Demand–Withdraw Communication Cycle

• Demand–Withdraw communication cycle is a recurring interpersonal feedback loop where one partner’s demand triggers the other’s withdrawal, modeled as a two-state coupled Markov process.
• The cycle is simulated through six distinct stages with LLM-driven agents, ensuring role fidelity and realistic state transitions via deterministic stage control.
• Quantitative evaluations indicate that the simulation boosts perceived conflict realism and training effectiveness, underpinning its value in clinical therapy settings.

The demand–withdraw (D–W) communication cycle is a recurrent two-agent feedback loop characterized by one partner’s pursuit or criticism (demand) provoking the other’s defensive avoidance or disengagement (withdraw), often resulting in mutually escalating conflict. In the context of couples therapy and dyadic interaction modeling, the D–W cycle is formally conceptualized as a coupled Markov process and operationalized within advanced multi-agent simulation frameworks. The simulation architecture, agent role policies, dialog stages, and evaluative metrics are central to reproducing and studying this phenomenon, especially to support the training of therapists in handling such complex relational dynamics (Wang et al., 16 Jan 2026).

1. Formalization and Mathematical Structure

The D–W cycle is instantiated as a two-state Markov chain representing demand $(d_t)$ and withdraw $(w_t)$ modes, with explicit probabilistic coupling. For partners $A$ (demand) and $B$ (withdraw), the transition dynamics are governed by:

$$P(d_{t+1}=1\mid w_t) = \sigma(\alpha_d + \rho w_t), \quad P(w_{t+1}=1\mid d_t) = \sigma(\alpha_w + \rho d_t),$$

where:

• $d_t, w_t \in \{0,1\}$ are binary indicators for demand and withdraw states at turn $t$;
• $\sigma$ denotes the logistic function;
• $\alpha_d, \alpha_w$ are the baseline propensities for demand and withdraw;
• $\rho > 0$ is the coupling parameter quantifying bidirectional reactivity.

When both $(w_t)$0 and $(w_t)$1, the interaction is in a high-escalation regime; conversely, $(w_t)$2 denotes a neutral state. Although these probabilities are not estimated online, they underpin the rule-based simulation logic and encode the cyclic dependency integral to D–W dynamics (Wang et al., 16 Jan 2026).

2. Six Interaction Stages and Policy Abstraction

Simulated sessions are segmented into six recurrent stages to reflect the evolving D–W trajectory:

1. Greeting (G): Minimal, neutral small talk.
2. Problem Raising (P): Introduction of complaints; D–W pattern initially emerges.
3. Escalation (Esc): Intensified pursuit and withdrawal; blame and counter-blame surface.
4. De-escalation (Desc): Therapist interventions prompt partial softening.
5. Enactment (En): Agents articulate primary emotions directly to one another.
6. Wrap-up (Wr): Concluding acknowledgments and moderated optimism.

For each stage $(w_t)$3, agent behavior is governed by a stage-specific policy $(w_t)$4, implemented through prompt-tuned LLM inputs. Sample directives include specifying tone, emotional intensity, and content constraints. These constraints ensure that agent outputs maintain stage fidelity and role realism. The policies are strictly enforced by a rule-based stage controller and form the basis for high-fidelity simulation of the full D–W cycle (Wang et al., 16 Jan 2026).

3. Multi-Agent Simulation Architecture and Logic

The architecture comprises:

• Two LLM-driven agents, corresponding to the demand and withdraw roles;
• One human-therapist proxy participant;
• A deterministic rule-based stage controller.

Simulation flow is articulated via pseudocode (see below), capturing joint conversational and state transitions:

$B$3

Key components:

• NextSpeaker: Determines speaker turn based on rules, managing therapist prompts versus partner looping.
• StageController: Applies deterministic triggers (e.g., blame cues for Escalation transition, emotional vulnerability for Enactment initiation).

This structure efficiently models both agent-to-agent and agent–therapist exchanges, capturing the staged, feedback-intensive nature of the D–W cycle (Wang et al., 16 Jan 2026).

4. Hyperparameters, Control Dynamics, and Emotional Calibration

Simulation dynamics are modulated by several hyperparameters:

Hyperparameter	Description	Stage-Dependent Use
max_loopₚ, max_loopₑ	Max partner–partner turns permitted in P and Esc before interrupt	P: 3, Esc: 5
auto_esc	Auto-escalate if Problem Raising exceeds 7 turns without escalation	P → Esc threshold
r_d	Resistance to therapist suggestions, levels {High, Medium, Low}	Stage prompt, diff. tuning
eᵢ(s)	Agent $(w_t)$5's emotion intensity for stage $(w_t)$6 on 1–5 scale	Feeds into TTS prosody

For example, emotion intensity in Escalation might be set to $(w_t)$7 (Angry) for the demander and $(w_t)$8 (Cautious) for the withdrawer. These knobs directly affect conversational tempo, resistance, and emotional realism, aligning transition frequencies with theoretical Markovian representations (Wang et al., 16 Jan 2026).

5. Illustrative Dialogue Fragments Across the Cycle

Empirically, the D–W cycle is instantiated through specific dialogue moves. Selected fragments reveal the cyclical triggers and transitions:

• Problem Raising:

Alex: “Jordan, last week you forgot to pay the rent again and I had to fix it at work—this happens all the time.” Jordan: “I’m not always late. You’re blowing it out of proportion.”

• Escalation:

Alex: “You always drop the ball. You never think about how it affects me!” Jordan: “I’m sick of you lecturing me! Stop nagging!”

• De-escalation:

Therapist: “Let’s slow down. Alex, I hear you’re angry. Jordan, what was that like for you?” Alex: “I just felt invisible…” Jordan: “I… I didn’t realize I hurt you that badly.”

• Enactment:

Alex: “I feel scared that you don’t care about me anymore.” Jordan: “I’m sorry you feel that way. I do care—I’ve been stuck in my own head.”

In Escalation, repeated demand escalates withdrawal, creating the characteristic feedback loop; sustained therapist intervention is required to break the cycle and permit de-escalation. The controller recognizes blame and vulnerability cues to modulate stage progression (Wang et al., 16 Jan 2026).

6. Quantitative Evaluation and Outcome Metrics

The operational fidelity of the D–W cycle simulation has been systematically evaluated in a within-subjects study with 21 licensed therapists. Comparative analysis between the experimental system (with explicit D–W and stage logic) and a baseline yielded the following metrics (5-point Likert scales; higher = stronger):

• Stage Identification: $(w_t)$9(experimental) = +0.082, SE = 0.035, $A$0, $A$1
• Demand–Withdraw Perception: $A$2(experimental) = +1.841, SE = 0.052, $A$3, $A$4
• Realism of Virtual-Patient Responses: $A$5(experimental) = +1.254, SE = 0.051, $A$6, $A$7
• Overall Realism: $A$8(experimental) = +1.451, SE = 0.052, $A$9, $B$0
• Perceived Training Effectiveness for Novices: Baseline mean = 2.62 (SD = 1.24), Experimental mean = 3.95 (SD = 0.86), $B$1, $B$2

The largest gains in realism occurred during Problem Raising, Escalation, and De-escalation—the stages with maximal D–W activity. These findings indicate that embedding a rule-based, tightly staged D–W cycle notably enhances perceived fidelity and effectiveness for clinical training use cases (Wang et al., 16 Jan 2026).

7. Integration and Implications for Therapy Training

By integrating a theoretically grounded D–W feedback loop with stage-specific, LLM-directed multi-agent policies, the system operationalizes the full trajectory of conflict, escalation, and repair as observed in actual therapy sessions. The embedding of hyperparameterized resistance and emotionality, enforcement of deterministic state transitions, and alignment with clinical dialogue exemplars all contribute to the realism and pedagogical utility of the simulation. Stage recognition, cycle detection, and realism judgments by experts converge with the engineered design intent, mapping the simulation outputs directly onto established clinical theory and practice (Wang et al., 16 Jan 2026). A plausible implication is that similar architectures could generalize to broader relational and multi-party conflict phenomena in other settings.