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Review of Industrial Organization

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16-10-2019

Competitive Intelligence and Disclosure of Cost Information in Duopoly

Author: Tao Wang

Published in: Review of Industrial Organization | Issue 3/2020

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Abstract

This paper considers a duopoly in which one firm doesn’t know its rival’s realized cost but can invest in competitive intelligence (CI) to gather information before competition. The incentive to invest in CI and the net benefit from CI investment are higher under Bertrand competition than under Cournot competition. Ex ante, both the firm that is being spied upon and the industry benefit (suffer) from a rival’s CI investment under Cournot (Bertrand) competition while consumer surplus suffers under both types of competition. Overall, CI investment increases (reduces) social welfare when firms compete à la Cournot (Bertrand). Ex post disclosure of cost information that is acquired may either increase or decrease the incentive to invest in CI but does not affect the qualitative results with respect to profit and welfare analyses.

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See Nasheri (2005), pp. 73–74. A related but different aspect of intelligence is industrial espionage, which involves acquisition of information by theft, bribery or coercion, and is regarded as illegal.

The following is an example that illustrates how the renowned American oil and gas entrepreneur and financier T. Boone Pickens gathered information about the rival’s costs of crude oil extraction with the use of CI:

We would have someone who would watch [the rival’s] drilling floor from a half mile away with field glasses. Our spotters would watch the joints and drill pipe. They would count them; each [drill] joint was thirty feet long. By adding up all the joints, you would be able to tally the depth of the well. (Quoted from Fuld (2010), page 41.)

Since the deeper is the well, the more costly it is to bring the oil to the surface. By counting the drill pipes, Pickens was able to form a better estimation of the rival’s costs.

https://www.gartner.com/en/newsroom/press-releases/2017-02-17-gartner-says-worldwide-business-intelligence-and-analytics-market-to-reach-18-billion-in-2017.

This assumption creates asymmetry between the two firms and allows us to highlight the impacts of CI on the two firms separately: the one that invests in CI and the one that is being spied upon. The symmetric model in which both firms do not know their rivals’ realized cost and invest simultaneously in CI is discussed in Sect. 6.1.

For example, Firm 2 can track the number of attempts to solicit information and use this statistic to form estimation of Firm 1’s expenditure on CI.

Since the two firms choose outputs/prices at the same time without knowing the choice of the other firm, the market competition is a static game with incomplete information. This is in contrast to the Stackelberg model in which the “leader” firm sets output/price first and the follower, after observing the choice of the leader, takes action accordingly.

Outputs \(q_1,\ q_2\) should also depend on signal precision \(\tau _\epsilon\), but since \(\tau _\epsilon\) has been determined prior to the Cournot competition stage and it is known by both firms, in the Cournot stage we regard \(\tau _\epsilon\) as a constant and suppress the dependence of \(q_1,\ q_2\) on \(\tau _\epsilon\) for notational simplicity.

More specifically, this property follows directly from the linearity of \(q_1^*(c_1,s)\) and that the equilibrium profit function \(\pi _1^*(c_1,s)=\beta [q_1^*(c_1,s)]^2\) is quadratic in output. But as we see in Proposition 1, they are direct consequences of the linear inverse demand function and the normal information structure. Hence for other information structures and inverse demand functions, the optimal choice of \(\tau _\epsilon\) may well depend on the realization of \(c_1\).

Here m is the Hicksian composite commodity, or the numeraire good. Since the utility function u(q, m) is separable and linear in the numeraire good, there is no income effect on this sector.

This can be derived easily with the use of the first order condition of the representative consumer’s problem: \(\max _q \alpha q-(\beta /2)q^2-pq\).

The demand system \(q_i(p_i,p_j)= a-p_i+\gamma p_j\) can be generated by considering a representative consumer with quadratic utility function \(u(q_1,q_2)=\theta _0(q_1+q_2)-(1/2)(\theta _1q_1^2+2\theta _2q_1q_2+\theta _1q_2^2)+m\) (where \(q_1,\ q_2\) are the amount consumed from each firm, m is additively separable numeraire and \(\theta _0=a/(1-\gamma ),\ \theta _1=1/(1-\gamma ^2),\ \theta _2=\gamma /(1-\gamma ^2)\) are positive constants) who chooses \(q_1,\ q_2\) to maximize net utility.

More precisely, the information disclosed, which is assumed to be a closed subset, must contain the true information. This notation of credibility follows Milgrom (1981), Okuno-Fujiwara et al. (1990) among others.

If we use (16) and the ex post equilibrium profit \(\pi ^\lozenge _1(c_1,s;\tau _\epsilon )=\beta [q_1^\lozenge (c_1,s;\tau _\epsilon )]^2\), Firm 1’s expected net equilibrium profit (conditional on \(c_1,\ \tau _\epsilon\)) can be reduced to \(E_s[\pi ^\lozenge _1|c_1,\tau _\epsilon ] = \pi ^0_1(c_1) + B^\lozenge (\tau _\epsilon )\), where \(B^\lozenge (\tau _\epsilon ):=\beta (\eta ^\lozenge )^2\mathrm {Var}(s|c_1)\) is the benefit function that is due to Firm 1’s CI investment.

Let \(\theta\) and s be random vectors such that \((\theta ,s)\sim {\mathcal {N}}(\mu ,\Sigma )\), where \(\mu \equiv \left( \begin{array}{c} \mu _\theta \\ \mu _s \end{array} \right) \ \text{and}\ \Sigma \equiv \left( \begin{array}{cc} \Sigma _{\theta ,\theta } &{} \Sigma _{\theta ,s} \\ \Sigma _{s,\theta } &{} \Sigma _{s,s} \end{array} \right)\), are partitioned expectations and variance-covariance matrix. The conditional distribution of \(\theta\) given s is normal: \((\theta |s)\sim {\mathcal {N}}(\mu _\theta +\Sigma _{\theta ,s}\Sigma _{s,s}^{-1}(s-\mu _s),\Sigma _{\theta ,\theta }-\Sigma _{\theta ,s}\Sigma _{s,s}^{-1}\Sigma _{s,\theta })\). For more details, see for Example DeGroot (1970), ch. 5, Sect. 4.

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Title: Competitive Intelligence and Disclosure of Cost Information in Duopoly
Author: Tao Wang
Publication date: 16-10-2019
Publisher: Springer US
Published in: Review of Industrial Organization / Issue 3/2020
Print ISSN: 0889-938X
Electronic ISSN: 1573-7160
DOI: https://doi.org/10.1007/s11151-019-09735-0

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