A Missing Piece of Mutual Learning Model of March (1991)

Abstract

(ProQuest: ... denotes formulae omitted.)IntroductionWhen multiple learners (including the organization) simultaneously affect each other, March referred to the process as the ecology of (Takase, 1991, p. 60). The ecology model of of March featured a selection process of organizational routines under the influence of other learners. A learner acquires other learners' experiences codified as technology, codes, procedures, and routines (Levitt & March, 1988). Furthermore, the diffusion (Rogers, 1962) of learners' experiences and routines in the organization makes this model even more complex.Mathematical analysis is typically abandoned and replaced by computer simulation analysis due to the complexity of the model. (e.g., Levinthal & March, 1981; Lounamaa & March, 1987). Throughout the 1980s, March was the primary proponent of this type of research (Huber, 1991).1 Levinthal and March (1993) called the phenomenon of preferring exploitation to exploration a myopia of learning (Sato, 2012). March (1991) entitled Exploration and Exploitation in Organizational primarily developed and analyzed two computer simulation models: (A) a mutual model and (B) a ecology model.However, Takahashi (1998) mathematically analyzes model (B) and does not require a computer simulation. In model (B), a reference organization having the normal performance distribution with mean m and variance v2 competes with N organizations having a standard normal performance distribution with mean 0 and variance 1. Let u be a value with an upper probability of 1/(N + 1) in the standard normal distribution table (u » 0.44 for N = 2, u » 1.34 for N = 10, u » 2.33 for N = 100), Takahashi (1998) obtains the following equation:... (1)Let P* be the probability of the reference organization having the best performance within the group. March (1991) constructs the competitive equality by conducting 5,000 simulations for each value v2 from 0 to 2 in steps of 0.05 and plotting points (m, v2) where P* = 1/(n + 1).The three lines of N = 2, N = 10, and N = 100 illustrated in Figure 6 in March (1991, p. 82) cross the vertical axis of mean m at approximately 0.2, 0.8, and 1.7, respectively. However, using Equation (1) the mean must be, respectively, 0.44, 1.34, and 2.33 when variance is 0. More specifically, Figure 1 illustrates the parabolas that touch the vertical axis at these points. Takahashi (1998) is suspicious regarding the validity of March's (1991) simulation program at least at the end point 0 of domain of variance.As March's (1991) programs have not been published, this paper creates a computer simulation program for model (A) (Appendix A) in free software language R for statistical computing, and checks the validity of the program at end points of the domain wherein we can analyze mathematically without simulation. We then compensate for the missing piece of March's (1991) mutual model (A) to identify the true conclusion.Mutual Learning ModelMarch's (1991) model is vaguely formulated because of less use of mathematical notation. This paper fully uses Takahashi's (1998) notation and reformulates March's (1991) model mathematically.RealityThere is an external reality, which is called the state of nature in statistical decision theory. A reality is an m-dimensional vector, with each component having a value of 1 or -1....Assumption 1: Each component ri of a reality is given an initial value of 1 or -1 with a probability of 1/2.The beliefs of nmembers and an organizational codeEach of n members has a belief for each component of the reality at each time period. This belief is not a probability, whereas the belief of statistical decision theory represents a probability. For each component in an m-dimensional vector of the reality, each belief has a value of 1, 0, or - 1. …