Abstract
In the information era, social software recently emerges as an effective tool for knowledge workers to collaborate and share knowledge. This article presents an analytical model in which a social software strategy is applied to complement an extant knowledge base to improve an organizational culture fit and achieve maximal profit. Capturing the mutual effects among social software, knowledge base and organizational culture fit, we determine the optimal level of social software and investigate how it changes with the crucial factors including the volume of knowledge base and initial organizational culture fit. This research provides valuable insights for practitioners to implement social software for knowledge management.
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Appendices
Appendices
Appendix A
Proof of Lemma 1
Proof
-
By examining the relationship between the cultural fit and PI of the KMS in the same period, we can clearly see that cultural fit can always be improved by increasing PI because
In addition, the first-order derivative of φ t with respect to λ is
and the first-order derivative of φ t with respect to p is
Therefore, φ t increases with λ and p. □
Appendix B
Proof of Proposition 1
Proof
-
The organizational culture fit at the end of a single period is
where
and
Therefore
In addition, we know that
Hence, the first-order condition yields that
In addition, the second-order derivative of the firm's payoff with respect to e is negative. Hence, the optimal level e* exists. □
Appendix C
Proof of Proposition 2
Proof
-
The left-hand side of equation (1) increases with λ, decreases with p and K0, so the optimal level of social software increases with λ, decreases with p and K0. □
Appendix D
Proof of Proposition 3
Proof
-
Solving the quadratic function 3pφ02−2(1+p)φ0+1=0 by regarding p as the parameter and φ0 as the variable, we obtain that
Because 3p(1−p)⩾0, therefore 1−p+p2⩾4p2−4p+1. It follows that , which is Because 1+p, φ L >0. Therefore, when 0<φ0<φ L , Θ>0, and when φ L <φ0⩽1, Θ<0. □
Appendix E
Proof of Corollary 1
Proof
-
We use Θ to denote the derivative of the left-hand side of equation (1) with respect to φ0, which is
Therefore, Θ⩾0 if
or
Θ⩽0 if
or
In addition, we know that when φ0∈(0, 1/3) and (2/3, 1]
when φ0∈(1/3, 2/3)
which, when combined with equations (E.1), (E.2), (E.3) and (E.4), indicates that Θ⩽0 when φ0∈(0, 1/3) and Θ⩽0 when φ0∈(2/3, 1). □
Appendix F
Proof of Proposition 4
Proof
-
In a multi-period setting
where
The first-order derivative of φ t with respect to e t indicates that
As
the first-order condition of the firm's total profit with respect to e t yields that, ∀t=1, 2, …, n
In addition, the second-order derivative of the firm's payoff with respect to e t is negative. Hence, the optimal level e t * in each time period t can be obtained. □
Appendix G
Proof of Proposition 5
Proof
-
The left-hand side of equation (2) increases with λ, decreases with p and φ0, so the optimal level of social software e t in time period t increases with λ, decreases with p and φ0. □
Appendix H
Proof of Proposition 6
Proof
-
By examining equation (2), we find that when φ0⩾1/2, the right-hand side of equation (2) for the time period t is always less than that for the time period t−1. In addition, when φ n <1/2 and K0⩾K̂, the right-hand side of equation (2) for the time period t is always greater than that for the time period t−1. □
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Zhang, Z. A social software strategy for knowledge management and organization culture. OR Insight 25, 60–79 (2012). https://doi.org/10.1057/ori.2011.14
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DOI: https://doi.org/10.1057/ori.2011.14