From Overload to Convergence: Supporting Multi-Issue Human-AI Negotiation with Bayesian Visualization

Mehul Parmar; Chaklam Silpasuwanchai

cs.HCMar 24, 2026

From Overload to Convergence: Supporting Multi-Issue Human-AI Negotiation with Bayesian Visualization

Authors: Mehul Parmar, Chaklam Silpasuwanchai

Organizations: Asian Institute of Technology Bangkok, Thailand

Abstract

As AI systems increasingly mediate negotiations, understanding how the number of negotiated issues impacts human performance is crucial for maintaining human agency. We designed a human-AI negotiation case study in a realistic property rental scenario, varying the number of negotiated issues; empirical findings show that without support, performance stays stable up to three issues but declines as additional issues increase cognitive load. To address this, we introduce a novel uncertainty-based visualization driven by Bayesian estimation of agreement probability. It shows how the space of mutually acceptable agreements narrows as negotiation progresses, helping users identify promising options. In a within-subjects experiment (N=32), it improved human outcomes and efficiency, preserved human control, and avoided redistributing value. Our findings surface practical limits on the complexity people can manage in human-AI negotiation, advance theory on human performance in complex negotiations, and offer validated design guidance for interactive systems.

Figures & tables

Figure 1. Heatmap of Pareto - optimal placements: 2 - D distribution of joint - optimum points across issues, showing dispersed optima that encourage exploratory search rather than midpoint convergence. A 2‑D heatmap (counts / density) plotting the locations of Pareto‑optimal (joint best‑outcome) option combinations derived from the task payoff matrices across the four issue conditions. Color intensity encodes the frequency of Pareto‑optimal points at each option index; axes show option index (horizontal) and issue or aggregated bin (vertical). The distribution demonstrates that Pareto optima are spread across the option space rather than concentrated at a single or central index, a deliberate design choice to promote exploratory behavior and avoid trivial midpoint strategies.

Sr. No.	Option	Human Payoff	AI Payoff	Joint Payoff	Remark
1	None	5	95	100	max AI (landlord) payoff
2	Internet only	15	85	100
3	Internet + Water	30	80	110
4	All except electric	55	65	120	middle option
5	All utilities	80	50	130
6	All utilities + cleaning	100	35	135	max joint utility

Table 1. Payoff distribution for one issue used in our study (“Utilities Included”). The design places the joint optimum at a non-obvious position, distinct from either party’s maximum or the central option, promoting exploration.

Figure 2. Sample conversation between a human participant and the AI agent, in the Decision Support condition, showing the visualization interface in action. Green bands of the Negotiation Horizon Grid indicate ZOPA, whereas the Global Convergence Panel shows overall convergence and favorability. Screenshot showing the negotiation chat alongside the Decision Support widgets: the Negotiation Horizon Grid (a multi-row 7-column grid with green ZOPA bands highlighting promising option ranges for each issue) and the Global Convergence Panel (a horizontal bar indicating overall convergence and favorability). The chat pane shows a recent human proposal and the AI counter-proposal; visual highlights indicate which options the system currently rates as most promising.

Figure 3. Panel (a) shows an early-stage negotiation where the wide colored zone indicates high uncertainty about likely agreement ranges; panel (b) shows a mid-stage negotiation with reduced uncertainty; panel (c) shows a potential late-stage convergence where the colored zone is much narrower (low uncertainty) and the ZOPA is increasingly favorable to the human participant. The Convergence Panel visualizes global agreement progress across three stages: (a) early-stage — a wide colored zone denotes high uncertainty about likely agreement ranges; (b) mid-stage — a reduced zone denotes declining uncertainty; (c) late-stage — a narrow zone shifted toward green denotes low uncertainty with the ZOPA favoring the human. The horizontal gradient bar therefore encodes both residual uncertainty (zone width) and strategic favorability (position on the red–amber–green spectrum).

Figure 4. Overview of the negotiation chatbot system architecture. System architecture diagram showing modules and data flow: user interface (human offers), AI Negotiator (generates counter-offers), AI Analyst (parses dialogue for metric computation), centralized logger, and the visualization widgets updated by the metric computation service. Arrows indicate real-time flow between components while labels denote information separation (private payoff matrices) and where Decision Support computations occur.

Figure 5. An overview of the Experimental Procedure. Flowchart of the experiment timeline: informed consent and pre-task questionnaires, training on the baseline interface, Block 1 (four Baseline negotiation tasks with post-task NASA-TLX and brief ratings), a short break, Block 2 (four Decision Support tasks with identical post-task measures), and final SUS and debrief. The diagram emphasizes the fixed Interface order (Baseline then Decision Support) and per-block timing of approximately 30–45 minutes.

	Baseline			Decision Support
Comparison	t -value	$p_{holm}$	Cohen’s d	t -value	$p_{holm}$	Cohen’s d
1 vs. 3 Issues	-2.32	.054	-0.668	-0.758	1.00 (n.s.)	-0.194
3 vs. 5 Issues	7.54	$<$ .001	1.12	0.899	1.00 (n.s.)	0.179
5 vs. 7 Issues	6.82	$<$ .001	0.967	1.470	1.00 (n.s.)	0.233

Table 2. Holm-adjusted post hoc pairwise comparisons of total human payoff across dimensionality levels in Baseline and Decision Support conditions. The table displays selected, non-exhaustive comparisons relevant to the main findings.

Panel of Figure 6 — Figure 6. Primary objective outcomes as box plots: (a) In the Baseline condition, total human payoff declines sharply after three issues; Decision Support prevents this decline and maintains stable payoffs across dimensionalities (no statistically significant effect of dimensionality in Decision Support). (b) Total turns to agreement increase with dimensionality; Decision Support requires relatively fewer turns than Baseline at higher dimensionalities. (c) Average first keystroke time (excluding turn no. 1) increases with dimensionality in Baseline; Decision Support reduces this latency, especially at higher dimensionalities. $\Delta$ represents the difference between mean Decision Support and mean Baseline conditions ( $\Delta=\text{Decision Support}_{\text{mean}}-\text{Baseline}_{\text{mean}}$ ). Three-panel figure of box plots: (a) total human payoff (vertical) across issue counts (horizontal) comparing Baseline and Decision Support, showing payoff decline in Baseline but preservation under Decision Support; (b) total turns (vertical) by issue count (horizontal), showing increased turns with complexity in Baseline and reduced turns under Decision Support; (c) average first keystroke time (vertical) by issue count (horizontal), showing increased latency with complexity in Baseline and reduced latency under Decision Support.

Objective Outcomes
Dependent Variable	Main Effect of Interface	Main Effect of Dimensionality	Interface × Dimensionality Interaction
Total Human Payoff	F (1, 31) = 59.87, $\eta_{p}^{2}$ = 0.659	F (2.318, 71.854) = 28.27, $\eta_{p}^{2}$ = 0.477	F (1.860, 57.675) = 11.48, $\eta_{p}^{2}$ = 0.270
Total Turns	F (1, 31) = 237.77, $\eta_{p}^{2}$ = 0.885	F (3, 93) = 879.22, $\eta_{p}^{2}$ = 0.966	F (2.329, 72.206) = 26.92, $\eta_{p}^{2}$ = 0.465
Total Chat Duration	F (1, 31) = 730.50, $\eta_{p}^{2}$ = 0.959	F (2.212, 68.557) = 7849.90, $\eta_{p}^{2}$ = 0.996	F (2.288, 70.917) = 227.50, $\eta_{p}^{2}$ = 0.880
Avg. First Keystroke Time	F (1, 31) = 1085.3, $\eta_{p}^{2}$ = 0.972	F (1.824, 56.558) = 3269.4, $\eta_{p}^{2}$ = 0.991	F (2.132, 66.088) = 399.3, $\eta_{p}^{2}$ = 0.928
Process & Behavioral Metrics

Table 3. Summary of 2×4 Repeated-Measures ANOVA Results for Key Dependent Variables. All p

<

.001 unless otherwise specified. Fractional dfs reflect Greenhouse–Geisser correction for sphericity violations

Panel of Figure 7 — Figure 7. Joint value optimization and exploration structure: (a) Box plot of sequence entropy across dimensionalities, showing greater uncertainty at higher dimensions in the Baseline condition. (b) Scatterplot of total human + AI payoffs for 7 issues, with Decision Support points clustered nearer the center and closer to the Pareto frontier. Two-panel figure combining joint-value and exploration structure: (a) a box plot of sequence entropy across dimensionalities comparing conditions, where Baseline shows a steep rise and Decision Support flattens that increase. Panels encode condition with color and illustrate that DS advantage increases with dimensionality; (b) scatter plot of negotiated joint payoffs versus theoretical Pareto frontier for 7-issue sessions, showing Decision Support sessions clustered closer to the frontier with more balanced outcomes compared with Baseline

Figure 8. Concession magnitude CDF (5 & 7 issues): CDFs of concession magnitudes by condition, showing that Decision Support shifts mass toward smaller, more frequent concessions (steeper rise at lower magnitudes), especially at higher dimensionality, indicating pacing recalibration and fewer large overshoot–correct cycles. CDF plots of concession magnitudes for 5- and 7-issue conditions, split by Baseline and Decision Support. The curves show that Decision Support shifts mass toward smaller, more frequent concessions (steeper rise at lower magnitudes), especially at higher dimensionality, indicating pacing recalibration and fewer large overshoot-correct cycles. Axes: concession magnitude (horizontal) and cumulative probability (vertical).

Figure 9. Heatmap of final option selections (2 - D histogram of counts) for 7 issues): In Baseline, negotiators concentrate on mid–low option values, whereas in Decision Support, participants exhibit a broader, more even spread across intermediate options while still avoiding extreme high-risk choices. Heatmap of final option selections aggregated across the seven issues. The distribution highlights behavioral differences: Baseline negotiators concentrate on mid-low option values, while Decision Support users show a broader, more even spread across intermediate options and avoid extreme high-risk choices. The plot's horizontal axis lists option values and vertical axis shows frequency of selection.

Figure 10. Option transition network at high dimensionality (7 issues): Baseline sessions show sparse early exploration (turns $\sim$ 2–6) with convergence occurring later (turns $\sim$ 12–15), whereas Decision Support sessions exhibit earlier exploration and faster convergence (turns $\sim$ 10–13). Network diagram of option-to-option transitions over negotiation turns (7-issue sessions). Nodes represent option states, edges represent transitions between states across turns, and edge thickness encodes transition frequency. Decision Support networks show denser, earlier convergence to higher-value regions (greater transition density in turns ~10–13) whereas Baseline networks remain more diffuse and extend convergence later (toward turn 15), illustrating trajectory efficiency differences.

Panel of Figure 11 — Figure 11. Objective vs. Subjective time, normalized to baseline condition: Decision Support yields longer interactions relative to Baseline, but lower perceived temporal demand at high dimensionality, indicating a reframed temporal experience. Two-panel figure: (a) normalized total chat duration by condition and dimensionality, showing Decision Support sessions longer on average; (b) TLX Temporal Demand by condition and dimensionality, showing lower perceived temporal demand under Decision Support despite longer durations.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Issue Sr. No	Issue	Total Human Payoff	Total AI Payoff
1	Monthly Rent	370	390
2	Security Deposit	365	385
3	Lease Duration	435	420
4	Utilities Included	395	430
5	Pet Policy	385	335
6	Parking Spaces	395	360

Appendix

Table 4. Aggregate total payoffs across all 16 negotiation issues for Human and AI agents.

Issue.Option	Option	Human	AI	Total
		Payoff	Payoff	Payoff
1.1	$2300	5	110	115
1.2	$2200	20	95	115
1.3	$2100	40	75	115
1.4	$2000	55	55	110
1.5	$1900	70	35	105

Appendix

Table 5. Detailed negotiation options and corresponding payoffs for Issues 1–3. The remaining negotiation issues (Issues 4–16) utilized in this study are publicly available in the repository at https://doi.org/10.5281/zenodo.20545331 .

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