The Cricket and the Ant: Organizational Trade-offs in Changing Environments

Abstract

Organizations face trade-offs when they adopt strategies in changing resource environments. The type of trade-off depends on the type of resource change. This paper offers an organizational trade-off model for quantitative resource changes. We call it the “Cricket and Ant” (CA) model, because the pertaining strategies resemble the cricket and ant's behavior in La Fontaine's famous fable. We derive theorems in this CA model in First Order Logic, which we also use to demonstrate that two theory fragments of organizational ecology, i.e., niche width theory and propagation strategy theory, obtain as variant cases of CA; their predictions on environmental selection preferences derive as theorems once their respective boundary conditions are represented in the formal machinery.

Keywords:

• logical formalization
• market strategy
• niche
• organizational ecology

Thank you to Arjen van Witteloostuijn, César Garcia-Díaz, and anonymous reviewers for their helpful comments on earlier versions of this paper.

Notes

¹Other scholars use non-monotonic logic, an extension of First Order Logic (Pólos, Hannan and Carroll, 2001; Hannan, Carroll and Pólos, 2003). An advantage of non-monotonic logic is that it can deal with exceptions, by replacing the universal quantifier (“for all”, ∀) by “normally,” for empirical generalizations, or by “ad hoc,” for model simplifications that aren't part of the substantive theory. Accordingly, conclusions drawn from a premise set containing such quantifiers lose their (potential) universally quantified status, because “for all” is replaced by “presumably.,” An important reason for us to use First Order Logic is that it can be handled by current theorem prover softwares. Our formalization can be transformed into non-monotonic logic by appropriately substituting the above-mentioned quantifiers for our universal quantifiers.

²A formal theory is a set of sentences in a formal language, such as First Order Logic, with an inference system; the set of sentences is closed under logical deduction, and its theorems are validly inferred from premises according to rules of inference. For sufficiently detailed but still easy to read textbooks on First Order Logic, the reader may consult Gamut (1991) or Barwise and Etchemendy (1990). Our formal theory has been checked by Otter and Mace, which are freely available on the Web (http://www-unix.mcs.anl.gov/AR/otter/).

³This conceptualization of resource as demand concerns the output side of organizations, i.e., their products and services. In other disciplines, resource typically concerns organizational input (e.g., raw materials, employees, and financial resources).

⁴There are other possible interpretations of variability (e. g., the breadth of the product range offered), but they are not captured by our model.

⁵Maintaining parallel routines is not always costly. For example, robotics allows producing specialized versions of generic car models at request, without considerable additional costs (mass customization). Then, the “principle of allocation” may not hold, and the predictions of niche theory do not hold either.

⁶We are grateful to an anonymous reviewer for this example.

⁷Business system comparisons emphasize the institutional environment. Institutions may also facilitate cooperation between competitors, e. g., establishing industrial chambers, or pooling resources for training workers in CMEs.

⁸The complet set of formulae, which includes technical assumtions, e. g., on properties of inequalities, is available upon request from the first author.

⁹The derivation of theorems usually requires a number of premises stating background knowledge (e.g., on inequality and on scales) that we do not mention in the running text.

¹⁰The current formal machinery doesn't detail out the trajectory of populations reaching their maximal or minimal mass. Figure 3 displays one possibility for illustration.