Price and quality (privacy) are intertwined in a complex unknown relationship

R. Chandramouli
Hattrick Chair Professor
Department of Electrical and Computer Engineering
Stevens Institute of Technology

The mobile App ecosystem is huge and growing. The Apple iOS App store offers nearly 1 million Apps (average price ~ $1.39) with 60 billion total downloads. Price sensitive buyers (mobile App users) are willing to take security risks to get free Apps or cheap Apps from App sellers with unproven reputation. A recent study shows that a price discount for iPad Apps experienced an average first-day revenue increase of 52% and a subsequent 19% increase during the discount sale period.

A typical buyer accepts the terms and conditions of a mobile App without even reading them. A recent report from the Federal Trade Commission (FTC) indicates that many Apps for kids do not even disclose the information they collect about the users.  Therefore, price and quality (privacy) are intertwined in a complex unknown relationship.

Fig. 1: Private user information collected by Android Apps. Source: Bitdefender.

Fig. 1 shows the breakdown of private user information collected by Android Apps. A study by Bitdefender shows that about 13% of 130,000 free Android Apps sent user phone numbers to third party servers. According to the Android Malware Genome Project, in the worst case only 20% of known malicious Apps are detected as dangerous while the best case value is 80%. Mobile data security breaches results in a significant churn rate if consumer privacy is compromised. Therefore mobile App markets (and sellers) compete against each other for price while attempting to minimize churn due to real or perceived privacy breaches or other reasons. App sellers react to competition by controlling their own strategies (e.g., price, privacy policy, incorporating customer feedback, etc.). However, deceptive practices are used as well---App developers and their marketers have posted positive comments about their own products, posing as regular consumers. The FTC has even sued a company for this type of deception.

Even though Google and Apple use a rigorous App certification process to minimize malware, when users synchronize their devices with 3rd-party cloud services (e.g., web-based calendars) it can potentially expose sensitive data stored on these devices to outside systems. A virus called GG Tracker impersonated the Android Market without the users even being aware that their data was compromised. An average mobile security App to guard against privacy or security breaches could result in one more of the following: (a) additional memory consumption thereby slowing down the mobile device; (b) adware supporting a free security App results in mobile data usage; and (c) higher battery drain rate. These issues could discourage a typical user from buying or installing a mobile security App.

Therefore, the mobile App ecosystem comes with inherent privacy/security risks (known, unknown and partially known), uncertainties, costs and benefits, both to the App buyers and sellers. Clearly, concrete mathematical models are needed to understand the complex dynamic interactive behavior between the mobile App buyers and sellers. Such models can provide insights on how buyers and sellers make their individual or collective decisions (e.g., choosing the correct App, install/do not install, App pricing, offered privacy policies, etc.)

We identify the following three cases that capture the App buyer-seller dynamics:

  • Complete information case: The buyer has complete knowledge about the adversarial malware App. That is, it knows the strategies at the disposal of the adversary as well as the probability distribution,of the n types of attacks; e.g., publicly known Android malware Apps and the damages caused by them.
  • No information case: The buyer has no information about  or the value of n. Clearly, this type of analysis may produce pessimistic results with the App buyers and sellers seeking extreme payoffs. An Android malware disguised as a security App is an example of this case.
  • Incomplete information case: The user does not know the values of but only an ordering, say, p1 p2 . . . pn (without loss of generality), is known. This may be due to incomplete historical data, App reviews, subjective priors, etc. Note that this sub-case is mid-way between the complete information and no information cases.

For example, if private photos in a mobile phone are found in a third party website without authorization then it is possible to identify the most likely type(s) of malware(s) that caused this. The ordering of the likelihood probability can be computed from an extensive list of malwares and the vulnerabilities they cause.

Therefore, we see that selling or buying mobile Apps brings to the forefront a number of complex inter-related issues. Some of these are: (a) decision making (e.g, which security App to install), (b) competition (e.g, competing App sellers), (c) cooperation (e.g, every user installs a mobile security App to limit the spread of malware), (d) modeling risks, costs and threats, (e) learning from the past.

        (a)                                                                                           (b)

Fig. 2: Best response reaction function dynamics of two App sellers when (a) buyers are price sensitive and (b) quality sensitive.

Fig. 2(a) and (b) show two sample results from mathematical modeling and analysis.  These results capture the dynamics between two App sellers when the buyers are price and quality (e.g., preserving privacy) sensitive, respectively. We see in Fig. 2(a) that the price dynamic, starting from an initial point (P1, P2) eventually converges to a price war cycle.  That is, the two App sellers cyclically increase or decrease their prices in response to each other, to cater to price sensitive users. On the other hand, when the buyers are quality sensitive the price war is eliminated and there is an equilibrium pricing strategy (point of intersection in Fig. 2(b)) for both the sellers that satisfies the minimum quality or privacy needs of the buyers.

In summary, price vs. quality (privacy/security) trade-off results in complex interactions between mobile App buyers and sellers. This has not been well understood so far. Our research attempts to mathematically model this basic problem using socio-economic theory and test it using real-life data gathered from different mobile App markets.