Distributed Mechanism Design for Network Resource Allocation Problems

Abstract

In the standard Mechanism Design framework, agents' messages are gathered at a central point and allocation/tax functions are calculated in a centralized manner, i.e., as functions of all network agents' messages. This requirement may cause communication and computation overhead and necessitates the design of mechanisms that alleviate this bottleneck.We consider a scenario where message transmission can only be performed locally so that the mechanism allocation/tax functions can be calculated in a decentralized manner. Each agent transmits messages to her local neighborhood, as defined by a given message-exchange network, and her allocation/tax functions are only functions of the available neighborhood messages. This scenario gives rise to a novel research problem that we call "Distributed Mechanism Design".In this paper, we propose two distributed mechanisms for network utility maximization problems that involve private and public goods with competition and cooperation between agents. As a concrete example, we use the problems of rate allocation in networks with either unicast or multirate multicast transmission protocols. The proposed mechanism for each of the protocols fully implements the optimal allocation in Nash equilibria and its message space dimensionality scales linearly with respect to the number of agents in the network. general area of communication and information theory, with emphasis in channel coding and multi-user channels; control theory with emphasis in decentralized stochastic control and its connections to communications and information theoretic problems; analysis of dynamic games and mechanism design for resource allocation on networked systems.

Distributed Solution of GNEP over Networks via the Douglas-Rachford Splitting Method

“…Recent years have witnessed increasing efforts in generalized Nash equilibrium problems (GNEP) [2], [3], motivated by numerous applications, e.g., communication networks [4], charge scheduling of electric vehicles [5], formation control [6], and demand management in the smart grid [7]. In many cases, multiple self-interested players/decision-makers aim to optimize their individual objectives under some global resource limits while unwilling to share their private information with the public.…”

Mechanism Design for Demand Management in Energy Communities

“…Specifically, environments with non-monotonic utilities, external fixed unit prices, and the requirement of peak shaving are tractable with the proposed mechanism. (b) Inspired by the vast literature on distributed non-strategic optimization [17][18][19][20][21], as well as our recent work on distributed mechanism design (DMD) [22,23], we modify the baseline mechanism and design a "distributed" version of it. A distributed mechanism can be deployed in environments with communication constraints, where users' messages cannot be communicated to the central planner; consequently the allocation and tax/subsidy functions for each user should only depend on messages from direct neighbors.…”

“…The first attempts in designing decentralized mechanisms were reported in [22,23], where mechanisms are designed with the additional property that the allocation and tax functions for each agent depend only on the messages emitted by neighboring agents. As such, allocation and taxation can be evaluated locally.…”

“…Similar to the works in [22,23], the centralized mechanism in our work can be modified into a decentralized version (contribution (b)). Unlike the previous two works, however, the distributed mechanism in this paper has a straightforward form for the allocation function, making the proofs much less involved.…”

A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks

“…The aggregative coupling structures have been used to model numerous applications, e.g., network congestion control [6], demand side management in smart grids [7], and charging control of electric vehicles [8]. Besides the aggregative coupling in the objective functions, in many circumstances, the decisions of the agents may be subject to some global resource constraints [9], [10], such as total energy and communication channel capacity [11]. The coupled objectives and strategy sets of the agents are at odds with local privacy concerns and limited scalability.…”