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The article is a computational modeling and simulation article published in Strategy Science. It extends the NK fitness landscape framework to study how social reference points shape organizational search, adaptation, and competitive survival. The article does not use survey data, interviews, archival firm data, or regression analysis. Its evidence comes from formal modeling and simulation experiments.
Research question
How do reference points shape the constraints and outcomes of problemistic search?
More specifically, the article asks how aspiration levels and survival points affect which parts of a complex search landscape organizations can access, whether peer comparison improves search outcomes, and when reference-point-guided search helps organizations adapt rather than trapping them.
Hypotheses
Not specified.
The article does not test formal numbered hypotheses. Instead, it develops a simulation model and uses three sets of simulation experiments to examine how different combinations of upper and lower reference points affect search behavior, adaptation, performance, and survival.
Method
The article develops an extension of the NK fitness landscape model.
In the standard NK model, agents search across a landscape made up of possible configurations. Each configuration has a performance value. The parameter N captures the number of binary choice dimensions, while K captures the degree of interdependence among those dimensions. When K is low, the landscape is smoother and easier to search. When K is high, the landscape is more rugged, with more local peaks that can trap local search.
Zeijen, Romagnoli, and Marengo modify the standard NK model by adding two social reference points:
- an upper bound, representing the aspiration level;
- a lower bound, representing the survival point.
The upper bound is the performance ranking at or above which the agent is satisfied and stops searching. For example, an upper bound of 0.75 means the agent aims to be in the top 25% of the population.
The lower bound is the performance ranking below which the agent considers an option unacceptable. For example, a lower bound of 0.25 means the agent refuses to take an action that would place it in the bottom 25% of the population.
Both reference points are social, meaning they are defined relative to the performance of other agents rather than as fixed absolute performance targets.
The key modeling idea is that reference points transform a rugged landscape into a subjective terraced landscape. Instead of evaluating every local option only by whether it improves current performance, agents classify positions into three terraces:
- desirable positions at or above the upper bound;
- acceptable but not satisficing positions between the lower and upper bounds;
- unacceptable positions below the lower bound.
Figure 1 on page 2 illustrates this transformation. The original rugged landscape is cut by an upper plane and a lower plane. These planes divide the landscape into desirable, acceptable, and unacceptable zones. As the population improves, the absolute performance levels associated with the social reference points rise, so the terraces shift upward over time.
The article uses three main simulation experiments.
First, it studies a homogeneous population in which all agents share the same reference points. The baseline illustration uses an upper bound of 0.75 and a lower bound of 0.25 with 100 agents.
Second, it explores all combinations of upper and lower reference points in homogeneous populations. This identifies which combinations produce better short-run and long-run collective outcomes.
Third, it studies heterogeneous populations in which different groups of agents have different reference points. In this setting, the model also introduces competitive pressure: five agents per period exit and are replaced by new entrants using a roulette-wheel selection mechanism.
The article reports that all main results are based on averages of 10,000 simulations. Each simulation generates a new landscape, and landscape fitness values are rescaled to the zero-one interval. Time is shown on a logarithmic scale to highlight short-run and medium-run dynamics.
The robustness checks examine alternative specifications, including SoftMax decision rules, absolute rather than rank-based reference points, reference points based on both past and peer performance, imperfect evaluation, and random movement when all available options are below the lower bound.
Results / key findings
The article’s first major finding is that reference points change the structure of search.
In a standard NK model, agents often climb to the nearest local peak and then become stuck. Search stops because no neighboring alternative improves current performance. With social reference points, agents can move across a wider middle terrace of options that are acceptable but not yet desirable. This allows them to access larger portions of the landscape and sometimes avoid local traps.
This does not mean reference points directly tell agents where better outcomes are. The article describes reference points as signposts. They indicate what level of performance is desirable or unacceptable, but they do not reveal the path to high performance. Agents still need to search locally and may still become trapped.
The baseline homogeneous simulation uses an upper bound of 0.75 and a lower bound of 0.25. At the start, 25% of agents are already satisfied because they are above the upper bound, while the rest search. Over time, some searching agents reach desirable positions and stop, while others continue moving through acceptable positions. As better outcomes are discovered, the absolute performance levels linked to both the upper and lower bounds rise. This gradually shrinks the accessible middle terrace.
Figure 2 on page 8 shows this process. Average performance rises over time, but the increase mainly comes from agents moving from the middle terrace to the upper terrace. Performance conditional on being on a given terrace remains relatively stable. This means aggregate improvement is driven less by smooth incremental improvement and more by agents crossing the upper reference boundary.
The second major finding is that upper and lower reference points play different roles over time.
The upper bound matters more in the short run. Higher aspirations push agents to search more aggressively early on, increasing the chance that they reach better outcomes quickly.
The lower bound matters more in the long run. A low lower bound makes the acceptable middle terrace wider, allowing agents to tolerate temporary performance declines and move through more of the search space. This can help them escape local peaks and eventually find better long-run outcomes.
Figure 3 on page 9 shows performance across combinations of upper and lower bounds. In the short run, performance patterns are mostly shaped by the upper bound. In the long run, they are mostly shaped by the lower bound. The long-run pattern is especially clear: populations with very low lower bounds can achieve the highest collective performance, even when their upper bound is only moderately high.
The third major finding is counterintuitive: very low survival points can produce excellent long-run collective performance. In homogeneous populations, agents with very low lower bounds and upper bounds above roughly 0.4 can eventually reach the best possible outcomes. This happens because a low lower bound prevents premature trapping. Agents are willing to accept temporary performance losses, so they can move through larger parts of the landscape.
However, this comes at a cost. Search with low lower bounds can be slow and risky. Agents may accept low-performing intermediate positions while looking for better long-run outcomes. In a competitive environment, that can expose them to exit before the long-run payoff arrives.
The fourth major finding is that complexity increases the value of a wider search space. Figure 4 on page 10 compares performance under low complexity, medium complexity, and high complexity. As expected, high K values make adaptation harder because the landscape becomes more rugged. A low lower bound helps agents overcome competency traps, especially in complex landscapes, but the benefits appear more slowly.
The fifth major finding is that the best reference-point strategy changes when agents compete with others that use different reference points.
In heterogeneous populations with competitive pressure, the best-performing agents are not those with the lowest lower bounds. Instead, agents with moderate upper bounds and moderate lower bounds perform best. The article’s key competitive setting uses nine groups of 10 agents with upper bounds of 0.51, 0.75, or 1.0 and lower bounds of 0.01, 0.25, or 0.5. In this setting, the strongest survival outcomes occur for agents with an upper bound of 0.75 and a lower bound of 0.25.
Figure 5 on page 11 shows why. Agents face a dynamic trade-off. If the upper bound is too low, agents become satisfied too easily, stop searching, and may be overtaken by competitors. If the upper bound is too high, the target may be too difficult to reach. If the lower bound is too low, agents may search too broadly and risk falling behind before they find a strong outcome. If the lower bound is too high, agents may search too narrowly and become trapped.
The sixth major finding is that reference points require both internal fit and external fit.
Internal fit concerns the relationship between the upper and lower bounds. If the distance between them is too narrow, agents search too little. If the distance is too wide, agents search too much. The relationship between performance and the distance between the bounds follows an inverted U-shape.
External fit concerns the match between reference points and environmental conditions. The best reference points depend on landscape complexity, competitor reference points, and competitive pressure. A reference-point combination that works well in a homogeneous population may perform worse in a competitive heterogeneous population.
Figure 6 on page 12 illustrates this external-fit logic. Agents with the same reference points, an upper bound of 0.75 and lower bound of 0.25, perform differently depending on the population around them and whether competitive pressure is present. Worse-performing peers can keep the distance between reference points wide for longer, which sustains search opportunities. Competitive pressure pushes performance upward but also creates exit risk.
The robustness checks support the article’s core argument. Alternative assumptions change the speed or strength of effects but do not eliminate the central result: decision makers need a middle terrace that is neither too wide nor too narrow. Search fails when reference points constrain search too much or when they permit excessive wandering.
Overall, the article shows that reference points do not merely determine whether organizations search. They determine where search can unfold, how much local performance loss organizations tolerate, and which long-run outcomes remain reachable.
Practical implications
For managers, the article’s core implication is that performance targets do not only motivate search. They shape the kind of search that becomes possible.
A high aspiration level can be useful because it prevents premature satisfaction. If managers set aspirations too low, organizations may stop searching too early and settle for mediocre outcomes. However, high aspirations alone are not enough. If the organization also has a high survival point, meaning it refuses to accept short-term performance losses, search may become too narrow to escape local traps.
The lower reference point is especially important for strategic adaptation. Firms often need to accept temporary setbacks, experimentation costs, or performance dips to reach a better future position. If managers treat every short-term decline as unacceptable, they may trap the organization in a familiar but inferior position.
This is particularly relevant for established firms facing technological or market change. The article discusses Research In Motion, known for BlackBerry, as an illustrative case. RIM faced pressure from iPhone and Android smartphones and made some adaptations, such as adding a clickable screen and an app store. However, it resisted deeper changes, such as fully abandoning the physical keyboard. In the article’s terms, RIM may have been constrained by a lower bound that made some necessary adaptations seem too damaging.
The article also warns that more search is not always better. A very low survival point can help in the long run, but in competitive environments it can expose the organization to failure before the benefits arrive. Managers therefore need a balanced search space: broad enough to escape local peaks, but not so broad that the firm drifts or becomes vulnerable.
For strategic decision-making, the article suggests that managers should explicitly discuss both aspiration levels and survival points. Many organizations focus on what they want to achieve, but they pay less attention to how much temporary decline they are willing to tolerate while adapting. The survival point may be the hidden constraint that determines whether transformation is possible.
The article is also useful for target-setting and benchmarking. Peer comparison can be helpful because it reveals that better outcomes are possible. But peer comparison can also mislead if peers are on very different trajectories or occupy different parts of the strategic landscape. A firm should not assume that because a peer performs better, the path to that peer’s position is locally accessible.
For practitioners, useful diagnostic questions include:
- What is the organization’s upper reference point or aspiration level?
- What is the lower reference point below which leaders refuse to go?
- Is the gap between aspiration and survival wide enough to allow meaningful search?
- Is the gap so wide that the organization risks drifting or taking excessive short-term losses?
- Are performance targets based on peers that are actually comparable?
- Are leaders using peer performance as a signal that better outcomes are possible, or as a misleading map of how to get there?
- Does the organization tolerate temporary performance declines when they open access to better future options?
- Does competitive pressure make a long search strategy too risky?
- Are targets suited to the complexity of the environment?
Theoretical implications
The article contributes to the behavioral theory of the firm by unpacking the search process behind problemistic search.
Much research on problemistic search focuses on when organizations search: usually when performance falls below aspirations. Zeijen, Romagnoli, and Marengo focus on how reference points shape the search space itself. This moves the literature beyond search triggers and risk-taking toward the constraints and reachable outcomes of search.
The article also contributes by distinguishing the roles of aspiration levels and survival points. Prior research often treats both reference points as influencing attention and risk-taking. This article shows that they play different roles over time. The upper bound is more important in the short run because it determines whether the agent keeps searching. The lower bound is more important in the long run because it determines how much of the landscape remains accessible.
The article contributes to research on complex adaptive systems by connecting problemistic search with NK fitness landscapes. Standard NK models often assume that agents search for performance improvements relative to their current position. This article shows that when agents evaluate outcomes through social reference points, the perceived landscape becomes terraced rather than rugged.
The terraced landscape idea is theoretically important. It shows that neutrality or indifference is not only an external feature of the environment. It can be created internally by the organization’s evaluation rules. If multiple outcomes are all classified as acceptable but not aspirational, the organization may treat them similarly even if their actual performance values differ.
The article also contributes to organizational inertia theory. Inertia can arise not only from routines, capabilities, or adjustment costs, but also from reference points. A high lower bound can trap an organization because decision makers refuse to move through temporarily worse positions that would open paths to better outcomes.
The article further contributes to strategy research on firm heterogeneity. Firms may perform differently not only because they occupy different landscapes or possess different resources, but also because they use different reference points to evaluate the same environment.
Limitations
The article uses a simulation model rather than empirical firm-level data. The results should be interpreted as theoretical mechanisms, not direct estimates of real-world effect sizes.
The model simplifies organizational decision-making. Real firms have multiple goals, political coalitions, changing leadership, imperfect information, resource constraints, and internal conflicts that are not fully captured.
The model assumes agents can observe local fitness values before adopting a configuration. Real organizations often do not know the performance consequences of a strategic move until after implementation.
The main model focuses on social reference points defined by population rank. Real organizations may use multiple reference points at once, including historical performance, analyst expectations, regulatory targets, budget commitments, stakeholder claims, and absolute survival thresholds.
The model treats the upper and lower bounds as relatively simple decision rules. In real organizations, aspiration levels and survival points may be ambiguous, contested, and interpreted differently across units.
The model’s competitive selection mechanism is stylized. Real exit depends on financing, slack resources, legitimacy, regulation, customer relationships, and strategic support from owners or governments.
The model does not directly test specific industries or firms. Examples such as BlackBerry help illustrate the logic, but they are not empirical tests of the model.
Future research
Future research could empirically test whether firms with different aspiration and survival points adapt differently to technological change.
Researchers could examine how managers set survival points in practice. Survival points may depend on financial slack, debt, investor patience, organizational identity, political constraints, or fear of legitimacy loss.
Future studies could analyze when peer comparison helps adaptation and when it misleads firms by pointing to peers that are too distant in technology, business model, or organizational capabilities.
Another useful research direction would be to study how firms adjust reference points over time. Organizations may need different aspiration and survival points in stable environments, transformation periods, and crisis situations.
Researchers could examine reference points in strategic transformation cases such as electric vehicles, artificial intelligence adoption, digital platform shifts, energy transition, or software-defined manufacturing.
Future research could connect this model to middle-management behavior. Middle managers may translate, soften, resist, or intensify upper and lower reference points during implementation.
Another direction would be to examine how multiple reference points interact, such as social aspirations, historical aspirations, budget targets, analyst expectations, and minimum liquidity thresholds.
Researchers could also study how boards, investors, and incentive systems affect the width of the search space by rewarding high aspirations while either tolerating or punishing temporary performance decline.
Finally, future work could test how reference-point design affects innovation portfolios: whether firms with moderate search spaces are better able to balance exploitation, exploration, and survival under competitive pressure.