A multi-agent model of hierarchical decision dynamics

TL;DR

The paper develops a minimal hierarchical multi-agent model built on a binary-tree topology to study how observation, judgement, and action propagate across levels. Agents share only judgements while observations and actions remain local, with level-dependent noise and asynchronous timing introducing realistic dynamics. Through simulations under invariant, foggy, clear, and malleable world conditions, the work demonstrates convergence of actions to align with world assessments, while revealing persistent gaps between absolute and perceived success, especially under noise and actuation feedback. The findings illuminate how hierarchy and communication shape collective decision making and motivate extensions to include adaptive behavior, constraints, and richer world dynamics with potential applications in modeling organizational decision processes and distributed control systems.

Abstract

Decision making can be difficult when there are many actors (or agents) who may be coordinating or competing to achieve their various ideas of the optimum outcome. Here I present a simple decision making model with an explicitly hierarchical binary-tree structure, and evaluate how this might cooperate to take actions that match its various evaluations of the uncertain state of the world. Key features of agent behaviour are (a) the separation of its decision making process into three distinct steps: observation, judgement, and action; and (b) the evolution of coordination by the sharing of judgements.

Figures (6)

• Figure 1: A small three-level agent decision treee (agent-tree), indicating the typical agent state values as described in the main text, the sharing of judgements between agents, and the speed of operation of the different levels.
• Figure 2: Timing diagram: higher level agents act first, but lower level agents act more frequently. The step labelled M is the measurement step T1, that labelled J is the judgement step T2, and that labelled A is the action step T3.
• Figure 3: Noiseless nohammer: results for a small four-level tree with $N=16$ compared to a larger six-level tree with $N=64$.
• Figure 4: Noisy nohammer: results for a small four-level tree with $N=16$ compared to a larger six-level tree with $N=64$. The size of the observation noise parameter is indicated on the panels.
• Figure 5: Noiseless hammer: results for a small four-level tree with $N=16$ compared to a larger six-level tree with $N=64$. The size of hammer parameter is indicated on the panels. The near-horizontal dotted indicates the gradually increasing value of the world state $\mathscr{W}$; the numerical size of the change is indicated with the label $\Delta$World.