Abandwidth-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.[citation needed]
The game involves players.
Each player has utility for units of bandwidth.
Player pays for units of bandwidth and receives net utility of .
The total amount of bandwidth available is .
Regarding , we assume
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 popular idea to find the price is a method called fair sharing.[1] In this game, every player is asked for the 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.