When some country takes a disproportionate hit by a largescale turmoil-just like Italy did during the COVID-19 pandemics-the share prices of its companies plunge. Suddenly, it becomes feasible to attempt foreign takeovers of national assets, including those of strategic interest. To avert this risk, the Government can veto transactions by summoning the so-called “Golden Powers”. Or, it can work to proactively identify structural weaknesses in the control or shareholding chains of key companies, in order to reinforce them without resorting to special powers. Sometimes, vulnerabilities and attacks hide in plain sight due to how complex and intertwined the network of mutual company shareholding is. In this work, we show how to leverage Knowledge Graphs (KGs) as a representation and reasoning framework to analyze both reactive and proactive measures against takeover attempts, however intricate the setting where they take place. We formally characterize a set of reasoning tasks that define when and if to employ Golden Powers, plus others that aim at pinpointing companies prone to attacks. These criteria are exercised on the real network of all Italian companies, built for the occasion. A rich set of experiments is provided, including on several large synthetic instances, to prove the robustness of our method.
The COVID-19 outbreak has had an immense impact on our society. Besides the critical health crisis, it has become clear that preventing, or at least managing, its large-scale economic effects will become critical as well. The work we present here deals with reasoning about company takeovers. To this end, we employ Knowledge Graphs (KGs) as a representation and reasoning framework: Our approach analyzes automatically a large graph of knowledge (representing the
The views and opinions expressed in this paper are those of the authors and do not necessarily reflect the official policy or position of Banca d’Italia. Copyright c 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). entire set of Italian companies and their mutual financial relationships) in search for ongoing or potential hostile takeovers over companies of strategic national interest. Specific reactive or proactive defence measures by the Government, possibly involving the use of the so-called “ Golden Powers ” (GPs), are automatically produced as a result of our analysis. This initiative forms one pillar of a flagship project launched by the Central Bank of Italy in reaction to the COVID-19 crisis,5 and is in line with a call to action by the President of the European Commission6 on counteracting hostile takeovers of strategic companies.
It is essential that the ownership of — or, more importantly, the control upon — companies deemed of strategic relevance (e.g., in the energy, military, transport, telecommunications sectors) remains in the hands of trusted shareholders. Yet, with the COVID-19 outbreak, companies stretched by massive shutdowns and production plunge are subject to an abnormal number of hostile takeover attempts because, in conditions of market turbulence, attackers try to take advantage of lowered share prices. A hostile takeover consists in gaining the control of a target company against the will of its management. Company control can be gained directly by acquiring the majority of the target company shares, or indirectly, by gaining control over a set of companies that jointly own the majority of the shares of the target. In real-world company networks, such indirect undertakings with very long and intertwined control chains are regularly present.
Multiple countries have historically resorted to legal frameworks to protect
strategic companies against foreign takeovers [
Golden Power Settings. Unfortunately, an effective application of the
mentioned legal frameworks (and of GPs in particular) is by no means trivial. How
can we tell whether a transaction is a takeover attempt? Will a transaction
lead to a takeover? What is the minimum amount of share that must shift to
public control in order to protect a company? And, how to protect against
coordinated, collusive, transactions aiming at a takeover? These problems lend
themselves to be addressed by a declarative and fully explainable approach, and
encoded as reasoning tasks on the KG of the Italian companies, built and
maintained by the Bank of Italy [
The formalization of the company control problem and the GP settings in this
paper are encoded in Vadalog, a language from the Datalog family [
Vadalog supports monotonic aggregations, whose full details can be found
in [
0.2 B
A 0.8
0.2 based on stratified semantics, where the basic idea for our case is very simple: An aggregation function (e.g., sum, in Section 4) is computed only when its input operands are completely known. All our use cases admit such simplification. 3
Underlying the study of hostile takeovers is the notion of company control. It concerns decision power, i.e., when a company can direct the decisions of another company by controlling the vote majority via the majority of the shares. Let us consider an ownership graph, i.e., the directed graph where nodes are shareholders and edges represent share ownership.
Along the lines of existing formulations from the logic and database
literature [
A company G controls a company H, if: (i) G directly owns more than 50% of H; or, (ii) G controls a set of companies that jointly (i.e., summing their shares), and possibly together with G, own more than 50% of H.
Figure 1 shows basic cases of company control. In Figure 1(a), the first clause applies: Company directly controls company . In Figure 1(b), the second clause applies: Company does not directly control ; nevertheless, it has an 80% share on company and hence it controls . Thus, the total share of company that controls rises to 61%, which is the sum of the direct 30% ownership of on and the 31% ownership of the controlled company on . In the end, controls . Figure 1(c) demonstrates a more convoluted form of control: An entity can control a company anywhere in the graph, given that can indirectly control the majority of the shares of even if no direct control exists between and or even between any intermediate company and . Company control can be formulated as a Vadalog reasoning task:
Control¹G Hº Own¹H I Fº E = sum¹Fº E ¡ 05 ! Control¹G Iº Assuming that every company has control on itself (Rule 1),7 we inductively define control of G on I by summing the shares of I owned by any company H over all companies H controlled by G (Rule 2). The presence of cycles in the ownership graphs, a common case indeed, is irrelevant for control purposes.
7This formalization of the base case is slightly different from the natural definition but commonly assumed in the literature as it is more compact and formally equivalent.
(1) (2)
In this section we elaborate on a set of KG-based applications revolving around the use of GPs. The framework we develop covers five fundamental concerns raised by business stakeholders, related to: Decision and policy making, advice to be given to companies, and proactive actions to be taken. We present a number of core reasoning tasks providing insights on: 1. detecting cases of transactions hiding possible takeover attempts; 2. suggesting limits within which GPs may be exercised; 3. giving options for proactively protecting companies from takeover attempts. Figure 2 summarizes the scenarios under consideration. Each column describes one scenario, specifying its goal, general setting, business question, and resulting insight. At the bottom of each column, we report one example.
At the core of our cases, there is the Company Control setting from Section 3. Companies are assigned different roles: trusted (e.g., public companies or Governmental bodies, pink in the figure), attacker (e.g., a company out of the national border in the figure, i.e., incorporated or organized under the law of another country), or target (e.g., the strategic company to be protected, green); all the others are assumed to be neutral (gray).
We perform both reactive analysis, checking whether specific variations to the graph generated by candidate transactions (acquisition of shares) culminate in unwanted takeovers, and proactive analysis, detecting structural vulnerabilities and possible countermeasures, independently of any possibly ongoing attack.
In the following paragraphs, we introduce the Vadalog formulations of the five cases. Each one is an extension of Company Control, so Rules 1 and 2 from Section 3 are assumed to be inherited by all the formulations. Attackers, target, and trusted companies are respectively denoted by atoms V, T, and P.
Encoding these criteria as rules in an expressive and scalable declarative framework such as Vadalog is of the essence here because while we have analyzed the key reasoning patterns in this work, more emerge on a daily basis during the interactions with business experts: Changes that would radically impact a procedural approach (requiring a substantial rewrite) are just a minor amendment away when the domain knowledge is captured declaratively. Not only does Vadalog allow us to quickly test and deploy new criteria, but the amount of time we spend to get sure we are on the same page as our business colleagues — i.e., to convince them that the implementation is actually computing what we have agreed on paper — dramatically shortens.
Golden Power Check. We show how to detect individual transactions that cause some target company to be taken over. This is a case where Golden Power may be an option to exercise. We call this problem: Golden Power Check. Example. Let us consider the example shown at the bottom of Figure 2(1). We first consider the setting. Company 1 is in the set of attackers, e.g., potentially attacking companies under investigation (forming the set + in the definition shown in Figure 2), while the colored node is in the set of target companies (forming the set ) in our definition shown in Figure 2).
Candidate transactions are shown using dashed edges. Our first candidate transaction is C1, where an ownership of 51% of is acquired by 1. The second candidate transaction is C2 where an ownership of 90% of is acquired by . Let rseaoPw tteakvn eoaqvb trseap li)yybu ilissobp iItsghn reeoovn iaynnp 2)H) f(romG tseon iisenn iseanp iitsson tseuQ from+ t(schu fttseo caopnm eab+ ftreago ittegnS treeoavk itseon tryb irseanh laoG: anA P ()3 oG treonn rseeov itseonu seanhw rsseaoh itt(teoym i:sondC i?n) itcoagn+ llsoaaynw ,ittohwH ftrscaaon trgaaun% iybn) frsseaoh ion:ichW.)adn) itsah% trsceodu .itseeL ftseoa tcoapnm :tebL) .s treevpn tsedu trceenm itopuCm ilssy:roP ittrceoo leodnPG leondPw ee (G to tre f) e t e c o h d m % tta ie e n a n ow e .)edd leodn -rep teoh iav% -rroap treh ltroon -com2,G+ isonC tteah -oapm f-com i-caqu iijtson iseapn eab icgkn sadn tsea iltseoh -coapm eeendd tegh itcev re ttreS i n G s Y I a + Q w s G fe a t n a o S n s p t s a G leoondP iliittoyb ,sconSE itsghn:fI coypnm itgaon itseonu 2ithG+ frseoah toyub irsseud ttrscaan lrcoapm ,iseand fttseao fttrcega ittegn: iitscean fttteao lisscoyb trceoga ,ttsceok iscaqun lao:hC laynA oPw loC)(4 rsew lob ired teh iayn ijton :oD2,H caom aanm ayb i(eon i.sean sa# itcakn oapm teL) icgn icakn troon apnm .)cca iit(on icekn iss:P Cre lisou . ck teh san ?n) tcon seC [)
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a t f p n C n B a us first consider transaction C1 as our transaction of interest. This would give 1 control of , and hence a 20% ownership of . So far, the total ownership of target company by company 1 is thus 20% with no need to block C1.
Now assume that transaction C1 was processed (i.e., it becomes a solid line), and consider transaction C2, where an ownership of 90% of is obtained by 1. This would give 1 control of and hence 31% ownership of . Together with the ownership of 20% of target company that 1 already holds, it now has 51% ownership of company and thus controls it. Transaction C2 must be blocked using Golden Power if the target company should not come under the control of 1. Finally, we remark that had transaction C2 come before C1, it would have been fine to process C2 and block C1. This concludes our example.
This line of reasoning can be formalized as a Vadalog reasoning task by extending Company Control with the following rules: Rule 1 defines that, for the purpose of our analysis, we consider transaction ) G to be virtually applied, i.e., leading to actual ownership even if it has not taken place. Then, Rule 2 captures our goal by computing all companies in + that control at least one company in ) . If GPCheck is empty, there is no reason to use Golden Powers. In case it is non-empty, it gives a list of the companies which are possible subject of takeovers caused by the single acquisition of share ) G. Golden Power Limit. The second relevant problem is to advise companies about what transactions are allowed to take place (without requiring the use of GPs to prevent a takeover). We call this problem Golden Power Limit. The definition and an example are given in Figure 2(2). A full explanation of this (and following) examples can be found in the appendix,8 while the definition can be formulated with the following Vadalog rules:
Control¹G Hº Own¹H I Fº E = sum¹Fº ! PControl¹G I Eº
V¹Gº T¹Hº PControl¹G H Eº E 05 ! GPLimit¹G H 05 Eº
Tx¹G H Fº GPLimit¹G H º w<h ! Allowed¹G H Fº Rule 1 captures the case of partial control, i.e., the sum of shares does not necessarily lead to control. Rule 2 evaluates the threshold F = 05 E, representing the limit of shares of H that company G can buy without obtaining control. In Rule 3 the transaction Tx is validated against the limit computed in Rule 2. Golden Power Protection. The use of Golden Power comes with political and economic consequences, so in many cases it may be desirable to proactively prevent takeovers. The third problem is about preventing the use of Golden Powers from becoming a necessity. The definition and an example are given in Figure 2(3). A Vadalog formulation is the following:
Control¹G Hº Own¹H I Fº E = sum¹Fº ! PControl¹G I Eº
P¹Gº T¹Hº PControl¹G H Eº E 05 ! Prot¹G H 05 Eº (1) (2) (3) (1) (2) We use the same approach as in Golden Power Limit. Value E, computed by Rule 2, quantifies the additional direct share (“beef-up”) that a trusted company G needs to secure in order to gain control over a target company H. Collusion Golden Power Check. We now formulate the Golden Power Check problem under the possibility of collusive attackers, which we call Collusion Golden Power Check. In general, there is a range of possibilities in defining what types of “collusion” we address, with choices that need to be validated at the business level. The definition and an example are given in Figure 2(4).
The definition of Figure 2 can be formulated as the following Vadalog reasoning task, which extends the definition we have seen before:
We have already discussed Rules 2 and 3 when considering Golden Power Check. Rule 1 captures the intuition that companies in + may be acting collusively, i.e., surreptitiously exerting control over one another.
Cautious Golden Power Check. We now consider the case of missing or unknown information. So far, in our examples we have assumed that if only a partial percentage of the ownership of a company is represented, the remaining shares are not relevant. However, in a cautious scenario, we may want to presume that the most unfavorable conditions hold, namely that the non-represented shares are already in the hands of the attackers. This pessimistic assumption can be combined with any of our base scenarios; here we introduce Cautious Golden Power Check, in Figure 2(5). The following Vadalog rules formalize our concept of caution:
:+ ¹Gº :+ ¹Hº Own¹G H Eº F = sum¹Eº ! Assigned¹H Fº Assigned¹H Fº F 1 ! 9I Company¹Iº + ¹Iº Own¹I H 1 Fº V¹Gº :V¹Hº Tx¹G H Fº E = sum¹Fº ! Own¹G H Eº
V¹Gº T¹Hº Control¹G Hº ! GPCCheck¹G Hº (1) (2) (3) (1) (2) (3) (4) We compute the total amount of currently (un)assigned shares, for each company, with Rule 1. Then, by Rule 2 we depict the worst case scenario where if a non-attacker company (neutral or target) has unassigned shares, there exists an attacker retaining all of them. We assume this is true when reasoning on transactions (Rule 3) and while performing the control check (Rule 4). 5
We applied our technique to the ownership graph of the Italian companies [
In comparable graphs (e.g., N7D1 vs Real), all the GP scenarios are faster than pure Company Control (Figure 4(e)). Proactive cases curb input cardinal
(a)
0 100 200 300 400
(e) 0 100 200 300
Execution time (sec) )c250 e (s200 e itm150 ion100 t ceu 50 xE 0 (b) (f )
Protection )c6000 e s ( iem4000 t n ito2000 u c e x E 0 1 1 1 1 7ND9ND11D 14D
N N )c1000 e (s 800 e itm600 ion 400 t ceu 200 x E 0 ity by filtering on the considered companies (+ and ) predicates); reactive cases produce smaller output than Company Control: Although Limit and Protection consider all partial controls, they concentrate on control of attackers resp. trusted companies over targets. While Collusion artificially adds new Control facts, it does not add edges and therefore simplifies into an attackers-to-target constrained version of Company Control. Cautious is the more demanding case: Reasoning generates at most j) [ # j companies and edges, depending on the number of nodes having unassigned shares. In the worst case, this doubles the graph size, so it does not affect problem complexity. In fact, Figure 4(f ) shows a polynomial growth of the elapsed time of Cautious caused by the number of companies having unassigned shares, which affects the other cases only marginally.
Our cases exhibit good scalability with number of nodes (Figure 4(g)), with a polynomial trend consistently less steep than pure Company Control. The trend of Cautious is slightly steeper than the other cases, as a result of the addition of new attackers (due to existential Rule 2 for the Cautious case in Section 4), which amplify the growth in node count. Interestingly, our cases show good (c) 1 D 1 2 N (g)
Collusion )c1000 e (s 800 e itm600 ion 400 t ceu 200 x
E 0 1 D 8 2 N ) sce400 ( e itm300 n ito200 u c xEe100
(d) 1 D 7 N 2 D 7 N 3 D 7 N (h) 4 D 7 N scalability w.r.t. graph density (Figure 4(h)), and the time difference between the cases keeps stable when nearing to the worst case. This is coherent as growth in density does not over-activate the mentioned existential rule. 6
The reasoning tasks we have presented exemplify how graph database
technology has insufficient expressive power for our goals (e.g., for the joint need for
recursion and value creation). Indeed, Regular Path Query languages [
In graph processing, partial evaluation techniques [
Under the economic angle, many approaches study hostile takeovers at macro
level [
The AI and database communities have shown theoretical interest in
problems related to company graphs [
Driven by the ongoing effort to prevent strategic companies from becoming the target of hostile takeovers, in this work we recognize the power of reasoning on KGs and contribute a set of foundational use cases and formalisations to detect takeover attempts; we also suggest countermeasures and avoidance strategies in a fully explainable fashion. To the best of our knowledge, this is the first use of reasoning techniques in the takeover setting.
We tested all proposed reasoning tasks in the Vadalog System with both real-world and synthetic data. We focused on clarity, by showing only the key rules governing each use case, while leaving out for brevity the large number of auxiliary rules necessary for data extraction, cleaning, integration, etc.
The formalisation we have presented in this work is at the basis of our future work, which concerns the construction of a set of more sophisticated reasoningbased indicators, meant to build automatically a fully explainable ranking of the most vulnerable national companies.