# A Game-Theoretic Rent-Seeking Framework for Improving Multipath TCP Performance +
## 2 Model Overview
### Background and Related Work  
Of particular relevance to this work are the core foundational works on charging and rate control for elastic traffic and their analyses reported in [6; 7; 13; 14; 15; 16; 17; 18; 19; 20; 21]. [PERSON]'s approach in [7] presented price-taking users to attain system optimality or efficiency. However, when the users are price-anticipating (or strategic), the users exhibit rent-seeking behavior. This problem then falls within [PERSON]'s rent-seeking framework [13], and there is an efficiency loss [17; 18]. For a finite-capacity single-path TCP user's case where the path is shared by all TCP users/flows, there are a few important works, viz. [PERSON] and [PERSON] [16], [PERSON] and [PERSON] [17], and [PERSON] et al. [13; 14], among others. The analyses in [16; 17] deal with the so-called _'posted prices'_ setting in which all users perceive the same price on the path. The works [13; 14] deal with differential pricing. For a discussion on the advantage of differential pricing over posted prices, see the implementation-theoretical perspective explained in [19].To this end, the existence and uniqueness of the Nash equilibrium were proved independently in [16; 17] and by using [PERSON] [18] in [13] or variations of [PERSON] [14]. The authors of [17] also dealt with network settings where agents can use multiple paths. [PERSON]'s theory on _network utility maximization_ (NUM) [6] provides a rigorous foundation for the design of efficient TCP algorithms. It has proven useful for understanding the structural properties of networks under end-to-end congestion control and for the design of optimal TCP algorithms. For path selection in multipath congestion control, [PERSON] et al. [22] developed another novel approach in order to study the potential benefits of coordinated congestion control. This enables users to select (or reselect) routes by adopting the notion of a Nash equilibrium. There are two distinct steps in most existing optimization frameworks for TCP congestion control design. First, one develops a mathematical model for the resource allocation problem (e.g., fluid and/or queueing model [23]). Second, one designs an algorithm to solve the model (e.g., convex optimization based on its properties) [23; 24]. A limitation of such NUM-based approaches is that they often assume a stable and steady-state network. As a result, they may lead to TCP algorithms that struggle in the presence of highly fluctuating and time-varying characteristics, such as those in wireless networks (e.g., 5G and next-generation WiFi). Specifically, the rapid variation in the capacity of these wireless channels may cause their state to change before the TCP algorithm converges on its optimal solution. In NUM and current TCP design, utility is typically a function of the instantaneous packet-sending rate (i.e., throughput). This approach leads to bandwidth-sharing networks [6], which are suitable for bulk data transfer flows over slowly varying channels. In addition, all of the TCP algorithms proposed (and deployed) have strictly concave utility functions, implying a unique stable equilibrium. However, the case for MPTCP is much more complex. This is because the existence of an underlying utility function depends on the design of the coupling function between the subflows (see Table 1 in [23]). For many well-known MPTCP algorithms, such as LIA [4], OLIA [9], and BALIA [23], a utility function does not even exist. Therefore, _utility maximization for MPTCP is highly challenging._  
Existing MPTCP congestion control algorithms [4; 9; 10; 23] have used common coupled constraints (e.g., loss/delay) to represent the channel characteristics and congestion conditions of the network paths (see Table 1 for a concise summary of the TCP window update operations for LIA, OLIA, and BALIA; as mentioned earlier, if one path fails to meet the constraints, the subflows on other paths may also suffer [9; 10; 11]).