Strategic decision-making under ambiguity: a new problem space and a proposed optimization approach

Most research in management focuses on decision-making in risky contexts, given the ease of modeling and experimenting on expected utility maximization (e.g., Malecka 2020; Starmer 2000). However, ambiguity poses a more important type of uncertainty context facing managers making strategic decisions (Paraschiv and Shyti 2016). Where with risk the probabilities of the focal outcome possibilities are known ex ante, with ambiguity they are not, and that makes objective optimization over choices impossible. Thus, we propose a new approach for dealing with strategic decision-making under ambiguity (SDMUA).

Current SDMUA approaches are severely limited. Either they do not move away from a behavioral perspective that simply describes what managers do when confronted by ambiguity in a lab or in a unique case setting, or they do not actually capture ambiguity instead reducing it to risk by invoking subjective beliefs over unknowable expected outcomes. And, none yet extend the DMUA to strategic competitive issues. That leaves a gap for a new SDMUA approach that retains the effects of ambiguity and provides a normative path to better decision-making.

Better dealing with ambiguity is an important and widely-applicable concern. Most daily decisions involve incomplete knowledge, and specifically the kind that generates uncertainty over outcome probabilities, better known as ambiguity (e.g., Peysakovich and Karmarkar 2016). Such decisions include everything from choosing a dish from a menu to choosing a medical or retirement plan to contemplating the value of a stock (e.g., Jia et al. 2020; Peysakovich and Naecker 2017). Such decisions also confront managers facing decisions that can affect firm performance, like hiring, tactical policy setting and target valuation (e.g., Cinelli 2020; Pike et al. 2018; Peysakovich and Karmarkar 2016).

As many scholars astutely have noted, “…empirical evidence (e.g., Becker and Brownson 1964; Curley and Yates 1985; Gardenfors and Sahlin 1982; Yates and Zukowski 1976) has shown that ambiguity affects judgments and choices and should not, therefore, be ignored” (Einhorn and Hogarth 1986: S227). For example, Hahn et al. (2014) find that ambiguity significantly affects decision-makers’ proclivity to choose more radical alternatives. These decisions do not involve risk; rather, they are often described as involving Ellsbergian ambiguity (1961)—a form of Knightian (1921). Ambiguity is a concept that decision-makers must address, and one that can be used to create strategic value (e.g., Petkova et al. 2014; Srivastava 2015). The main reason is that ambiguity prohibits the calculation of first-best solutions to those decisions in reality (e.g., Elbanna and Child 2007); the optimal choices for such decisions cannot be identified in the standard way ex ante. But, at present, there is no accepted, standard approach to dealing with SDMUA. There are descriptions of what humans do. There are mathematical models that reduce ambiguity to the risk and determine what humans should do based on their subjective beliefs. But, there is no prescription for what to do when ambiguity remains ambiguity. That is why it is important to provide an approach that improves decision-making in situations where managers are forced to commit to resource investments while facing important, indeterminate, uninsurable, competitive futures that will affect organizational performance.

To fill that gap, we focus on what a logical, rational, objective, properly-incentivized manager should decide when confronted by ambiguity. As such, our approach is necessarily theoretical; it is provided at a general problem level. That means it is not immediately applicable in a real world because, at that level, the specifics of the problem, of the ambiguity and of the manager’s incentive contract, are all likely to affect how our approach would be implemented on-sight. While decision-making is most often not conducted in a rational, objective or general way, we nevertheless do see value in analyzing it as such. We follow the rich tradition in the theoretical literature for conducting such analysis because we expect it to be of value not only as a benchmark for decision-makers to draw upon but also because we expect that for strategic decisions, such greater rationality, objectivity and efforts will actually be present. And, because of the theoretical nature of our approach, we can draw on several powerful tools in our solution to SDMUA, including game theory and contract design. Game theory is relevant because these problems deal with interdependent payoffs and rivals. Incentive contract design is relevant because we focus on choices made by a firm manager, who is expected to rationally behave based on how they are compensated in ways that align with the owners’ interests. To our knowledge, based on keyword searches across business journals, no papers have combined all of the tools we have in one approach, let alone to address a SDMUA problem. So, this is new and speaks to the leverage that current economic concepts can generate when packaged together in an appropriate context.

Our intended contribution threefold: first, we describe SDMUA as a new branch of SDM. Second, we outline our theoretical second-best solution approach as a new combination of existing economic tools. Third, we offer a set of new prescriptions and predictions based on the use of that approach.

We argue for our new SDMUA approach in the remainder of the paper. We review the research to put our contribution in perspective. We specify the example we use to capture SDMUA. Then, we provide our new resolution to the challenge of SDMUA–one that is theoretically implementable. Based on that, we propose several performance-related relationships, and discuss the implications our approach has for academics, practitioners and policy-makers.

Ambiguity has many definitions in the literature, so there is a need to be clear on which one is used (as we are in the next section). Most of the ambiguity research has been conducted at the level of individual decision-making, and mostly in a behavior way, and even more specifically, in terms of its avoidance. However, there exists some research relating to how to deal with it in important decisions and what the costs are associated with its effects. It can affect strategic decision-making, but there is insufficient work on that topic at present. With that summary, we proceed in reviewing the relevant literature in more detail now.

Perhaps ironically, one problem with making progress in addressing ambiguity is the ambiguity involved in that term. There exist significant imprecision and disagreement over the concept of ambiguity in the literature. Ambiguity has been conceptualized as a specific type of informational context facing a decision-maker. The nature of that context has been characterized in several ways. The context has most often been characterized in terms of the quantity and determinacy of information available (Forbes 2007). The context has been characterized in terms of the heterogeneity of the underlying available data, the imprecision of that data, and the lack of consensus over its applicability. Further, the context has been characterized by the lack of quality and frequency in that underlying data, its noise, its relevance, its type, its reliability, and the credibility of its source. The context has been characterized by the extent of expert disagreement over that underlying data, and the potential for multiple interpretations of it (Eichberger and Guerdjikova 2013; Pich et al. 2002). And, the context has been characterized in terms of unknown outcomes (Camerer and Weber 1992), in terms of the unknowns about the processes that generate them. Conceptualizing ambiguity in this way also entails assessing the range of unknown information defining it (Lant and Mezias 1990), its level of uniqueness (Ellsberg 1961), and the nature of how the ambiguity was transmitted to decision-maker.

Ambiguity has also been studied in terms of individual-level factors affecting SDMUA. For example, it has been studied in terms of the decision-maker’s strength of prior beliefs over the probabilities of the decision’s alternative outcomes, the decision-maker’s level of experience dealing with similar decisions, and the decision-maker’s strategic motive in becoming involved (e.g., Sillince et al. 2012). It has been studied in terms of the decision-maker’s stance as reactive or proactive, protective, invited, adaptive, or something else. It has been studied by analyzing the source of the decision-maker’s strategic concern regarding the ambiguity (Bajtelsmit et al. 2015) in terms of whether it is based on the lack of control or on some fear or on the maximum downside. It has been studied in terms of the effects on the capacity of the decision-maker to process the choices, based on the information load, complexity, numerousity, diversity, and interdependencies involved in the decision.

Finally, ambiguity has also been studied in terms of its possible ways strategic effects and ways to address them. In terms of how its effects can be addressed, the literature has considered several possible ways to mitigate the downsides (Cerreia-Vioglio et al. 2013; Gollier 2014), such as choosing a maximin alternative or building some insurance or some exit option. Research has involved assessing the costs to reduce the ambiguity (Rindova et al. 2010) and to what extent it can be reduced over a set time period. The literature has also attempted to identify the range and variance of the possible outcomes involved in the ambiguous decision and its interventions (Machina 2014). In terms of attempting to clarify ambiguity’s possible strategic effects, studies have taken several paths. One path consists of distinguishing the level of surprise potentially involved in the ambiguous situation, and specifically whether any outcomes involve violations of laws or norms. Another path consists of identifying the level of analysis of the ambiguity affects (Miller 1993) in terms of the potential strategic consequences at the national, industry, firm, and project levels. Such consequences assess the types of externalities potentially involved, in addition to establishing whether the ambiguity is interconnected with other choices and to what extent (Langley et al. 1995).

The ambiguity over what ambiguity means is much lower in the behavioral economics literature related to decision-making. Work in the theory of evidence (Shafer 1976), fuzzy sets (Zadeh 1978), ambiguous probabilities (Marschak 1975), and probability ranges (Curley and Yates 1985; Wallsten et al. 1983) all relate to the type of ambiguity we use here and as defined in gambles over colored balls in urns, as described by Ellsberg (1961, 1963). For example, from Ellsberg’s work, there has emerged strong agreement over the observed and experimentally-verified individual-level bias termed ambiguity aversion (e.g., Budescu et al. 2002; Curley and Yates 1989; Gilboa and Schmeidler 1989; Heath and Tversky 1991; Schmeidler 1989). That bias describes an overweighting low likelihoods and an underweighting high likelihoods of possible outcomes (Paraschiv and Shyti 2016). There is also high consistency in terms of how DMUA research has mathematically explained ambiguity aversion. That research has mostly invoked models based on prospect theory-as-behavioral-predictions over how people make risky choices based on subjective beliefs and utilities. Such models include the decision-maker’s utility function combined with her probability weighting function over possible outcomes (e.g., Kahneman and Tversky 1979; Tversky and Kahneman 1992). However, such models struggle to explain observed behaviors in SDMUA-like settings (e.g., Li et al. 2017).

Ambiguity is a recognized, and often explicitly described, factor that makes strategic decisions even more challenging. It appears as one main reason that incomplete contracts exist in transaction cost economics (Tadelis 2002). It appears as one main reason why waiting to invest is important in real options theory (McGrath 1999). And, it appears as one main reason for the popularity of approaches like fast-fail, rapid-prototype, and focused experimentation when businesses enter new frontiers (Newman 2009).

To illustrate how our new approach to SDMUA works, we first need to describe an example decision. And, to do that, we need to define our main concepts, list our assumptions and then detail the model of that decision facing the firm manager.

Figure 2 is a flowchart depicting our new approach to the SDMUA problem. The manager is given the set of possible investment choices structured into subsets of choices, with each subset being defined in a row or a column of a normal form competitive game. It is a simultaneous-move game, given our definition of T and, without loss of generality, it is played against one rival firm’s manager. An irreducible ambiguity exists, denoted by ‘p’. The decision-making manager knows the incentive system that the firm owners are applying to influence her investment decision.

We summarize the approach first and then provide details in the subsections that follow. The proposed approach begins with the manager trying to maximize the payoff in each cell of the game. The manager understands that she is choosing a specific action that defines a specific subset of the investment choices while her rival is also choosing a specific action. The first step in the approach involves constructing the efficiency frontier for the subset of investment choices in the cell. This is accomplished by computing the conditional payoffs for each investment choice in the cell, and then plotting the ‘p’ versus ‘1 – p’ points that can be used to calculate a continuous frontier made up of combinations of the investments. The second step in the approach involves choosing a point along that frontier that the principals direct from the incentive scheme they use to reward the manager; this is done through backward induction. The third step involves solving the full game that is made up of the computed information in the cells of the game. This involves: (i) entering that point as the chosen payoff in the cell for the manager, and then running the same analysis for the rival manager and entering its point in that cell as well; (ii) repeating all previous steps for the remainder of the cells for both the focal manager and the rival manager; and, (iii) then identifying the Nash equilibrium based on the full game. The approach is complete when the manager chooses the firm’s Nash equilibrium strategy that also indicates the specific investment choice in that equilibrium cell.

Second, from step two we know that it is likely some firms can gamble their way into a potential short-term advantage by taking an aggressive stance on investment choices. For example, we know that those firms betting it all on one outcome with a maximax attitude, if lucky, can gain an immediate advantage over firms taking a maximin approach. In markets characterized by pro-entrepreneurial factors (e.g., forgiving bankruptcy laws and possible first-mover advantages), we expect that aggressive firms (i.e., those choosing the maximax reward system) will attempt to enter those markets more when SDMUA problems arise, and that the ones which survive will have a temporary advantage from having guessed right. So, we prescribe, when possible, for the incumbent to ‘take options’ (e.g., have an expandable ownership stake) in such entrants to share in their good fortunes. When that is not possible, we advise purchasing complementary assets that a lucky entrant would need to monetize on its own investment choice. The second prediction is that the firms proactive enough to mitigate the effects of lucky new entrants (e.g., through investing in relevant options or complementary assets) should perform relatively better than those that do not.

Third, from step three we know that interdependencies will affect the optimal choice of investments. The practical advice is for principals to tailor their firms’ reward systems to the interdependencies involved. This could be as simple as including a relative performance term in the reward along with an absolute performance term. The third prediction is that the firms that implement reward systems that explicitly account for interdependent payoff effects when their managers are confronted by SDMUA problems should perform relatively better than those that do not.

The fourth prediction arises from the combination of the three steps: We expect the firms—through their managers and principals—that more closely follow our new approach when confronted by SDMUA problems will perform better than those that do not.

We have described a new type of problem—the SDMUA—and a new approach to solving such challenges in the DMUU literature. Ours is the first approach to not violate the assumption of ex ante unknowable outcome probabilities. It is the first approach to explicitly exploit conditional probabilities regarding what could occur if the focal outcome—the one generating the ambiguity—does not occur. It exploits those probabilities by applying the standard efficiency frontier tool to remove dominated alternatives. Ours is the first approach to explicitly consider decision-maker incentives through backwards induction logic. It does so to identify the payoff-maximizing point on the efficiency frontier for the decision-maker. Ours is the first approach to explicitly account for competitive payoff interdependencies. It applies standard game-theoretic analysis to address interdependencies with payoff-related effects of a rival’s manager who is also making investment choices relating to the ambiguity. We suggest that the payoffs for each decision choice combination in the overall decision game need to be calculated to identify the Nash equilibrium. We also contribute to the literature with new prescriptions and predictions based on the three steps underlying our approach.

We proposed SDMUA as a new branch in the rich DMUA literature, a literature that is growing in importance for management for several reasons. First, it is a reality that organizations are more regularly facing problems that are both strategic and ambiguous. Second, the firms facing more of these problems are the firms that policy-makers are more interested in because those firms are innovating in new technologies, markets, and business models where such unknowable outcome probabilities are more likely to occur. Third, the presence of ambiguity in strategic decisions is growing. It is growing due to the added dynamics and complexities of the marketplace, the increasing velocities of competition and cooperation (e.g., Joseph and Gaba 2015), the rapid pace of technological and regulatory progress, the consistently unstable global landscape, and the often-lagging or non-existent regulatory regimes that all make strategic decisions and actions more challenging. In other words, our approach to addressing SDMUA is timely and has widening importance as a benchmark to practical application.

As such, we believe that it is not sufficient to continue to tolerate managers who rely on intuition, pattern-following, history-based-extrapolation, imitation, stalling, experimentation, or other simple behaviors when they address SDMUA. Such attempts to avoid it or reduce it simply are inferior and ineffective. However, up to this point, the literature has appeared hesitant and fragmented in building alternative approaches, with new ideas like anti-fragility (Taleb 2012) only trending as initial avenues to do so. Until now, there was no generalizable approach for managers to use to maximize value under ambiguous, competitive contexts. Certainly, there were many heuristics offered, including famous ones such as simple rules (Eisenhardt and Sull 2001), but none have had widespread empirical support for their superior long-term, general effectiveness based on how they handle true ambiguity specifically. This is problematic because human decision-makers are bad at dealing with ambiguity, whether as an umbrella concept or across many of its possible dimensions such as non-linearity and complexity, and are even worse when ambiguity is combined with having to deal with competition simultaneously (e.g., Dominiak and Duersch 2019). As such, we believe our SDMUA approach is a useful contribution.

To DMUA research, and to DM research more broadly, this paper also signifies a need to focus attention on building the bridge between the past studies of individual behaviors in relative isolation and the needed new studies of such behaviors in monitored, competitive, organizational contexts. Clarifying the translation from observations of willing participants in controlled lab gambles to noisy outcomes of incentivized managers making strategic investment choices that involve unknown probabilities, where multiple parties are interdependent, remains a challenge (e.g., Eason and Mazzei 2019). We simply need more work on how simplified lab studies inform complex field realities, and whether we are missing something crucial in the reductionism made to get to the lab level or the projections made to get to the field level. We expect more holistic issues to be involved, issues that are often addressed through heuristics by boundedly-rational managers, heuristics that may generate exploitable and harmful biases. We have advocated in our proposed approach to SDMUA the use of several small world tools to provide a structured, understandable, objective, and reliable process to deal with ambiguity, and argued for several consequent propositions. We are fully aware, though, that important things can be lost in translation (e.g., legal constraints that restrict compensation contract completeness), and so we advocate testing our approach and our propositions in the field.

There are many other forms that future work on SDMUA can take. We suggest that, besides testing the approach proposed here, that case studies be conducted in various organizational contexts to determine what other approaches are being used, when, where, by whom, and why. Further, we advocate the study of the ‘meta’-decisions that organizations make: (i) about which contexts they wish their manager-decision-makers to be involved in, especially when there are contexts that involve ambiguity rather than versus risk; and, (ii) about how they perceive and even strategically generate ambiguities, such as causal ambiguity (Reed and DeFillippi 1990), for others.

The first camp is characterized by simple decision rules (Eisenhardt and Sull 2001), simple in that almost none are customized to decisions involving ambiguity specifically. These are simple rules that are agnostic about ambiguity-versus-risk, and include maximin, maximax, Hurwicz weighted maximin-maximax, and Savage minimax-regret (e.g., Su and Tung 2012). In management, this simple rules camp is more of a discussion over the amount of structure a firm needs in a less predictable world or over adaptive project management, rather than a direction over specifically how to make an investment decision (e.g., Davis et al. 2009; Lévárdy and Browning 2009). The one simple rule that does acknowledge ignorance over probabilities is the Laplace or uniform investment approach that simply assumes that each possible outcome is equally likely. The approaches in the first camp fall short for several reasons: There is nothing strategic about the approaches in this camp, as none consider interdependencies. Except for one rule, there is no customization for the ambiguity involved in the decision, and even for that exception there is an intuitive guess made about the distribution of the unknown probabilities. All of the rules produce a single investment choice, without giving any visualization of the sensitivities to proximate alternative choices. All of the rules implicitly assume that the firm’s owners agree with the approach, and that the manager is properly incentivized to follow. And, none of the rules separates the identification of efficient investment trade-offs (our step one) from the choice among them (our step two), which makes the customization of the incentive system to specific possible rival moves (our step three) much more difficult to do and thus less likely to occur.

In contrast to the first camp, the second camp is defined by a focus on the effects of ambiguity in real decision-making behavior. The approach in the second camp is to model and describe individual-level DMUA behavior, most often by capturing observable ambiguity avoidance or decision-making inertia (Sautua 2017). This approach relates to two directions in the management literature—to understand how real managers deal with DMUA (e.g., by simplifying the problem—Hey et al. 2010) and to provide a way to mathematically model the effect of ambiguity on subjective beliefs over those objectively unknowable probabilities (Bryant 2014; Galaabaatar and Karni 2013). In the latter, based on observed individual-level DMUA behavior, scholars construct a function, or a process description, consistent with the consensus outcomes about how much participants pay to avoid the choices that include ambiguous probabilities. Such functions are constructed so that they become consistent with subjective expected utility (SEU) theory (Savage 1954) when the ambiguity reduces to zero. There are several functional forms put forth in the literature, with most appearing as variants to prospect theory (Kahneman and Tversky 1979; Tversky and Kahneman 1992). Such variants depict individuals placing subjective beliefs on outcomes, applying weights to those probabilities dependent on the belief levels and payoff outcomes involved, and then combining those weighted subjective probabilities with a utility function that is most often also weighted by contextual information, to get to their preferred choice. But, there are several problems that arise when applying models from this camp to real DMUA situations: First, there is no instruction about how to generate reasonable initial beliefs when ambiguity exists. Second, there is no direction on how to determine an accurate utility function for the manager, an agent who would have her own personal agenda, anchors, and ambiguity tolerance that may differ from those of the organization’s owners or may be unknown to them. And third, there is no method given for determining an accurate probability weighting system that is likely to be used by this manager, let alone by rival managers, to influence or use these to the firm’s advantage. Table 1 describes the main points of differentiation between our approach to the SDMUA problem and that of the second camp’s approach to the DMUA problem.

In summary, we look forward to continued work in ambiguity to find better ways to understand and address it. For example, ambiguity research could be more explicitly linked to the literatures on information processing, communications, deception, signaling, and perception, to leverage related insights. Deeply considered, ambiguity even affects the very concept of knowledge itself, and of science-as-prediction, given that we can only know something when we can form a justified true belief over it—something that ambiguity prevents. Thus, addressing ambiguity remains important for the strategy field to research; and, it may even embody an endeavor that provides the means to improve the core of how social scientific progress is made.