Network utility maximization (NUM) is a fundamental framework for optimizing next-generation networks. However, self-interested agents with private information pose challenges due to potential system manipulation. To address these challenges, the literature on economic mechanism design has emerged. Existing mechanisms are not suited for large-scale networks due to their complexity, high implementation costs, and difficulty to adapt to dynamic settings. This paper proposes a large-scale mechanism design framework that mitigates these limitations. As the number of agents$I$approaches infinity, their incentive to misreport decreases rapidly at a rate of$\mathcal {O}(1/I^{2})$. We introduce a superimposable framework applicable to any NUM algorithm without modifications, reducing implementation costs. In the dynamic setting, the large-scale mechanism design framework introduces the decomposability of the problem, enabling agents to align their own interests with the objectives of the dynamic NUM problem. This alignment helps overcome the additional, more stringent incentive constraints encountered in dynamic settings. Extending our results to dynamic settings, we present the design of a Dynamic Large-Scale mechanism with desirable properties and the corresponding Dynamic Superimposable Large-Scale mechanism. Our numerical experiments validate the fact that our proposed schemes are approximately$I$times faster than the seminal VCG mechanism.

The optimal coding scheme for Additive White Gaussian noise (AWGN) channels with noisy output feedback has been unknown for several decades. The best-known linear scheme is by Chance and Love, where the coefficients of the linear scheme are numerically optimized based on unique observations. In this paper, we introduce a new class of linear coding schemes, calledsequential linear schemes, where the encoder sequentially updates a linear state process based on feedback. We then derive the optimal scheme within this class, in a closed form, by formulating a novel Markov decision process and solving it via dynamic programming. We demonstrate that our scheme outperforms the Chance-Love scheme for channels with noisy feedback and coincides with the Shalkwijk-Kailath scheme for channels with noiseless feedback. This problem is an instance of decentralized controlwithout any common informationand, to the best of our knowledge, the first such scenario where we can derive analytical solutions using dynamic programming.

In this paper, we consider a communication system where a sender sends messages over a memoryless Gaussian point-to-point channel to a receiver and receives the output feedback over another Gaussian channel with known variance and unit delay. The sender sequentially transmits the message over multiple times till a certain error performance is achieved. The aim of our work is to design a transmission strategy to process every transmission with the information that was received in the previous feedback and send a signal so that the estimation error drops as quickly as possible. The optimal code is unknown for channels with noisy output feedback when the block length is finite. Even within the family of linear codes, optimal codes are unknown in general. Bridging this gap, we propose a family of linear sequential codes and provide a dynamic programming (DP) algorithm to solve for a closed form expression for the optimal code within a class of sequential linear codes. The optimal code discovered via DP is a generalized version of which the Schalkwijk-Kailath (SK) scheme is one special case with noiseless feedback; our proposed code coincides with the celebrated SK scheme for noiseless feedback settings.

This paper studies node cooperation in a wireless network from the MAC layer perspective. A simple relay channel with a source, a relay, and a destination node is considered where the source can transmit a packet directly to the destination or transmit through the relay. The tradeoff between average energy and delay is studied by posing the problem as a stochastic dynamical optimization problem. The following two cases are considered: 1) nodes are cooperative and information is decentralized, and 2) nodes are strategic and information is centralized. With decentralized information and cooperative nodes, a structural result is proven that the optimal policy is the solution of a Bellman-type fixed-point equation over a time invariant state space. For specific cost functions reflecting transmission energy consumption and average delay, numerical results are presented showing that a policy found by solving this fixed-point equation outperforms conventionally used time-division multiple access (TDMA) and random access (RA) policies. When nodes are strategic and information is common knowledge, it is shown that cooperation can be induced by exchange of payments between the nodes, imposed by the network designer such that the socially optimal Markov policy corresponding to the centralized solution is the unique subgame perfect equilibrium of the resulting dynamic game.