model the real-world allocation of bandwidth to many users in a network. The game is popular in game theory because the conclusions can be applied to real-life networks. The game is described as follows:
- each player has utility for amount of bandwidth
- user pays for amount of bandwidth and receives net utility of
- the total amount of bandwidth available is
We also use assumptions regarding
- is increasing and concave
- is continuous
The game arises from trying to find a price so that every player individually optimizes their own welfare. This implies every player must individually find . Solving for the maximum yields .
With this maximum condition, the game then becomes a matter of finding a price that satisfies an equilibrium. Such a price is called a market clearing price.
A possible solution
A popular idea to find the price is a method called fair sharing. In this game, every player is asked for amount they are willing to pay for the given resource denoted by . The resource is then distributed in amounts by the formula . This method yields an effective price . This price can proven to be market clearing thus the distribution is optimal. The proof is as so:
Comparing this result to the equilibrium condition above, we see that when is very small, the two conditions equal each other and thus, the fair sharing game is almost optimal.
- Tsitsiklis, Johari. "Qualitative Properties of a-Fair Policies in Bandwidth-Sharing Networks" (PDF). Massachusetts Institute of Technology. Retrieved 15 May 2012.