Analysis of emerging technology adoption for the digital content market

Abstract

The digital content market is undergoing an evolution in networking and digitalization technologies, offering diverse information and services. Due to the characteristics of these emerging technologies, the digital content market is growing rapidly and traditional content providers face service transformation decisions. While a majority of the previous technology adoption studies have focused on the viewpoints of users and customers, cost reduction, or electronic channel related technologies, in this research we analyze the emerging technology adoption decisions of competing firms for providing new content services from a strategic perspective. Utilizing game theoretical models, we examine the effects of market environments (technology cost, channel cannibalization, brand power, brand extension, information asymmetry and market uncertainty) on firms’ adoption decisions. This research contributes a number of unique and interesting implications for the issues of emerging technology adoption for new content service provision.

Appendix

1.1 Proposition 1

Proof

The conditions for Nash equilibrium outcome (I, I) are $\pi_{A}^{II} > \pi_{A}^{NI} \;{\text{and}}\;\pi_{B}^{II} > \pi_{B}^{IN} .$ That is $\eta \Uptheta_{N} > C_{A} \;{\text{and}}\;\left( {1 - \eta } \right)\Uptheta_{N} > C_{B} ,$ we have $\Uptheta_{N} > \max \left\{ {C_{A} /\eta , < C_{B} /\left( {1 - \eta } \right)} \right\}.$

The conditions for Nash equilibrium outcome (I, N) are $\pi_{A}^{IN} > \pi_{A}^{NN} \;{\text{and}}\;\pi_{B}^{IN} > \pi_{B}^{II} .$ That is $\Uptheta_{N} - \alpha \delta \Uptheta_{T} > C_{A} \;{\text{and}}\;\left( {1 - \eta } \right)\Uptheta_{N} < C_{B} ,$ we have $C_{A} + \alpha \delta \Uptheta_{T} < \Uptheta_{N} < C_{B} /\left( {1 - \eta } \right).$

The conditions for Nash equilibrium outcome (N, I) are $\pi_{A}^{NI} > \pi_{A}^{II} \;{\text{and}}\;\pi_{B}^{NI} > \pi_{B}^{NN} .$ That is $\eta \Uptheta_{N} < C_{A} \;{\text{and}}\;\Uptheta_{N} - \delta (1 - \alpha )\Uptheta_{T} > C_{B} .$ We have $C_{B} + \delta (1 - \alpha )\Uptheta_{T} < \Uptheta_{N} < C_{A} /\eta .$

The conditions for Nash equilibrium outcome (N, N) are $\pi_{A}^{NN} > \pi_{A}^{IN} \;{\text{and}}\;\pi_{B}^{NN} > \pi_{B}^{NI} .$ That is $\Uptheta_{N} - \alpha \delta \Uptheta_{T} < C_{A} \;{\text{and}}\;\Uptheta_{N} - (1 - \alpha )\delta \Uptheta_{T} < C_{B} .$ We have $\Uptheta_{N} < \min \left\{ {C_{A} + \alpha \delta \Uptheta_{T} ,C_{B} + \left( {1 - \alpha } \right)\delta \Uptheta_{T} } \right\}.$

1.2 Corollary 1

Proof

The conditions for pure Nash equilibrium adoption strategy $\left( {\text{I,N}} \right),\;\left( {\text{N,I}} \right)$ are $C_{A} + \alpha \delta \Uptheta_{T} < \Uptheta_{N} < C_{B} /\left( {1 - \eta } \right)$ and $C_{B} + \delta (1 - \alpha )\Uptheta_{T} < \Uptheta_{N} < C_{A} /\eta$ respectively.

Multiple pure Nash equilibra $\left( {\text{I,N}} \right) ,\left( {\text{N,I}} \right)$ occur when all the above conditions are satisfied or equivalently,

$$ \max \left\{ {C_{A} + \alpha \delta \Uptheta_{T} ,C_{B} + \left( {1 - \alpha } \right)\delta \Uptheta_{T} } \right\} < \Uptheta_{N} < \min \left\{ {C_{A} /\eta , < C_{B} /\left( {1 - \eta } \right)} \right\}. $$

Multiple pure Nash equilibra, $\left( {\text{I,I}} \right),\;\left( {\text{N,N}} \right)$ occur when all the above conditions are satisfied or equivalently,

$$ \max \left\{ {C_{A} /\eta , < C_{B} /\left( {1 - \eta } \right)} \right\} < \Uptheta_{N} < \min \left\{ {C_{A} + \alpha \delta \Uptheta_{T} ,C_{B} + \left( {1 - \alpha } \right)\delta \Uptheta_{T} } \right\}. $$

1.3 Corollary 2

Proof

The conditions for the existence of mixed Nash adoption strategy is all the conditions in Eq. 9 are not satisfied. $( {\text{I, I)}}$ and $( {\text{I, N)}}$ will not occur if $\Uptheta_{N} < \min \left( {C_{A} + \alpha \delta \Uptheta_{T} ,C_{B} /\left( {1 - \eta } \right)} \right).$ $( {\text{N, I)}}$ and $( {\text{N, N)}}$ will not occur if $\Uptheta_{N} > \max \left( {C_{B} + \delta (1 - \alpha )\Uptheta_{T} ,C_{A} /\eta } \right).$ We have

$$ \max \left( {C_{B} + \delta (1 - \alpha )\Uptheta_{T} ,C_{A} /\eta } \right) < \Uptheta_{N} < \min \left( {C_{A} + \alpha \delta \Uptheta_{T} ,C_{B} /\left( {1 - \eta } \right)} \right) $$

Similarly, the other scenario is $( {\text{I, I)}}$ and $( {\text{I, N)}}$ will not occur if $\Uptheta_{N} < \min \left( {C_{B} + \delta (1 - \alpha )\Uptheta_{T} ,C_{A} /\eta } \right).$ $( {\text{N, I)}}$ and $( {\text{N, N)}}$ will not occur if $\Uptheta_{N} > \max \left( {C_{A} + \alpha \delta \Uptheta_{T} ,C_{B} /\left( {1 - \eta } \right)} \right).$ We have $\max \left( {C_{A} + \alpha \delta \Uptheta_{T} ,C_{B} /\left( {1 - \eta } \right)} \right) < \Uptheta_{N} < \min \left( {C_{B} + \delta (1 - \alpha )\Uptheta_{T} ,C_{A} /\eta } \right)$.

1.4 Proposition 2

Proof

The mixed strategy Nash equilibrium is described by both Eqs. 16 and 17 are satisfied. We have $\left( {\gamma_{A}^{*} ,\gamma_{B}^{*} } \right) = \left( {\hat{\gamma }_{A} ,\hat{\gamma }_{B} } \right).$

1.5 Corollary 3

Proof

(i) From (18), we have $\partial \gamma_{i}^{*} /\partial C_{i} = 0\quad {\text{for}}\quad i \in \left\{ {A,B} \right\}.$ (ii) $\partial \gamma_{A}^{*} /\partial C_{B} = \frac{{ - \left( {\eta \Uptheta_{N} - \left( {1 - \alpha } \right)\delta \Uptheta_{T} } \right)}}{{\left( {\eta \Uptheta_{N} - \left( {1 - \alpha } \right)\delta \Uptheta_{T} } \right)^{2} }} < 0\quad {\text{given}}\quad G_{1} > 0.$ (iii) $\frac{{\partial r_{B}^{*} }}{{\partial C_{A} }} = \frac{{\alpha \delta \Uptheta_{T} - \left( {1 - \eta } \right)\Uptheta_{N} }}{{\left( {\alpha \delta \Uptheta_{T} - \left( {1 - \eta } \right)\Uptheta_{N} } \right)^{2} }} > 0$ when G ₂ < 0 (brand extension), but $\frac{{\partial r_{B}^{*} }}{{\partial C_{A} }} < 0$ when G ₂ > 0 (brand counter-extension).

1.6 Corollary 4

Proof

(i) Since $0 \le r_{A}^{*} \le 1,$ we have $\left( {1 - \eta } \right)\Uptheta_{N} - C_{B} \le 0$ and $\frac{{\partial r_{A}^{*} }}{{\partial \left( {\delta \Uptheta_{T} } \right)}} = \frac{{\left( {1 - \alpha } \right)\left( {\left( {1 - \eta } \right)\Uptheta_{N} - C_{B} } \right)}}{{\left( {\eta \theta_{N} - (1 - \alpha )\delta \Uptheta_{T} } \right)^{2} }} \le 0.$ (ii) Since $0 \le r_{B}^{*} \le 1$, we have $\eta \Uptheta_{N} - C_{A} \le 0$ when G ₂ > 0 and $\eta \Uptheta_{N} - C_{A} \ge 0$ when G ₂ < 0. Therefore, $\frac{{\partial r_{B}^{*} }}{{\partial \left( {\delta \Uptheta_{T} } \right)}} = \frac{{\alpha \left( {\eta \Uptheta_{N} - C_{A} } \right)}}{{\left( {\alpha \delta \Uptheta_{T} - (1 - \eta )\Uptheta_{N} } \right)^{2} }} \le 0$ when G ₂ > 0 (brand counter-extension) but$\frac{{\partial r_{B}^{*} }}{{\partial \left( {\delta \Uptheta_{T} } \right)}} \ge 0$ when G ₂ < 0 (brand extension).

1.7 Corollary 5

Proof

(i) Since $r_{A}^{*} \ge 0$ and G ₁ ≥ 0, we have $\left( {\Uptheta_{N} - (1 - \alpha )\delta \Uptheta_{T} } \right) - C_{B} \ge 0$ and $\frac{{\partial r_{A}^{*} }}{\partial \eta } = \frac{{\Uptheta_{N} \left( {C_{B} + \left( {1 - \alpha } \right)\delta \Uptheta_{T} - \Uptheta_{N} } \right)}}{{\left( {\eta \Uptheta_{N} - \left( {1 - \alpha } \right)\delta \Uptheta_{T} } \right)^{2} }} \le 0.$ (ii) Since $r_{B}^{*} \ge 0,$ we have $\left( {\Uptheta_{N} - \alpha \delta \Uptheta_{T} } \right) - C_{A} > 0$ when G ₂ > 0 (brand counter-extension) and $\left( {\Uptheta_{N} - \alpha \delta \Uptheta_{T} } \right) - C_{A} < 0$ when G ₂ < 0 (brand extension). $\frac{{\partial r_{B}^{*} }}{\partial \eta } = \frac{{\Uptheta_{N} \left( {\Uptheta_{N} - C_{A} - \alpha \delta \Uptheta_{T} } \right)}}{{\left( {\alpha \delta \Uptheta_{T} - (1 - \eta )\Uptheta_{N} } \right)^{2} }} > 0$ when G ₂ > 0 (brand counter-extension) but $\frac{{\partial r_{B}^{*} }}{\partial \eta } = \frac{{\Uptheta_{N} \left( {\Uptheta_{N} - C_{A} - \alpha \delta \Uptheta_{T} } \right)}}{{\left( {\alpha \delta \Uptheta_{T} - (1 - \eta )\Uptheta_{N} } \right)^{2} }} < 0$ when G ₂ < 0 (brand extension).

1.8 Proposition 3

Proof

Firm A adopts technology when $\tilde{C}_{A} \le \hat{C}_{A} .$ Solving Eq. 22, we obtain

$$ \begin{gathered} \Upphi_{B} \left( {\hat{C}_{B} } \right)\left( {\alpha \left( { 1 { - }\delta } \right)\Uptheta_{T} { + }\eta \Uptheta_{N} \, - \, \tilde{C}_{A} } \right) + \left( {1 - \gamma_{B} } \right)\left( {\alpha \left( { 1 { - }\delta } \right)\Uptheta {}_{T} + \Uptheta {}_{N} - \tilde{C}_{A} } \right) \hfill \\ \, > \Upphi_{B} \left( {\hat{C}_{B} } \right)\left( {\alpha \left( { 1 { - }\delta } \right)\Uptheta_{T} } \right) + \left( {1 - \gamma_{B} } \right)\left( {\alpha \Uptheta {}_{T}} \right). \hfill \\ \end{gathered} $$

The equation $\tilde{C}_{A} \le \left( {\Uptheta {}_{N} - \alpha \delta \Uptheta {}_{T}} \right) - \Upphi_{B} \left( {\hat{C}_{B} } \right)\left( {\left( {1 - \eta } \right)\Uptheta_{N} - \alpha \delta \Uptheta {}_{T}} \right) = \hat{C}_{A}$ is achieved. Similarly, firm B adopts technology when $\tilde{C}_{B} \le \hat{C}_{B} .$ Solving Eq. 23, we obtain $\begin{gathered} \Upphi_{A} \left( {\hat{C}_{A} } \right)\left( {\left( {1 - \alpha } \right)\left( { 1- \delta } \right)\Uptheta_{T} { + }\left( {1 - \eta } \right)\Uptheta_{N} \, - \tilde{C}_{B} } \right) + \left( {1 - \Upphi_{A} \left( {\hat{C}_{A} } \right)} \right)\left( {\left( {1 - \alpha } \right)\left( { 1- \delta } \right)\Uptheta {}_{T} + \Uptheta {}_{N} - \tilde{C}_{B} } \right) \hfill \\ > \Upphi_{A} \left( {\hat{C}_{A} } \right)\left( {\left( {1 - \alpha } \right)\left( { 1- \delta } \right)\Uptheta_{T} } \right) + \left( {1 - \Upphi_{A} \left( {\hat{C}_{A} } \right)} \right)\left( {\left( {1 - \alpha } \right)\Uptheta {}_{T}} \right). \hfill \\ \end{gathered}$ We have $\tilde{C}_{B} \le \left( {\Uptheta {}_{N} - \left( {1 - \alpha } \right)\delta \Uptheta {}_{T}} \right) - \Upphi_{B} \left( {\hat{C}_{B} } \right)\left( {\eta \Uptheta_{N} - \left( {1 - \alpha } \right)\delta \Uptheta {}_{T}} \right) = \hat{C}_{B} .$

1.9 Corollary 6

Proof

(A). Under the scenario of brand counter-extension (G ₂ > 0), from (24) and (25) we have $\partial \Upphi_{i} \left( {\hat{C}_{i} } \right)/\partial \hat{C}_{j} < 0$ and $\partial \Upphi \left( {\hat{C}_{i} } \right)/\partial \Upphi \left( {\hat{C}_{j} } \right) < 0,\quad i \ne j \in \left\{ {A,B} \right\}.$ $\Upphi_{i} \left( {\hat{C}_{i} } \right)$ will become lower as the mean of technology cost becomes higher. As a result, $\Upphi_{j} \left( {\hat{C}_{j} } \right)$ and $\hat{C}_{j}$ becomes higher and $\hat{C}_{i}$ becomes smaller.

(B). Under the scenario of brand extension (G ₂ < 0), we have $\partial \Upphi_{A} \left( {\hat{C}_{A} } \right)/\partial \hat{C}_{B} < 0$ and $\partial \Upphi_{B} \left( {\hat{C}_{B} } \right)/\partial \hat{C}_{A} > 0$ No matter whether the equilibrium adoption tendency is high or low, a higher disperse degree (variance) of technology cost may increase or decrease the decision threshold for each firm $\hat{C}_{i} ,\quad i \in \left\{ {A,B} \right\}.$ Consequently, the impact of cost disperse on the adoption tendency is unclear.

1.9.1 Corollary 7

Proof

(A). Under the scenario of brand counter-extension (G ₂ > 0), from (24) and (25) we have $\partial \Upphi_{i} \left( {\hat{C}_{i} } \right)/\partial \hat{C}_{j} < 0\quad {\text{and}}\quad \partial \Upphi \left( {\hat{C}_{i} } \right)/\partial \Upphi \left( {\hat{C}_{j} } \right) < 0\quad i \ne j \in \left\{ {A,B} \right\}.$ When the equilibrium adoption tendency is low (e.g. $\hat{C}_{i} < \mu_{i}$), $\Upphi_{i} \left( {\hat{C}_{i} } \right)$ will become larger as the disperse degree (variance) of technology cost becomes higher. As a result, $\Upphi_{j} \left( {\hat{C}_{j} } \right)$ and $\hat{C}_{j}$ becomes lower and $\hat{C}_{i}$ becomes larger. On the contrary, if the equilibrium adoption tendency is high (e.g. $\hat{C}_{i} > \mu_{i}$), $\Upphi_{i} \left( {\hat{C}_{i} } \right)$ will become smaller as the disperse degree (variance) of technology cost becomes higher. As a result, $\Upphi_{j} \left( {\hat{C}_{j} } \right)$ and $\hat{C}_{j}$ becomes larger and $\hat{C}_{i}$ becomes smaller.

(B). Under the scenario of brand extension (G ₂ < 0), we have $\partial \Upphi_{A} \left( {\hat{C}_{A} } \right)/\partial \hat{C}_{B} < 0$ and $\partial \Upphi_{B} \left( {\hat{C}_{B} } \right)/\partial \hat{C}_{A} > 0.$ No matter the equilibrium adoption tendency is high or low, a higher disperse degree (variance) of technology cost may increase or decrease the decision threshold for each firm $\hat{C}_{i} ,\quad i \in \left\{ {A,B} \right\}.$ Consequently, the impact of cost disperse on the adoption tendency is unclear.

1.10 Corollary 8

Proof

(i) $\partial \gamma_{A}^{*} /\partial \Uptheta_{N} = \frac{{\eta C_{B} - \left( {1 - \eta } \right)(1 - \alpha )\delta \Uptheta_{T} }}{{\left( {\eta \Uptheta_{N} - \left( {1 - \alpha } \right)\delta \Uptheta_{T} } \right)^{2} }} > 0,$ given $0 \le \gamma_{A}^{*} \le 1\quad {\text{and}}\quad G_{1} > 0.$ Since $\partial \Uptheta_{N} /\partial \sigma_{D} < 0,$ we have $\partial \gamma_{A}^{*} /\partial \sigma_{D} < 0.$ (ii) Since $\frac{{\partial r_{B}^{*} }}{{\partial \Uptheta_{N} }} = \frac{{\left( {1 - \eta } \right)C_{A} - \eta \alpha \delta \Uptheta_{T} }}{{\left( {\left( {1 - \eta } \right)\Uptheta_{N} - \alpha \delta \Uptheta_{T} } \right)^{2} }}$, we $\frac{{\partial r_{B}^{*} }}{{\partial \sigma_{D} }} > 0$ when G ₂ < 0 (brand extension), but $\frac{{\partial r_{B}^{*} }}{{\partial \sigma_{D} }} < 0$ when G ₂ > 0 (brand counter-extension).