## NETWORK CONGESTION / RESOURCE ALLOCATION GAME

##### Abstract

We first consider the K-user(player) resource allocation problem when the resources
or strategies are associated with homogeneous functions. Further, we consider
the K-user(player) matroid resource allocation problem satisfying the specified requirements
of the users, which are maximal independent sets of a matroid. The objective is to
choose strategies so as to minimize the average maximum cost incurred by a user where
the cost of a strategy is the sum of the costs of the elements comprising the strategy.
For k commodity networks with heterogeneous latency functions, we consider the
price of anarchy (PoA) in multi-commodity selfish routing problems where the latency
function of an edge has a heterogeneous dependency on the flow commodities, i.e. when
the delay is dependent on the flow of individual commodities, rather than on the aggregate
flow. Further we consider the price of anarchy (PoA) in multi-commodity atomic flows
where the latency function of an edge has a heterogeneous dependency on the flow commodities,
i.e. when the delay is dependent on the flow of individual commodities, rather
than on the aggregate flow. Lastly, we show improved bounds on the price of anarchy for
uniform latency functions where each edge of the network has the same delay function.
We prove bounds on the price of anarchy for the above functions. Our bounds illustrate
how the PoA is dependent on θ and the coefficients gij .
At the end, we consider security aspects of network routing in a game-theoretic
framework where an attacker is empowered with the ability for intrusion into edges of the
network; on the other hand, the goal of the designer is to choose routing paths.