The knowledge flow analysis on multimedia information using evolutionary game model

Abstract

Knowledge flow of multimedia information can trigger the formation of alliances and clusters. Our study focuses on the conditions when alliances or clusters emerge subsequent to the perception of knowledge flow. Based on several fundamental assumptions, we build an evolutionary game model for quantitative calculation and further conclude several propositions via geometrical analysis. The findings show that when originators participate in games without perception to the outflowing of knowledge via multimedia, the similarity, complementarity and spillage of knowledge all facilitate alliances formation after spillovers, and when originators participate in games with perception to the outflowing information, alliance formation is still positively related to the similarity and complementarity of knowledge, while the effect of spillage depends on initial conditions. This study not only analyzes the multimedia information from knowledge spillover perspective, but also introduces the evolutionary game model into the exploration of multimedia information flow, thus it provides novel guidance for the further research.

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Acknowledgements

We would like to thank the editor and three anonymous reviewers for their insightful comments on this paper.The authors are very indebted to Prof. Cao and Dr. Yang for their valuable comments on the earlier draft of this paper. In addition, this research is supported by ‘the Fundamental Research Funds for the Central Universities’, HUST: No. 2015AB021. The authors wish to thank related funding agencies.

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Correspondence to Zhenyu Jiang.

Appendix

Appendix

Proof for Theorem 3.

It is easy to find the four fixed points in (i) are zero-value points of eq. (6) and (12). Also, (x4, y4) satisfies the equilibrium condition thatF(x4) = 0; F(y4) = 0; (x4, y4) ∈ [0, 1] × [0, 1].

Proof for Theorem 4.

Based on eq. (25) and (26), we can get the Jacobian matrix of this evolutionary game system as follows:

$$ {\boldsymbol{J}}_2=\left[\begin{array}{cc}\frac{\partial F(x)}{\partial x}& \frac{\partial F(x)}{\partial y}\\ {}\frac{\partial F(y)}{\partial x}& \frac{\partial F(y)}{\partial y}\end{array}\right]=\left[\begin{array}{cc}\left(1-2x\right)\left( y\varphi {K}_B+ y\delta \alpha {K}_A^{\lambda }{K}_B^{\phi }+ y\beta {k}_a-{C}_A\right)& x\left(1-x\right)\left(\varphi {K}_B+\delta \alpha {K}_A^{\lambda }{K}_B^{\phi }+\beta {k}_a\right)\\ {}y\left(1-y\right)\left(\varphi \left({K}_A-{k}_a\right)+\delta \alpha {K}_A^{\lambda }{K}_B^{\phi}\right)& \left(1-2y\right)\left( x\varphi \left({K}_A-{k}_a\right)+ x\delta \alpha {K}_A^{\lambda }{K}_B^{\phi }-{C}_B\right)\end{array}\right] $$
(36)

According to replicator dynamics of originator A and recipient B, we can obtain five possible stationary points (0, 0), (0, 1), (1, 1), (1, 0), (x4 + y4). It is easy to inspect the stability of the points by calculating the determinants and traces and the results are listed in Table 6. Exceptionally, if \( \frac{C_A}{\varphi {K}_B+\delta \alpha {K}_A^{\lambda }{K}_B^{\phi }}>1\vee \frac{C_A}{\varphi {K}_B+\delta \alpha {K}_A^{\lambda }{K}_B^{\phi }}>1 \) (no solution to x4 or y4)implying that the expenditure for allying surpasses the revenues from allying, which triggers the avoidance to ally.

Table 6 stability of the points

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Li, Z., Wang, Z., Liu, C. et al. The knowledge flow analysis on multimedia information using evolutionary game model. Multimed Tools Appl 78, 965–994 (2019). https://doi.org/10.1007/s11042-018-6025-2

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Keywords

  • Knowledge flow
  • Multimedia information
  • Complementarity
  • Similarity
  • Evolutionary game