Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Multi-agent coordination via communication partitions

Wei-Chen Lee, Alessandro Abate, Michael Wooldridge

TL;DR

This work tackles equilibrium selection with multiple Nash equilibria by introducing a partitioned pre-play communication mechanism among coalitions in Singleton Congestion Games (SCGs) with identical resources. By leveraging a symmetry-based epistemic framework, coalitions can reach envy-free, credible, Pareto-optimal agreements that, when aggregated across a balanced partition, yield socially optimal and evenly distributed outcomes. The analysis shows that such partition-induced equilibria are $\bar{c}$-optimal and $\hat{c}$-optimal, and extends to settings with differential resource costs under known distributions. This approach provides a scalable design principle for coordinating decentralized, anonymous resource allocations and informs future work on weighted agents and cost-structure variations.

Abstract

Coordinating the behaviour of self-interested agents in the presence of multiple Nash equilibria is a major research challenge for multi-agent systems. Pre-game communication between all the players can aid coordination in cases where the Pareto-optimal payoff is unique, but can lead to deadlocks when there are multiple payoffs on the Pareto frontier. We consider a communication partition, where only players within the same coalition can communicate with each other, and they can establish an agreement (a coordinated joint-action) if it is envy-free, credible, and Pareto-optimal. We show that under a natural assumption about symmetry, certain communication partitions can induce social optimal outcomes in singleton congestion games. This game is a reasonable model for a decentralised, anonymous system where players are required to choose from a range of identical resources, and incur costs that are increasing and convex in the total number of players sharing the same resource. The communication partition can be seen as a mechanism for inducing efficient outcomes in this context.

Multi-agent coordination via communication partitions

TL;DR

This work tackles equilibrium selection with multiple Nash equilibria by introducing a partitioned pre-play communication mechanism among coalitions in Singleton Congestion Games (SCGs) with identical resources. By leveraging a symmetry-based epistemic framework, coalitions can reach envy-free, credible, Pareto-optimal agreements that, when aggregated across a balanced partition, yield socially optimal and evenly distributed outcomes. The analysis shows that such partition-induced equilibria are -optimal and -optimal, and extends to settings with differential resource costs under known distributions. This approach provides a scalable design principle for coordinating decentralized, anonymous resource allocations and informs future work on weighted agents and cost-structure variations.

Abstract

Coordinating the behaviour of self-interested agents in the presence of multiple Nash equilibria is a major research challenge for multi-agent systems. Pre-game communication between all the players can aid coordination in cases where the Pareto-optimal payoff is unique, but can lead to deadlocks when there are multiple payoffs on the Pareto frontier. We consider a communication partition, where only players within the same coalition can communicate with each other, and they can establish an agreement (a coordinated joint-action) if it is envy-free, credible, and Pareto-optimal. We show that under a natural assumption about symmetry, certain communication partitions can induce social optimal outcomes in singleton congestion games. This game is a reasonable model for a decentralised, anonymous system where players are required to choose from a range of identical resources, and incur costs that are increasing and convex in the total number of players sharing the same resource. The communication partition can be seen as a mechanism for inducing efficient outcomes in this context.

Paper Structure

This paper contains 14 sections, 8 theorems, 8 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related literature
  3. Preliminaries
  4. Singleton Congestion Games
  5. Communication partition
  6. Correlated actions
  7. Epistemic uncertainty and the symmetry principle
  8. Expected cost under a common prior
  9. Envy-freeness, credibility, and Pareto-optimality
  10. Efficiency of augmented SCG
  11. Optimal outcomes
  12. Efficient partition
  13. Differential cost functions
  14. Conclusion

Key Result

Proposition 4

The expected cost faced by some player in $C$ who chooses some resource $x$, among a total of $v$ players in $C$ choosing the same resource, can be expressed as $g_\mu(v) \coloneqq \sum_{u=0}^{\infty} \mu(u) \cdot f(u + v)$, where $\mu: \mathbb{N} \to [0, 1]$ is the probability distribution on the n

Figures (4)

  • Figure 1: Payoff profiles of well-known games
  • Figure 2: A 3-player coordination game
  • Figure 3: Venn diagram of agreements that are Pareto-optimal (P), covering (Co), credible (Cr), and envy-free (E).
  • Figure 4: Examples of 7-player 3-resource outcomes. Players are represented as coins and resources as columns. A partition is represented by dotted lines and coloured coalitions.

Theorems & Definitions (25)

  • Definition 1: Generalised strategy profile
  • Definition 2: Feasible strategy profile
  • Remark 3
  • Proposition 4
  • proof
  • Remark 5
  • Corollary 6: Coalition as subgame
  • Definition 7
  • Example 8
  • Definition 9: Covering agreements
  • ...and 15 more