1. Introduction

Negotiation sits at the centre of how organisations allocate resources, resolve disputes, and build Negotiation is at the heart of the ways organisations allocate resources, solve problems and forge partnerships. In the last few decades, a few models have emerged that have defined practitioner training and academic debate: the interest-based approach of Fisher and Ury (1981); the tactical psychology of Voss and Raz (2016); the structured rationalism of Conti (2019); the behavioural process discipline of The Gap Partnership (2023); and the transparency-based economics of Jensen (2018). Although these frameworks differ in their underlying principles, few studies have compared their performance directly under the same conditions. Much of the evidence is from case studies, small group experiments and practice reports, which are limited in size, variation of situation and difficulty in controlling for negotiator skill.

Computational simulation is a solution to these limitations. By coding the logic of each framework into separate agents, and by conducting thousands of negotiations from the same initial conditions, the effect of the framework can be separated from the ability of the agent implementing it. However, the agents are simplified representations of human negotiators and cannot capture factors such as experience, judgement, or interpersonal behaviour.

In this study, the five frameworks are compared by using a matched-pair agent simulation. Eight hundred buyer-supplier dyads with randomly assigned endowments negotiated in all five of the frameworks resulting in 4,000 negotiations with full logs of offers at each level of negotiation. The matched design allows performance differences between frameworks to be examined under the same negotiation conditions.

Three outcome variables are analyzed: joint value captured, which indicates the amount of the available surplus that the agents captured; concession-process quality, which indicates the smoothness and reciprocity of the bargaining path; and outcome asymmetry, which indicates how evenly the final agreement split the value between buyer and seller. The fourth variable, the trust index, was found to be constant within four of the five frameworks and is considered to be an architectural variable and not an outcome. The study therefore examines whether the frameworks perform differently across the three outcome dimensions.

2. Literature Review

2.1 Negotiation Frameworks in Theory and Practice

Research on negotiation has developed across psychological, strategic, and behavioural perspectives. Early scholars treated negotiation mainly as a psychological issue related to persuasive, concession-making and perception management in the face of uncertainty (Spector, 1977). Hausken (1997) added strategic rationality to this scene and cast the negotiator not as an emotional player but as a utility-maximizing agent making cooperative or competitive moves. For practical applicability, these formal models were less important than for what they had created conceptually: negotiation outcomes were more a function of information, incentives, and decision structure than of personality.

The most significant practical change was the introduction of interest-based bargaining by Fisher and Ury (1981) who made it a trainable methodology. The Harvard model suggested four disciplines: separate the people from the problem, concentrate on interests, not positions, invent options for mutual gain, and commit to objective standards. The practical value was immediately apparent, and the model prevailed in legal, diplomatic and commercial education for the next forty years (Druckman, 2010). What it did not do, however, was to give a systematic account of how preference disclosure impacts the set of attainable outcomes, which Jensen (2018) subsequently did.

The Black Swan Method of Voss and Raz (2016) is from a different tradition altogether. While Fisher and Ury were interested in mutual satisfaction, Voss was interested in information advantage, using calibrated empathy, emotional labelling and the strategic use of silence to shape the opponent's psychological state before substantive bargaining. Schweitzer, DeChurch, and Gibson (2005) had previously shown that competition affects the offers that negotiators make as well as the type of deceptive tactics they will use. The Black Swan Method incorporates these competitive dynamics into a practical negotiation approach. Some say it takes value at a relational expense which only shows up in subsequent transactions; others say that in one-shot, high-stakes transactions, it just works better than principled goodwill.

Conti (2019) and The Gap Partnership (2023) fall somewhere in the middle of these extremes, but with different foci. Conti emphasizes the importance of preparation discipline and the logical sequence of trade-offs, and negotiators enter each session with a ranked list of concessions, a clear reservation point, and a resistance strategy based on the opposition they expect. The Gap Partnership takes the rationalist approach and introduces behavioural situational awareness with conditionally concession logic and procedural checkpoints. Neither maximise joint gains like Harvard or SMARTnership, and both claim to deliver repeatable, auditable outcomes, which is a different value proposition and one particularly relevant for procurement environments where repeatability of the process is more important than creative surplus.

Jensen (2018) builds on the Harvard tradition, making transparency itself an economic variable. Logrolling is possible when both sides reveal their actual priorities of the issues, because by giving up on low-priority issues they can gain on high-priority ones, and the resulting trades increase the total surplus to be divided. This is based on the negotiation analysis literature (Lax & Sebenius, 1986; Raiffa, 1982), which showed that Pareto improvements can be made that are not available to positional bargainers when preference heterogeneity is known. Jensen (2018) proposed a disclosure-based methodology for adversarial commercial negotiations, where revealing true preferences involves considerable strategic risk.

The links between these frameworks and outcomes have been well theorised but less tested comparatively. Druckman (2010) pointed this out explicitly: Negotiation scholarship had created sophisticated models, but there was a lack of controlled comparative evidence that would enable practitioners to select between them on the basis of results. The present study is a response to that observation.

2.2 What Computational Simulation Adds

It is not the case that computational negotiation simulation is a matter of agents behaving like people. They do not. The reason is that there is no other controlled comparison under the same circumstances. If two trained practitioners negotiate, each with a different framework, the result is a product of their frameworks, their skill, their history with each other, their cognitive state on the day, and many other factors that cannot be controlled. All of these are removed by a computational agent except the framework.

Initial automated negotiation research provided the basic framework of agents with utility functions that make offers and concession schedules and belief updating rules that are passed around a fixed number of times (Debenham, 2003, 2004). Sierra, Jennings, Noriega, and Parsons (1997) and Amgoud, Dimopoulos, and Moraitis (2007) incorporated argumentation-based mechanisms that enable agents to provide justification for proposals, based on structured reasoning, instead of just utility optimisation. This was later broadened to adaptive systems that could change their strategy in the middle of negotiation based on observed opponent behaviour by Zhang, Shen, and Ghenniwa (2008).

One thing that was always missing from this literature was any linkage to named practitioner frameworks. The agents were designed to test abstract propositions, e.g., early concession vs. late concession, preference disclosure vs. no preference disclosure, but not to map these propositions onto the specific set of rules that practitioners learn. Lai and Sycara (2009) were the closest to designing a generic multi-attribute architecture that can be flexible enough to encode a variety of strategies, but their comparison was still at the level of strategy type and not institutional frameworks. Li, Vo, Kowalczyk, Luo and Zhang (2013) and Zhang, Ghenniwa and Shen (2007) improved the adaptive learning mechanisms without trying to encode Harvard, Voss or any identified school.

Research testing abstract concession functions cannot answer the practically useful question, would a procurement manager's outcomes be different if he or she learned the SMARTnership model instead of the Harvard model? This study is an attempt at a direct encoding, but it is also recognised that there are interpretative choices to be made in translating a behavioural philosophy into computational parameters, which limits the claims that can be made.

In the field of pharmaceutical price negotiation, Syversen et al. (2024) find some overlap, as they find that procedural transparency was consistently linked to higher rates of agreement and lower rates of post-agreement disputes across countries. That result in a human-participant setting is broadly consistent with the simulation results reported here, although the mechanisms will almost certainly be different.

2.3 Measuring Negotiation Outcomes

The selection of outcome variables is not innocuous. It embodies assumptions on the purpose of negotiation.

Joint value is an integrative perspective that is the ratio of the available surplus captured by both parties. By this measure, a negotiation that has not resulted in a Pareto improvement is a failure even if both parties are happy with the outcome. It is well grounded in the economics of bargaining (Nash, 1950; Raiffa, 1982) and is suitable for evaluating the efficiency of various bargaining frameworks in exploiting the deal space.

Process quality is not as clear-cut. The measure employed here reflects the symmetry and smoothness of the concession path: the extent to which the sequence of offers is reciprocal and the extent to which each party moves. It is a proxy for what practitioners refer to as procedural fairness, which Trötschel, Loschelder, Höhne and Backhaus (2015) showed to have a significant impact on satisfaction of both parties, regardless of the outcome. A negotiation may produce a favourable outcome while still involving irregular or excessive concessions that negatively affect perceptions of the process. The computational measure is only capturing the behavioural pattern and not the subjective experience, and the variable is called concession-process quality to make this distinction. Outcome asymmetry (absolute difference between buyer and seller utility shares) deals with distributional fairness. Two negotiations that result in the same joint value can vastly diverge in allocation: one party might take seventy per cent of the value, or it might be divided evenly. Both outcomes are not necessarily good, but if they are highly asymmetric they tend to breed resentment and renegotiation, especially in repeated interaction situations (Olekalns, 1994; De Dreu, Carnevale, Emans, & Van de Vliert, 1995). This feature can help identify frameworks that increase total surplus from frameworks that redistribute it evenly, a distinction that will be shown to have an empirical relevance.

One thing that is not included in this list is a metric of trust as a per-negotiation outcome. The original design was to have a trust index based on concession reciprocity correlations. As explained in section 3.4, that measure was not viable for the purpose it was intended to serve: deterministic concession logic resulted in a constant value in four of five frameworks, reducing the variable to a framework-level label. This is a real constraint of the simulation architecture and is an indication of the need for stochastic trust modelling in future work. Although there is a long history of reputation and trust in the computational literature in multi-period settings (Louta, Roussaki, & Pechlivanos, 2006), the modelling of emergent, experience-based trust in a single ten-round negotiation is still an open design challenge.

3. Methods

3.1 Design Overview

The study was conducted using a within subjects’ experimental design. Eight hundred buyer–supplier agent pairs were generated by drawing reservation utilities, aspiration utilities, and issue-level ideal points from uniform distributions, using the Mersenne Twister pseudo-random number generator with two fixed seeds (42501 and 42502), that is, two randomisation blocks of 400 pairs each. There were 4,000 negotiations, each pair negotiating under all five frameworks. Block was added to initial analyses as a control factor and was not significant for any outcome variable (all p > 0.42).

All negotiations were conducted in a stylised industrial procurement situation with four interdependent issues: price (weight 0.40), delivery time (0.25), service duration (0.20), and payment terms (0.15). A synthetic construction was used for the scenario, and no proprietary contract data were used.

The design parameters used across all 4,000 negotiations are summarised in Table 1

Table 1. Experimental design summary

3.2         Agent Architecture

Every agent has a private utility function defined on the four issues, a reservation utility, an aspiration utility and a concession schedule defined by a framework-specific elasticity coefficient. All frameworks share the same simulation engine, with the only differences being the information-disclosure rule and the different values of the agents' parameters.

Utility function. For agent i and offer vector x, utility is defined as:

Uᵢ(x) = Σⱼ wⱼ · vᵢⱼ(xⱼ)

where wⱼ denotes the issue weights given in Section 3.1 and vᵢⱼ normalises issue j linearly onto the interval [0, 1] between the agent’s reservation and aspiration points. Joint value is then computed as the mean of the two agents’ final utilities, expressed as a percentage of the Pareto-efficient maximum for that scenario instance:

Joint Value = [ (U_buyer + U_seller) / 2 ] ÷ U_max × 100

Concession schedule. At round t of T = 10, the agent’s target utility follows:

Tᵢ(t) = U_res + (U_asp − U_res) · [ 1 − (t / T)^(1/βᵢ) ]

where βᵢ is the concession-elasticity parameter. Higher values of β produce earlier, more linear concessions; lower values produce back-loaded ones. A reciprocity multiplier scales β in response to the opponent’s prior concession.

where βᵢ is the concession-elasticity parameter. The higher the value of β, the earlier and more linear the concessions will be, the lower the value of β, the more back-loaded the concessions will be. A reciprocity multiplier is a factor that scales β according to the opponent's previous concession.

Offer selection. At every round, the agent looks for the offer in the offer space that maximises the utility of the opponent based on the current belief state and has the target utility. An agent that reveals their weight vector enables the opponent to accurately estimate their weight vector from the disclosure round onwards.

Agreement guarantee. At round 10, all 4000 negotiations reached an agreement. This is not an empirical property of the design. The minimum acceptable share parameter is lower than the minimum possible utility share in all the instances of scenarios, and the concession schedule is designed to guarantee that the target utilities of both agents will converge monotonically to the minimum acceptable ones as t gets closer to T. Thus, an impasse condition cannot occur in the architecture. The simulations would have to be broken down with a walk-away threshold above the convergence point or with an exogenous termination probability, neither of which was done. The uniform agreement rate should thus be interpreted as a limit of the design and not as proof that these frameworks are always able to deliver deals.

3.3         Framework Operationalisation

A parameter configuration and disclosure rule were created for each framework. The translation is an interpretive act, and the results are a description of the performance of these operationalisations and not of all the possible computational renditions of the same philosophy. Table 2 contains the full parameterisation which can be used to replicate or re-specify any agent independently.

Table 2. Computational operationalisation of each framework.

Note. β = concession elasticity; Reciprocity = multiplier applied to β when the opponent concedes; Disclosure round = round at which the agent reveals its issue-weight vector; Min. share = minimum acceptable utility share; Explore = propensity to search alternative offer configurations; Claim = value-claiming propensity; Volatility = stochastic variation in offer generation.

Three design features are worthy of comment. Both the SMARTnership and Harvard agents have the same base concession elasticity (β = 1.00, which results in linear concession), but with different reciprocity and disclosure: SMARTnership increases concessions to the extent that the opponent does, and it also reveals full issue weights at round 3, whereas Harvard increases concessions symmetrically and it reveals interests but not reservation values at round 2. The Voss agent has a back-loaded concession (β = 0.40), which means it waits until late rounds to move and is also the agent with the highest minimum-share threshold, indicating tactical anchoring and controlled information flow. No agent was given access to the opponent’s concession algorithm or private parameters.

There is a special caution with the operationalisation of tactical empathy in the Voss agent. There is no unambiguous computational analogue of the construct, and here it is modelled as the accurate opponent-preference inference deployed for value claiming. This is one defensible interpretation of the framework, but not the only one, and an alternative specification might change the Voss agent's behavior.

3.4         Outcome Variables

Three dependent variables were computed from the simulation logs at the conclusion of each negotiation.

Joint value captured is the mean of the two agents’ final utilities expressed as a percentage of the Pareto-efficient maximum for that scenario instance, as defined in Section 3.2.

Concession-process quality captures the symmetry and smoothness of the concession path on a 0–10 scale:

CPQ = 10 · [ 1 − |ΔU_buyer − ΔU_seller| / (ΔU_buyer + ΔU_seller) ] · [ 1 − σ_c / μ_c ]

where ΔU denotes each agent’s total utility movement across the negotiation, and σ_c and μ_c denote the standard deviation and mean of round-by-round concession magnitudes. The result is floored at zero. Higher values indicate a more reciprocal and less erratic bargaining process.

Outcome asymmetry is the absolute difference between the two agents’ final normalised utility shares:

Asymmetry = |U_buyer − U_seller|

The index is bounded [0, 1], with zero denoting perfectly symmetric division. Lower values indicate a more balanced allocation of value.

In the simulation logs, a fourth variable, the trust index, was calculated as 10 · max(0, r_c) · (1 − retraction rate) with r_c being the correlation between the two agents' round-by-round concession magnitudes. This metric resulted in one constant score from four of the five frameworks: SMARTnership (9.20), Harvard (6.00), Conti (8.20), and Gap Partnership (9.20), with the only within-framework variation being the Voss agent (M = 7.27, SD = 0.43). This reflects the architecture of the simulation. Deterministic concession schedules produce the same round-by-round concession correlations no matter what endowment draws are made and so the trust formula reduces to a framework-level constant. The trust index is therefore not an observation-level result, but a design parameter. It cannot be used in any analysis that involves within-group variation, such as analysis of variance or regression, and is only included in Table 3 as a design characteristic. The theoretical implications are discussed in section 5.5.

3.5         Statistical Analysis

Each buyer–supplier pair was tested under all five frameworks, which means that the observations are not independent and between-subjects analysis of variance would be inappropriate. Nonparametric within-subjects tests are used for all primary analyses. Omnibus differences among the five matched groups were examined using the Friedman test. Post hoc contrasts were conducted with pairwise Wilcoxon signed rank tests with the Bonferroni correction for ten comparisons (α = 0.005). Effect size estimates were obtained using paired Cohen's d, which is the mean difference between the pairs divided by the standard deviation of the differences.

The Levene's test showed that the variances were significantly different among the frameworks on all three variables, justifying the use of nonparametric techniques. The coefficient of variation was calculated for each framework. Pairwise mean differences in joint value were calculated and 95% bootstrap confidence intervals (10,000 resamples, percentile method, seed 42) were calculated. The analysis was performed using Python (SciPy 1.11, NumPy 1.26) and verified in R.

3.6         Data and Code Availability

The entire set of raw simulation logs, including offer-by-offer records for 4,000 negotiations, the negotiation-level dataset, the analysis scripts, the simulation configuration file, and a data dictionary are placed in a public repository. A reviewer-access link is provided with this submission, and a permanent digital object identifier will be assigned on acceptance. Random seeds, all framework parameters and command sequence to reproduce all reported statistics are released.

4.           Results

4.1         Descriptive Statistics

Table 3 presents the mean and standard deviation for each outcome variable across the five frameworks. The rankings vary across the three dimensions.

Table 3. Descriptive statistics by framework (n = 800 per framework)

SMARTnership had the greatest percentage of available joint value (93.78%) and the lowest coefficient of variation (4.00%), which means that it had the highest mean value and the most consistent performance. Voss captured the least (78.07%) with the highest variability (CV = 9.17%). The ranking changes with respect to concession-process quality: Harvard was the smoothest and most reciprocal concession path (9.69), SMARTnership was fourth (6.33), and Voss last (5.16). In terms of outcome asymmetry, the low values from Harvard and SMARTnership were very similar (0.040 and 0.042, respectively), showing that both frameworks split value fairly evenly, whereas Voss had the most one-sided outcomes (0.097).

Figure 1. Mean joint value captured by framework, with 95% confidence intervals.

4.2         Omnibus Tests

Friedman tests indicated significant differences across frameworks on all three outcome variables: joint value, χ²(4) = 1,598.04, p < 0.001; concession-process quality, χ²(4) = 3,184.34, p < 0.001; and outcome asymmetry, χ²(4) = 1,086.58, p < 0.001.

Levene’s tests confirmed unequal variances across frameworks on all three measures: joint value, W

= 95.50, p < 0.001; process quality, W = 61.65, p < 0.001; and asymmetry, W = 271.58, p < 0.001. These results support the use of nonparametric methods throughout.

4.3         Pairwise Comparisons

Table 4 presents the results of pairwise Wilcoxon signed-rank tests with Bonferroni adjusted p-values and indicates that the SMARTnership improvement over all of the comparison frameworks was statistically significant and practically meaningful.

Table 4. Pairwise Wilcoxon signed-rank tests for joint value (Bonferroni-adjusted)

After Bonferroni correction all pairwise differences in joint value were still significant. The SMARTnership's advantage over each comparison framework was large (paired d = 0.99 to 1.99), and bootstrap 95% confidence intervals excluded zero in all instances, the comparison to Harvard for example being [6.40, 7.26].

Table 5 presents pairwise comparisons for concession-process quality and outcome asymmetry, where the ranking pattern differs from that observed for joint value.

Table 5. Selected pairwise comparisons for concession-process quality and outcome asymmetry

The Harvard agent showed the highest concession process quality with raw mean differences ranging from 1.33 to 4.53 points on the ten-point scale. On this measure, SMARTnership did better than all but Voss. There was no significant difference between Harvard and SMARTnership on outcome asymmetry (adjusted p = 1.00, mean difference 0.002 index units), and both were significantly more balanced than Conti, Gap Partnership, and Voss.

Figure 2. Performance profiles of the five negotiation frameworks across the three evaluation dimensions.

Figure 3. Forest plot of Cohen's d effect sizes for pairwise comparisons involving SMARTnership.

4.4         Summary of Rankings

 Table 6 summarises the framework rankings across the three outcome variables.

Table 6. Framework rankings by outcome variable (1 = best)

No framework achieved a top scoring position on all three dimensions. SMARTnership delivered the highest joint value and was fourth in concession-process quality. Harvard had the most symmetric value division and the smoothest bargaining process and ranked third on value creation. Conti was second in both process quality and value creation and thus had the most consistent overall profile. Gap Partnership finished fourth on two of the three indicators. Voss was last on all the measures.

Figure 4. Comparative ranking of negotiation frameworks across the three evaluation dimensions.