Making Important Decisions Under Ambiguity

In their article “Robust Decision-making Under Ambiguity”, Erat and Kavadias discuss how decision makers face ambiguity and deal with it when facing decisions. They state that ambiguity is different than risk in that ambiguity does not come with estimated probabilities from knowledge and previous experience. Risk is difficult to understand and deal with in and of itself, but when risk cannot be quantified it makes managers’ jobs even harder to carry out. The authors discuss portfolio theory, and how experts often cannot even agree on returns of investments, much less the probabilities of a given return being realized. Even with available past data, it is impossible to derive an accurate and reliable distribution. At best, they can only develop a confidence interval.
The authors begin by citing work done by Knight. Knight claimed that decision-making falls into three different types of environments. The known environment is when decision makers understand the state of the world to a meaningful degree. The uncertain environment is where the decision maker does not fully understand the state of the world, but understands the probabilities that they are facing. Finally, the ambiguous environment is where the decision maker is not aware of the likeliness of any state.
In the first case, maximizing the outcome is most straightforward. In the second case, the decision maker must try to maximize the outcome with the probabilities established from previous experiences and events. This is done by summing the probabilities multiplied by the expected outcomes associated with each given probability. The third case is very difficult to assess. In this case, the decision maker should maximize the worst case scenario, so that they can be certain that their outcome will be at least a certain minimum value. The authors discuss how it is possible to express the robust form in the ambiguous environment and the uncertain environment in a way that makes them equal. This results in a state where the ambiguous result can be indistinguishable from an uncertain result.
The authors discuss a real world situation in which ambiguity plays a key role. Customers in the real world desire a certain minimum level of performance and are willing to pay a maximum price. The authors say that for most market needs applications such as this, it is usually assumed that the customer preferences show a normal distribution with a standard deviation. Also, the cost of developing the product increases with the increased performance. Therefore, in order to maximize the number of customers that will purchase the product, the firm has to pay higher development costs. Unfortunately, firms do not know the exact characteristics of their target customers. Since the firm must maximize profits by matching performance with customer expectations, it is difficult to know how to optimize their return. Their best bet is to develop a function for profit based on performance and try to make a good estimate on the performance requirements of the customers.
They illustrate this situation with a sophisticated equation:
Π(P, µ) = ∫ (1/√(2πσ2)е((θ-µ)2/(2σ2)M(θ)dθ – C(P)
The limits shown on the integral on pg. 6 go from the minimum required performance specifications (T) to the number of customers in the market.
This equation basically says that the profit is relatively a function of the price the customer segment is willing to pay minus the cost that it takes to produce the product. This means that summing up the contribution from the entire market will indicate the overall profit from the product.
The authors conclude this example by emphasizing the rest of the concepts that they had already addressed. They said that like any other situation, the managers of the firm should try to address their risks by maximizing their worst case scenerios. In this situation, there is a different worst case scenario for every action that is taken. Therefore, they would need to first identify their action, and then identify their worst case scenario from there.
The authors did a good job explaining the differences between uncertain and ambiguous environments. The message they seemed to be trying to give in the article was that in an ambiguous situation decision makers really cannot maximize their expected outcomes because it is impossible to predict or even guess what those outcomes will probably be. Therefore, the authors advocate maximizing the worst case scenario so that they can be sure to minimize their losses. Unfortunately, they didn’t provide many concrete examples to help illustrate these concepts, and they seemed to be presented in a theoretical way. Also, the model they introduced was very sophisticated and confusing. However, the basic concepts were clear and understandable.