A Monetary Mechanism for Stabilizing Cooperative Data Exchange with Selfish Users

This paper considers the problem of cooperative data exchange with selfish users. In this setting, each user has a subset of packets in the ground set $X$, and wants all other packets in $X$. The users can exchange coded combinations of their packets over a lossless broadcast channel, and monetary transactions are allowed between any pair of users. We define the utility of each user as the sum of two functions: (i) the difference between the total payment received by the user and the total transmission rate of the user, and (ii) the difference between the total number of required packets by the user and the total payment made by the user. A rate-vector and payment-matrix pair $(r,p)$ is said to stabilize the grand coalition (i.e., the set of all users) if $(r,p)$ is Pareto optimal over all minor coalitions (i.e., all proper subsets of users who collectively know all packets in $X$). Our goal is to design a stabilizing rate-payment pair with minimum sum-rate and minimum sum-payment for any given problem instance. In this work, we show that such a solution always exists, and we propose two algorithms to find such a solution. Moreover, we show that both algorithms maximize the sum utility of all users, while one also maximizes the minimum utility among all users.