Decision-facilitating information in hidden-action setups: an agent-based approach

The standard hidden-action model is a static model that captures a single-period situation in which a principal hires an agent for carrying out a task.¹ The principal’s main role is to supply capital and to construct incentives, while the agent’s main role is to act on behalf of the principal. The hidden-action model can be applied to a multiplicity of situations, such as economic relationships between employer and employee, homeowner and contractor, or buyer and supplier (Caillaud and Hermalin 2000; Eisenhardt 1989). The concept of the task delegated from the principal to the agent is, therefore, rather abstract and universal.

Main characteristics of the standard hidden-action model. The main features that describe the economic relationship between the principal and the agent are the following (Holmström 1979; Caillaud and Hermalin 2000):Figure 1 represents the sequence of events within the standard hidden-action model. In \(\tau =1\), the principal designs a contract and offers it to the agent, who in \(\tau =2\) decides whether to accept the contract or not. The contract specifies the task and the sharing rule and is valid for one period. Once the contract is accepted, it is binding for both parties. If the agent accepts the contract, he exerts (and completes) productive effort in \(\tau =3\). The model is strictly sequential, which prevents the agent from adjusting his effort after \(\tau =3\). The random state of nature \(\theta \) realizes in \(\tau =4\). Finally, in \(\tau =5\), the outcome and the principal’s and the agent’s utilities take effect.

Constraints to be considered from the principal’s point of view. The principal’s decision problem is to find a sharing rule \(s(\cdot )\)The optimization program. Given the main characteristics of the standard hidden-action model and the constraints to be considered as described above, the optimization program to generate pareto-optimal sharing rules can be formalized by where Eqs. (1b) and (1c) represent the participation and the incentive compatibility constraints, respectively. The notation ‘\({{\,\mathrm{arg\,max}\,}}\)’ denotes the set of arguments that maximize the objective function that follows, \({E}\) denotes the expectation operator (Holmström 1979). The solution to the standard hidden-action model, as formalized in Eqs. (1a)–(1c), is presented in “Appendix C”. Table 1 summarizes the notation used in this section.

The concept of information is central to the hidden-action model. In contrast to the competitive general equilibrium view that assumes that information is given and perfectly known (e.g., Arrow 1964), the principal-agent theory follows the stream of information economics and regards information as being imperfect and costly (Stiglitz 2003; Frieden and Hawkins 2010; Hawkins et al. 2010). Consequently, in the latter stream of research asymmetries of information play a central role.

The concept of information has a long history, is often domain-dependent, and is applied in multiple ways in the research literature (for an overview see, for example, Capurro 2009; Hofkirchner 2009; Madden 2000; McCreadie and Rice 1999). At a very general level, information can, for example, be defined as a fact which one is told, systematic data that conveys a message, or a numerical quantity that measures the uncertainty in the outcome of an experiment (Madden 2000; Khan 2018; Soofi 1994). Notions of information capture a wide spectrum ranging from semantic to technical definitions: The former notions use information in a rather intuitive sense, while in the latter ones, information is usually a well-defined function to capture the extent of uncertainty (Soofi 1994). McCreadie and Rice (1999) rather focus on semantic notions and provide a more detailed overview of conceptualizations and distinguish between information as

Asymmetric information in the hidden-action setup. The standard hidden-action model uses the concept of information as good or commodity (McCreadie and Rice 1999) and particularly focuses on the decision-influencing role of information (Demski and Feltham 1976). The principal is unable to observe or verify at reasonable costs the effort \(a\) made by the agent. The agent, of course, knows the effort level \(a\) (Spremann 1987). In addition, only the agent but not the principal can observe the exogenous variable \(\theta \) that realizes in \(\tau =4\) (see Fig. 1). The latter assumption assures that there is, indeed, asymmetry in information about effort \(a\), as the principal cannot perfectly infer \(a\) from outcome \(x\) without knowing \(\theta \) (Caillaud and Hermalin 2000). Please note that with respect to all other elements of the standard hidden-action model introduced in Sect. 2.1, the principal and the agent share the same state of information, i.e., there is only information asymmetry with respect to the effort \(a\) and the realized exogenous factor \(\theta \). The fact that (i) the outcome \(x\) is correlated to \(a\) and (ii) that it is observable for both the principal and the agent without costs opens up a way to overcome the asymmetry in information for the principal: She designs the reward scheme \(s(\cdot )\), which provides incentives for the agent to make a level of effort that does not only maximize his own but also the principal’s utility. This notion of information asymmetry is used in both the static hidden-action model (see Sect. 2.1) and the dynamic agent-based representation of the hidden-action model (see Sect. 3).

Information in the agent-based model. The agent-based model introduced in this paper also follows the concept of information as good or commodity. Recall that the standard hidden-action model assumes information other than the effort level \(a\) and the exogenous variable \(\theta \) to be given and available for both the principal and the agent; the transfer to the agent-based model allows for limiting the availability of these pieces of information and, therefore, for shifting the focus from the decision-influencing to the decision-facilitating role of information. At the same time, the dynamic features of the agent-based model allow for endowing the principal and the agent with learning capabilities, so that they can assemble the missing pieces of information over time. Thus, we extend the notion of asymmetric information (as introduced above) by the difference between information \(J\), which is intrinsic to a system and information \(I\), which represents information about a system (Frieden and Hawkins 2010; Hawkins et al. 2010): \(J\) stands for the most complete and perfectly knowledgeable information intrinsic to a system, while \(I\) can be interpreted as information about a system based on a number of observations. In the agent-based model variant, we particularly consider that information about the environment and the feasible actions to carry out the delegated task are not given but are to be learned or discovered by the principal and the agent over time. Information \(J\) could, for example, represent the distribution of exogenous variables, and \(I\) could stand for the realizations of the exogenous variable observed by the agent. An observation can, therefore, be modeled as an information-flow process \(J\rightarrow I\).³ Increasing (decreasing) the number of observations decreases (increases) the distance \(J-I\) and therefore allows for agents being better (less) informed about \(J\), which reflects some of the results presented in Kreps (1979), Puppe (1996), and Billot (1999).⁴ Both the principal and the agent store their observations in information systems. The different types of information systems (implicitly) included in the standard hidden-action model are discussed in the next section.

The standard hidden-action model in total captures (in parts implicitly) three types of information systems (ISs), which provide the principal and the agent with relevant pieces of information to make optimal decisions (cf. Fig. 2). We distinguish between internal and external information. Internal information is related to the business of an organization and captures, for example, information coming from an organization’s planning systems or information about an organization’s performance. External information refers to information about the economic environment in which the task is carried out. The following ISs are considered:

Figure 2 schematically represents ISs included in the hidden-action context. This paper focuses on the decision-facilitating role of information in the context of hidden-action problems. For the remainder of the paper, we particularly stress the assumptions regarding the ISs which provide external information (IS 1) and internal information about the action space (IS 2). We do not focus on IS 3, as the type of information provided by this information system is mainly used for decision-influencing purposes. It is also important to note that the standard hidden-action model assumes that the different types of ISs contain all the necessary pieces of information. For the standard hidden-action model described above, this means that all required information is entered into ISs 1 and 2 before \(\tau =1\).

In the agent-based representation⁶ of the hidden-action model, we indicate time periods by subscript \(t = 1,2,\ldots ,T\) and the sequence of events within one timestep \(t\) by subscript \(\tau =0,1,\ldots ,7 \). Figure 4 schematically represents the sequence of events within one timestep in the agent-based model and also indicates the types of information systems which the principal and the agent use during the different steps \(\tau \).

Characteristics of the principal, the agent, and the environment. We characterize the (risk-neutral) principal by the utility functionwhere \(x_t\) denotes the outcome and \(s(x_t)=x_t\cdot p_t\), where \(p_t \in [0,1]\), stands for the agent’s compensation in \(t\). We model the agent as being characterized by the productivity \(\rho \) (which is constant throughout the simulations), we denote the agent’s exerted effort in \(t\) by \(a_t\), and formalize outcome \(x_t\) in period \(t\) byWe model exogenous factors \(\theta _t\) follow a normal distribution, \(\theta _t\sim N(\mu ,\sigma )\). As it is assumed in the standard hidden-action model (see Holmström 1979), the principal aims at maximizing her utility subject to the participation constraint and the incentive compatibility constraint (see Eqs. 1a–1c): In order to do so, we allow the principal to adapt the parameterization of the sharing rule, i.e., the premium parameter \(p_t\), over time.

The (risk-averse) agent is characterized by the CARA utility function: where \(\eta \) represents the agent’s Arrow–Pratt measure of risk-aversion (Pratt 1975).

Information about the action space provided by IS 2-P and IS 2-A. In Sect. 3.1.2 we introduce information asymmetry regarding the set of feasible actions. In the agent-based model variant, we denote the set of feasible actions in timestep \(t\) by \({\mathbf {A}}_t\). Limited information about \({\mathbf {A}}_t\) hinders the principal from recognizing the optimal value for the premium parameter, \(p_t\), instantaneously—this is in contrast to the standard hidden-action model, which suggests that the principal always has the necessary information to set the premium parameter \(p_t\) so that the agent has incentives to exert the optimal effort level (cf. Sect. 2.1 and Eq. 7 below). As a consequence, the principal has to search for the value of the premium parameter, which induces the optimal effort level: In order to do so, the principal has the option to either exploit the known fraction of the action space (local search) or to explore the action space outside of the known area (global search) (cf. March 1991). In periods \(t=2,\ldots ,T\) the principal selects her search strategy in \(\tau =0\) and, according to this strategy, uses her IS 2-P to perform either a global or a local search for effort levels on which she will base the sharing rule \(s(\cdot )\) (cf. \(\tau =0\) in Fig. 4).⁷ In order to assure the existence of a solution to the principal’s decision problem, it is necessary to set boundaries for \({\mathbf {A}}_t\). We set the lower boundary by the participation constraint, \(E(U_A( s(x_t),a_t)\ge {\underline{U}}\), and the upper boundary by means of the incentive compatibility constraint, \(a_t \in {{\,\mathrm{arg\,max}\,}}_{a'_t \in {\mathbf{A}_\mathbf{t}}} E(U_A(s(x_t),a'_t))\) (cf. Eqs. 1b and 1c). It is important to note that both boundaries are endogenous: They include an expectation concerning the environmental variable, as \(s(x_t)\) is based on the outcome \(x_t=a_t\cdot \rho + \theta _t\) (cf. Eq. 3). The agent’s reservation utility \({\underline{U}}\), however, is an exogenous variable. Changes in the state of information about the environment (via learning in \(\tau =7\), see below) might lead to changes in the boundaries of \({\mathbf {A}}_t\). The principal uses her IS 1-P to compute her expectation as to the environment.

The principal’s IS for external information (IS 1-P). We denote the information which the principal retrieves from IS 1-P by the vector \(\varvec{{\tilde{\varTheta }}}_t = [{\tilde{\theta }}_{t-1} {\tilde{\theta }}_{t-2} \ldots {\tilde{\theta }}_{t-m} ]\). The elements of \(\varvec{{\tilde{\varTheta }}}_t\) stand for the principal’s estimations of the exogenous factor in previous periods, for their computation see Eq. (9) below. The length of \(\varvec{{\tilde{\varTheta }}}_{t}\) is defined by parameter \(m\in \{1,2,\ldots ,t \}\), which also stands for the sophistication of IS 1-P. A low level of sophistication indicates that only very recent information can be retrieved from IS 1-P, while a high level of sophistication means that information from a larger number of past periods is available for the principal.⁸ A higher value of \(m\), thus, indicates that the principal is better informed about the environment, as more historical information enables the principal to compute a more reliable expectation as to the environment.

Endogenous threshold to trigger the principal’s search strategy. As the information sources for the principal’s decision for a search strategy are now defined (IS 1-P and IS 2-P), we can focus on her decision rule: The principal’s decision to perform either a local or a global search (cf. March 1991) is based on (i) the principal’s estimated exogenous factor in \(t-1\), \({\tilde{\theta }}_{t-1}\), and (ii) her propensity to innovate \(\delta \in [0,1]\).⁹ Recall that in periods \(t=2,3,\ldots ,T\) the principal retrieves the (i) estimation of the exogenous factor from IS 1-P in \(\tau =0\). The (ii) propensity to innovate represents the principal’s tendency to search either locally or globally for effort levels which can be used as the basis for the sharing rule \(s(\cdot )\). A lower (higher) value of \(\delta \) decreases (increases) the principal’s tendency to search globally. Based on the principal’s exploration propensity \(\delta \), we compute an exploration threshold \(\kappa _t\) for timestep \(t\) which is implicitly defined bywhere \(\sigma (\cdot )\) and \(\mu (\cdot )\) represent the standard deviation and the mean, respectively. If \({\tilde{\theta }}_{t-1} > \kappa _t\) (\({\tilde{\theta }}_{t-1} < \kappa _t\)) the principal performs a global (local) search.

Endogenous boundaries of the principal’s exploration and exploitation spaces. The principal now has selected her search strategy for period \(t\). In order to carry out the search for candidates for the optimal effort level, the search spaces in which the principal performs her search for potential effort levels need to be defined. The search space for a local (global) search is referred to as exploitation (exploration) space (see also Fig. 5). Please recall that the set of feasible actions \({\mathbf {A}}_t\) is bounded by the incentive compatibility and the participation constraints. The search spaces can be defined as follows:The search spaces are schematically illustrated in Fig. 5. Once the search strategy is settled, the principal randomly finds 2 alternative effort levels in the search space (with uniformly distributed probabilities of discovery). The discovered effort levels will be evaluated in the next step.

The principal’s evaluation of effort levels. The principal evaluates the newly found effort levels together with the status-quo effort level with respect to increases in her expected utility (based on the utility function in Eq. 2) in timestep \(\tau =1\) (cf. Fig. 4).¹⁰ We denote the value-maximizing effort level in \(t\) from the principal’s point of view by \({\tilde{a}}_t\).¹¹ Please note that the fact that the principal evaluates all candidates for the optimal effort in \(t\) on the basis of Eq. (2), requires the principal to build an expectation as to the environment. She retrieves this expectation from her IS 1-P in \(\tau =1\) (cf. Fig. 4):Recall that parameter \(m\) indicates the sophistication of IS 1-P. The expected outcome in timestep \(t\) from the principal’s point of view, \({\tilde{x}}_{Pt}\), using value-maximizing effort level \({\tilde{a}}_t\) can, thus, be formalized by \({\tilde{x}}_{t}={\tilde{a}}_{t}\cdot \rho +E_P(\theta _t)\).

The contract. Now that the principal has decided on a desired effort level \({\tilde{a}}_t\) for period \(t\), she can move on fixing the incentive scheme \(s(\cdot )\). In order to do so, the principal computes the optimal premium-level in \(t\) in step \(\tau =2\) according to She, then, designs the contract and offers the contract to the agent, who decides whether or not to accept it in \(\tau =3\). In order to compute the premium level \(p_t\), the principal uses information about the environment provided by IS 1-P and information about feasible actions provided by IS 2-P (cf. \(\tau =2\) in Fig. 4). The agent uses IS 1-A and IS 2-A for his decision of whether to accept the contract or not (cf. \(\tau =3\) in Fig. 4).

The agent’s IS for external information (IS 1-A) and his decision for an effort level. In case the agent accepts the contract, he exerts effort \({a}_t = \max _{a_t \in {\mathbf{A}_\mathbf{t}}} U_A\left( s({\tilde{x}}_{At}), a_t\right) \) in \(\tau =4\), where \({\tilde{x}}_{At}=a_t \cdot \rho + E_A(\theta _t)\) includes the agent’s expectation as to the outcome in \(t\), \(E_A(\theta _t)\). In order to compute \(E_A(\theta _t)\), he retrieves his observations of realized exogenous factors from IS 1-A (cf. \(\tau =4\) in Fig. 4). Recall that the agent can observe exogenous factors after their realization. We denote the agent’s observations derived from IS 1-A by \(\varvec{{\varTheta }}_t = [{\theta }_{t-1} {\theta }_{t-2} \ldots {\theta }_{t-m} ]\). The agent computes his expectation as to the exogenous factor in \(t\) according to As for IS 1-P, parameter \(m\) indicates the sophistication level of IS 1-A. The agent’s rule to come up with an effort level introduced above also reflects that the agent knows the entire action space \({\mathbf {A}}_t\). This piece of information is provided by IS 2-A (cf. \(\tau =4\) in Fig. 4).

Realization of the outcome and of the principal’s and the agent’s utilities. After productive effort was exerted in \(\tau =4\) and the exogenous factor realized in \(\tau =5\), the outcome, \(x_t = {a}_t \cdot \rho + \theta _t\), materializes in \(\tau =6\), and the utilities for the principal and the agent realize (cf. Eqs. 2 and 4).

The principal’s estimation and agent’s observation of the environment. In \(\tau =7\), the agent observes the realization of the exogenous factor in \(t\), \(\theta _t\), and stores this observation in his IS 1-A. The principal can only observe \(x_t\) using IS 3. Based on this information she estimates the exogenous factor in \(t\) according toand stores \({\tilde{\theta }}_{t} \) in her IS 1-P.¹² Finally, \({\tilde{a}}_t\) is carried over to period \(t+1\) as ‘status-quo effort level’.¹³ This sequence explained above and depicted in Fig. 4 is repeated \(T\) times. The notation used for the formal representation of the agent-based variant of the hidden-action model is summarized in Table 2.

Parameters related to the principal. In addition to the utility function given in Eq. (2), the principal is characterized by a propensity to innovate (\(\delta \)) which represents her tendency to perform a local or global search, respectively (see Eq. 5 and subsequent paragraphs). With respect to the propensity to innovate, our analysis includes three different types of principals: This parameter and the selected parameterization reflect current research on organizational ambidexterity that focuses on the ability of organizations to simultaneously pursue incremental and discontinuous innovation (Tushman and O’Reilly 1996; O’Reilly and Tushman 2013). It is, amongst others, also noted in March (1991) that organizations need to find an appropriate balance between exploration and exploitation to make sure to continuously adapt in order not to become irrelevant in the market. The principal’s propensity for innovation reflects this balance between exploration and exploitation.

Parameters related to the agent The agent is risk-averse and characterized by a CARA utility function (cf. Eq. 4). The assumption of risk-aversion for the agent is transferred from the standard hidden-action model (Holmström 1979). We set the agent’s Arrow–Pratt measure, \(\eta \), equal to \(0.5\). In addition, the agent is characterized by a measure for productivity, which we set to \(\rho =50\).

Parameters related to the environment. We model environmental variables to follow a normal distribution. In our analysis, we set the mean of the distribution of environmental variables equal to zero and consider four levels of environmental turbulence, which we operationalize by altering the distribution’s standard deviation, \(\sigma \): We set the standard deviation relative to the optimal outcome, \(x^*\), computed by using actual parameter settings and the second-best solution of the standard hidden-action model (cf. “Appendix C”), and consider a total of four cases ranging from relatively stable environments (\(\sigma =0.05x^*\)) to relatively turbulent environments (\(\sigma =0.65x^*\)).¹⁴

Parameters related to ISs. For the principal’s and the agent’s external information systems (IS 1-P and IS 1-A, respectively), our analysis covers three levels of sophistication. Recall that the sophistication of these ISs is formalized by parameter \(m\) (see Eq. 6 for IS 1-P and Eq. 8 for IS 1-A). We set \(m=1\) and \(m=3\) for a low and medium level of sophistication, respectively. For highly sophisticated ISs, we set \(m=\infty \). The sophistication of P’s internal information system IS 2-P is captured by parameter \(q\), which identifies the fraction \(1/q\) of the set of feasible actions which is available for P. As discussed in Sect. 3.1.2, \(q\) is also a proxy for the extent of information asymmetry (regarding the action space) between the principal and the agent. Our analysis includes three sophistication levels of IS 2-P: We set \(q\in \{3,5,10\}\) for a high, medium, and low level of sophistication, respectively. The choice of parameters reflects the concept of information introduced in Sect. 2.2: Let \(J\) stand for the most complete information intrinsic to a system and \(I\) stand for information about a system and let observations about information intrinsic to a system be an information flow-process \(J \rightarrow I\) (Frieden and Hawkins 2010; Hawkins et al. 2010). Then, the sophistication parameters \(m\) and \(q\) shape the extent of information (intrinsic to a system and observed or observable by the agent) which is available for the agent. Higher values for \(m\) (lower values for \(q\)) indicate that more information is available, which we interpret as being better informed.

Global parameters. The possible combinations of the parameters which are subject to variation lead to a total number of \(3\times 4\times 3\times 3 = 108\) scenarios. For each scenario \(R=700\), simulation runs are performed, whereby the analysis focuses on the first 20 time periods, \(T=20\).

Scenarios. The first part of the analysis provides insights into the effects of the sophistication of the information systems employed within the contractual relationship between the principal and the agent on the level of performance obtained. In order to do so, this section presents results for the following parameter settings: This section particularly discusses cases in which \(m\in \{1,3,\infty \}\) and \(1/q=1/10\) (cf. Fig. 6), and \(1/q\in \{1/10,1/5,1/3\}\) and \(m=1\) (cf. Fig. 7). The results for all parameter combinations are presented in Fig. 10 in “Appendix A”.

Performance indicator. For each timestep \(t\), we report the averaged normalized effort level carried out by the agent as performance measure. For each timestep \(t =1,\ldots ,T\) and each simulation run \(r =1,\ldots ,R\), we track the level of effort \(a_{tr}\) exerted by the agent and normalize it by the optimal level of effort \(a^*\). The optimal effort level results from the second-best solution suggested by the standard hidden-action model (see Holmström 1979 and “Appendix C”). The reported performance indicator is formalized by:

Results on the sophistication of IS 1-P and IS 1-A. The results on the sophistication of the principal’s and the agent’s systems for information about the environment are presented in Fig. 6. For this analysis, we investigate variations of IS 1-P and IS 1-A as described above, and keep the sophistication of the principal’s IS 2-P constant at \(1/q=1/10\). Each subplot in Fig. 6 presents results for one investigated sophistication level of IS 1-P and IS 1-A. For each scenario, the subplots report the averaged normalized effort level introduced in Eq. (10). For scenarios with low environmental uncertainty (represented by triangles in Fig. 6), the results indicate that increasing the sophistication of IS 1-P and IS 1-A—and thereby increasing information about the organization’s environment—significantly increases the slope of the performance curves. Thus, effort for better information about the environment appears to pay off almost immediately in such scenarios. In addition to the slopes of the performance curves, the performances at the end of the observation period (i.e., after 20 periods) increase with the level of IS sophistication, too: While for the case of poor information about the environment, around \(0.74\) of the performance suggested by the standard hidden-action model can be achieved after 20 periods (see the top subplot in Fig. 6), increasing the sophistication so that good information is provided leads to a final performance of almost \(0.95\) (see the bottom subplot in Fig. 6). The described patterns can also be observed for situations in which the principal’s internal IS 2-A has higher sophistication levels: However, the less it is pronounced, the higher the sophistication of IS 2-P (see Fig. 10 in “Appendix A”).

As soon as we switch to scenarios with high environmental uncertainty (represented by black diamonds in Fig. 6), similar shapes of the performance curves emerge: For the case of poor external information, for example, performance increases only in the first 2 periods to around \(0.68\), before it remains on this level until the end of the observation period. In scenarios with good information about the environment, performance increases in the first 11 periods to around \(0.87\) and then remains stable until period 20. From the results, we can draw the conclusion that higher sophistication levels of the IS for external information lead to (i) longer time spans in which performance increases, but (ii) the slopes of the performance curves in the first few periods are not affected. Consequently, final performances increase with the quality of the provided information. The same pattern emerges for situations with higher sophistication levels of P’s IS 2-P (cf. Fig. 10 in “Appendix A”).

Results on the sophistication of IS 2-P. We depict the performance curves for variations in the sophistication level of the principal’s IS for internal information IS 2-P in Fig. 7, whereby each of the 3 subplots presents results for one of the investigated sophistication levels. We keep the sophistication levels of IS 1-P and IS 1-A constant at \(m=1\). For scenarios in which environmental uncertainty is low (\(\sigma =0.05x^*\), indicated by triangles in Fig.7), our results suggest that increasing the sophistication of the principal’s internal IS 2-P significantly increases the slope of the performance curve. Performance, thus, increases much faster in the first few periods. The final performance achieved after 20 periods is, however, only marginally affected: The final performance for the case of poor internal information (\(1/q=1/10\)) amounts to around \(0.71\) (see the right subplot in Fig. 7). Increasing the sophistication of IS 2-P to \(1/q=1/3\) only leads to a marginal increase, so that a final performance of around \(0.82\) can be achieved. For scenarios with a high sophistication of the principal’s and the agent’s information system for environmental information, the pattern is similar, but the increase in the slopes of the performance curves is less pronounced (cf Fig. 10 in “Appendix A”).

A totally different pattern emerges in situations in which environmental uncertainty is high (\(\sigma =0.65x^*\), indicated by black triangles in Fig. 7): Irrespective of the sophistication level of IS 2-P, performance immediately reaches a level of around \(0.71\). From period \(t=2\) onward, there are generally no significant changes on this performance level. A similar behavior can be observed for situations in which the principal and the agent are better informed about the environment (see Fig. 10 in “Appendix A”). This is a remarkable and counterintuitive result: The results suggest that—at least for the first few periods—a significantly higher level of performance can be achieved in turbulent environments, as compared to stable environments. This finding might be explained by the pressure to be innovative, which turbulent environments impose on the principal (Mendes et al. 2016). The time span in which this result can be observed is critically shaped by the sophistication of the principal’s internal information system: For \(1/q=1/10\) (\(1/q=1/3\)), the performance observed in stable environments exceeds the performance in turbulent environments after 10 (4) periods.

Discussion and policy reflection The results provide support for intuition, i.e., that coping with environmental turbulence is more successful when information about the environment is improved (Raghunathan 1999). In this sense, the results are in line with prior research in the tradition of the task-technology model (Goodhue and Thompson 1995): This line of research indicates that the relation between environmental uncertainty and task characteristics affects the satisfaction of the user with the data provided by ISs. This level of satisfaction, then, critically shapes the success of organizational ISs (Karimi et al. 2004; Schäffer and Steiners 2005; Petter et al. 2013). In the model used in this paper, a higher sophistication of the ISs for environmental information (IS 1-P and IS 1-A) and the internal IS (IS 2-P) provides more complete information, which results in ‘better’ decisions.¹⁵ A higher sophistication of our modeled ISs can, thus, be interpreted as a higher task-technology fit.

The results suggest that increasing the performance of the internal IS 2-P does not pay off in turbulent environment: This is an unexpected finding which puts calls for more sophisticated IS designs (e.g., Karimi et al. 2004) into perspective. Our results suggest that turbulent environments put a certain pressure to be innovative on decision makers, which is why performance increases immediately in the first few periods. Further performance increases can, then, only be achieved by improving the quality of information about the environment (IS 1-P and IS 1-A), which is why efforts to increase the sophistication of the internal IS 2-P prove to be ineffective.

The results presented so far suggest the necessity to differentiate the investment decisions regarding the sophistication of organizational ISs according to the degree of environmental uncertainty. If environmental uncertainty is low, enhancing the sophistication of external ISs (IS 1-P and IS 1-A) as well as internal IS 2-P increases the performance obtained: Investments in either direction appear to be beneficial. In contrast, when environmental uncertainty is high, investing into an improved internal IS 2-P appears to be ineffective: In such situations, the priority should rather be given to improving the quality of external information (provided by IS 1-P and IS 1-A).

Scenarios This part of the analysis focuses not only on variations in the sophistication of the ISs employed during the principal’s and the agent’s decision-making processes, but also takes the principal’s innovation propensity into account. The considered parameter setting is the following: The discussion in this section focuses on cases in which \(m\in \{1,3,\infty \}\) and \(1/q=1/10\) (cf. Fig. 8), and \(1/q\in \{1/10,1/5,1/3\}\) and \(m=1\) (cf. Fig. 9). The results for the remaining parameter combinations are presented in Fig. 11 in “Appendix B”.

Performance indicator. The performance measure used for the analysis in this section is based on the level of effort exerted by the agent. We, however, no longer present the averaged normalized effort level \({\tilde{p}}_{t}\) and the performance curves over time (as done in Figs. 6 and 7), but condense performance curves to the Manhattan distance \(d\), which, in this case, represents the distance between the averaged normalized effort level \({\tilde{p}}_t\) and the optimal effort level \(x^*\) over time. This allows us to present one performance measure per scenario, which can be formalized bywhere \(t=1,\ldots ,T\) represents timesteps and \({\tilde{p}}_{t}\) stands for the averaged normalized effort level in period \(t\) (cf. Eq. 10).

Results on the sophistication of IS 1-P and IS 1-A. Results for scenarios in which the sophistication levels of IS 1-P and IS 1-A for external information are varied are presented in Fig. 8. Each subplot presents the results for one of the investigated sophistication levels and depicts contours resulting from the condensed performance measure introduced in Eq. (11). We keep the sophistication level of the principal’s IS for internal information IS 2-P constant at \(m=1\) for this part of the analysis.

As soon as we switch to scenarios with medium (\(m=3\)) and high sophistication levels (\(m=\infty \)) of the ISs for external information (IS 1-P and IS 1-A), we can observe that a different pattern emerges. First, the largest distance between the achieved and the optimal performances can no longer be observed in stable but in turbulent environments. This finding is in line with the intuition that there is a negative relation between environmental turbulence and performance. Second, we can see that the contours are no longer nearly horizontal, but their slope increases with the quality of the information provided by the principal’s and the agent’s information systems for external information. This change in the pattern of contours indicates that the decision whether to perform exploitation or exploration becomes particularly critical, when the involved parties are well informed about the environment. In addition to the changes in the pattern, it can be observed that the distance between the achieved and the optimal performance decreases significantly with increases in sophistication of the principal’s Is 2-P: While for stable environments (\(\sigma =0.05x^*\)), indifferent principals (\(\delta =0.5\)), and poor external information (\(m=1\)), the Manhattan distance is around \(-7\), this distance reduces to around \(-3.15\) and \(-2.95\) for medium (\(m=3\)) and good (\(m=\infty \)) information, respectively. The marginal change in performance increase, thus, reduces with higher levels of IS sophistication. The same observations can be made for cases with a medium (\(1/q=1/5\)) and high (\(1/q=1/3\)) level of sophistication for IS 2-P (cf. Fig. 11 in “Appendix B”).

Results on the sophistication of IS 2-P. Figure 9 presents results from scenarios with variations in the sophistication level of the principal’s internal IS 2-P. For the ISs for external information, we fix \(m=1\) for this part of the analysis. As discussed above, for the scenarios with a low sophistication level of IS 2-P (\(1/q=1/10\)), the largest distance between the achieved performances and the optimal performance can be observed in stable environments, and the horizontal contours indicate that the choice of strategy does not affect performance.¹⁶ An increase in the sophistication level of the principal’s IS for external information so that medium (\(1/q=1/5\)) and good information (\(1/q=1/3\)) is provided for decision-making purposes, only leads to slight changes in the observed pattern: First, the largest values for the distance from the achieved to the optimal performance shift into the direction of more turbulent environments. The largest distances can, however, be observed for intermediate levels of environmental turbulence. This is surprising as one would expect the largest Manhattan distances in scenarios with the highest level of environmental turbulence. Second, for all sophistication levels of IS 2-P, we can observe nearly horizontal contours: This indicates that irrespective of the quality of internal information, the principal’s search strategy does not affect performance, as long as the sophistication of the IS for external information is \(m=1\). For higher sophistication levels of the ISs for external information (IS 1-P and IS 1-A), it can, however, be observed that a higher tendency for exploration leads to slightly better performances (cf. Fig. 11 in “Appendix B”).

Discussion and policy reflection. This section does not take a snapshot of one time period or analyze performance curves over time but provides a condensed measure for the efficiency of organizational search strategies and sophistication levels of information systems for time periods. From that perspective, the results presented here indicate that the intuition that it is harder for organizations to achieve a high performance in turbulent environments is only true if decision makers are well informed about the environment (i.e., in situations in which IS 1-P and IS 1-A provide medium or good information). In situations in which the principal and the agent only have poor information about the environment, there appears to be a pressure to be innovative in terms of carrying out tasks. This leads to an immediate boost in performance, so that—over the entire observation period—the distance between the achieved and the optimal performance decreases. This finding is in line with previous research: Eisenhardt (1989) and Alexiev et al. (2016), for example, argue that increased innovativeness is a common response of organizations to turbulent environments when information quality is poor. This is exactly what we observe for situations in which the principal and the agent have only limited information about the environment. In addition, our results show that this pressure does not exist in stable environments, which is why performance increases at a much slower pace. In addition, we analyze the effect of the search strategy’s impact on performance: Auh and Menguc (2005) argue that whether or not exploration or exploitation is the superior search strategy depends on the type of organization, which, in their case, is either defender or prospector. We show that as long as information about the environment is poor, the choice of the search strategy in fact does not matter. With an increase in quality of information about the environment, exploration becomes significantly superior to exploitation. For the sophistication of the principal’s information system for information about the action space, the results indicate that investments into highly sophisticated ISs only lead to very marginal increases of performance and no changes in the above discussed patterns. Thus, from a policy perspective, the findings presented here suggest a prioritization of ways to spend an organization’s resources: Every effort should be made to build an information system which provides good information about the environment before tackling the question of whether to develop new ways to carry out specific tasks.