# A Game-Theoretic Rent-Seeking Framework for Improving Multipath TCP Performance +
## 1 Introduction
Therefore, the competition between MPTCP subflows can be considered as a game with common coupled constraints. In such games, when a player fails to achieve the constraints common to other players, all other players will also be penalized. Such games can, therefore, be viewed as cooperative in the objectives of meeting common constraints and non-cooperative in the context of utilities. We exploit the _rent-seeking_ game framework for studying the contests between subflows, thus providing insights into the design of _cooperative MPTCP_ algorithms. [PERSON] et al. [12] used a similar framework to model contests over time for maximizing visibility in social networks. We observe that the _rent-seeking_ game has the potential to model MPTCP transmissions over multiple network paths. Each MPTCP subflow may bid its proposed packet-sending rate \(\lambda_{i}\) before transmitting. Then, each MPTCP subflow will pay a price \(p_{i}\) based on its bid. Based on this price, they eventually obtain the throughput \(\theta_{i}\) proportional to their bid. In a realistic network setting, since the achievable bandwidth across the network paths is finite, this approach will lead to (infinitely) many equilibria. Unfortunately, the difficulty in designing a mechanism for selecting a desired equilibrium point and, thus, maximizing the utility is a serious drawback with this approach. One possible solution to this is to use the _Karush-Kuhn-Tucker_ (KKT) conditions to solve a similar (relaxed) version of the game, rather than the exact constrained game. This relaxed game has the same equilibria as the original game, but is easier to solve. Using [PERSON]'s theory, the Lagrange multipliers can be interpreted as _pseudo-prices_ associated with the network path, and the equilibrium will satisfy the (desired) coupled constraints. However, the KKT conditions alone are not sufficient for our needs, since these do not guarantee that the _pseudo-price_ per unit bandwidth is the same for all contending subflows. Rather, this approach increases the already large state space of our MPTCP system model and makes it unscalable. More specifically, it becomes intractable, since once _pseudo_prices_ (Lagrange multipliers) are obtained, they depend not only on the policy adopted by an MPTCP subflow, but also on the corresponding strategies of other coupled subflows. Our idea is to find a _pseudo-price_ that is globally constant per unit resource across all network paths. Recall that such an equilibrium with a global fixed _pseudo-price_ is the desired _normalized_ equilibrium for our MPTCP dynamics over the multipath network. Therefore, the Tullock game framework is used to redesign MPTCP and analyze the existence and uniqueness of the equilibrium \((\mathbf{\lambda}^{\star},\mathbf{p}^{\star})\). Moreover, we prove that, starting from any initial point \((\mathbf{\lambda}(0),\mathbf{p}(0))\), the trajectory \((\mathbf{\lambda}(t),\mathbf{p}(t))\) generated by the cooperative MPTCP algorithm over multiple paths converges to a unique solution with a globally stable equilibrium \((\mathbf{\lambda}^{\star},\mathbf{p}^{\star})\)[13]. To summarize, the main contributions of our work are the following:  
* We design a utility function for MPTCP based on [PERSON]'s rent-seeking game. * We prove that this utility function implies a unique and stable solution to the MPTCP optimization problem. * We examine the convergence of no-regret learning in the underlying network games. * We provide extensive experimental results showing the performance of our MPTCP algorithm. The rest of this paper is organized as follows. Section 2 provides an overview of our MPTCP modeling approach and situates it in the context of prior work. Section 3 discusses the details of our approach, including the game theory framework and the equilibrium properties of our system. Section 4 extends our model to consider multiple MPTCP flows and no-regret learning. Section 5 presents the experimental results of the evaluation of the performance of our MPTCP solution using network emulation experiments.