Strong Complements Research Articles

Strong star complements in graphs

Let G be a finite simple graph with λ as an eigenvalue (i.e. an eigenvalue of the adjacency matrix of G), and let H be a star complement for λ in G. Motivated by a controllability condition, we say that H is a strong star complement for λ if G and H have no eigenvalue in common. We explore this concept in the context of line graphs, exceptional graphs, strongly regular graphs and graphs with a prescribed star complement.

Welfare‐improving cooperation with a consumer‐friendly multiproduct corporation

We consider a multiproduct corporation that adopts consumer‐friendly activities and cooperates with single‐plant firms for improving welfare. We show that full cooperation is socially beneficial if products are strong complements, whereas partial cooperation with higher consumer‐friendly activities is beneficial if products are substitutes. We also examine a sequential choice game of endogenous cooperation in which the multiproduct corporation can induce (partial or full) cooperation and show that our findings are still consistent at equilibrium. We finally compare different ownership of the single‐plant firms and find that foreign ownership decreases the benefits of cooperation.

Privacy Regulation and Quality Investment

This paper analyzes how a privacy regulation restricting data disclosure affects quality investment by a monopoly service provider - who derives revenues solely from sharing user data with third parties - and social welfare. In our model, a user's gross utility from the service depends on its quality and the amount of information shared. We show that in a fully covered market, the regulation reduces quality investment but may still be socially desirable when quality and information are not strong complements. In a partially covered market, the regulation may raise quality and social welfare even when quality and information are highly complementary

Design Rules, Volume 2: How Technology Shapes Organizations: Chapter 5 Complementarity

The purpose of this chapter is to relate the theory of task networks and technology set forth in previous chapters to theories of firm boundaries from economics and management. Complementary goods have more value when used together than separately. Complementarity may be strong or weak. Strong complements are specific and unique goods that have no value (or greatly diminished value) unless all are present in use. In the task network, dense technical interdependencies create strong complementarity, but it can arise for other reasons as well. Transaction cost economics and property rights theory advise that strong complements should be placed under unified governance, for example, through common ownership. Agency theory suggests that weak complementarity can be handled via arms-length transactions and contracts. Furthermore, strong or weak complementarity are not innate properties of tasks and assets, but can be the result of choices regarding task networks, incentives and job design. Supermodular complementarity exists when more of one input makes more of another input more valuable. Distributed supermodular complementarity (DSMC) exists when two or more independent actors can create complementary value by pursuing their own interests, and will not find it advantageous to combine in order to coordinate their actions. I derive formal conditions under which DSMC holds as a consistent pattern in a dynamic equilibrium. Given DSMC, clusters of firms making different complementary goods, including open platforms with surrounding ecosystems, can survive and compete effectively against integrated firms that control all complementary inputs.

Contests between groups of unknown size

We study group contests where group sizes are stochastic and unobservable to participants at the time of investment. When the joint distribution of group sizes is symmetric, with expected group size k¯, the symmetric equilibrium aggregate investment is lower than in a symmetric group contest with commonly known fixed group size k¯. A similar result holds for two groups with asymmetric distributions of sizes. For the symmetric case, the reduction in individual and aggregate investment due to group size uncertainty increases with the variance in relative group impacts. When group sizes are independent conditional on a common shock, a stochastic increase in the common shock mitigates the effect of group size uncertainty unless the common and idiosyncratic components of group size are strong complements. Finally, group size uncertainty undermines the robustness of the group size paradox otherwise present in the model.

Corporate control and credible commitment

The separation of control and ownership – the ability of a small group effectively to control a company though holding a minority of its cash flow rights – is common throughout the world, but also is commonly decried. The control group, it is thought, will use its position to consume excessive amounts of the firm's returns, and this injures minority shareholders in two ways: there is less money and the controllers are not maximizing firm value. To the contrary, we argue here that there is an optimal share of the firm that induces the control group to maximize shareholder value while inducing investors to fund the firm's projects. The concern that controlled companies raise is that the controlling group cannot easily commit not to consume more than the optimal share. A firm's cost of capital is increasing in the controllers’ inability to solve this credibility problem because potential investors will charge the firm for later consuming private benefits. Today, accurate judicial review of controlled transactions under mandatory fiduciary rules helps controllers to commit not to take more than the optimal share. Private contracting and judicial review are strong complements, however. Therefore, our principal normative recommendation is to open up the contracting space by reducing the fiduciary rules to defaults. This reform would be less helpful in developing countries that lack effective legal systems. The public corporations in such countries, however, also have controlling shareholders. We explore various non-legal methods by which these shareholders credibly commit to cap private benefits, although we also show that these methods are less efficient in a mature legal system than contracting would be.

A joint-space numerical model of metabolic energy expenditure for human multibody dynamic system.

Metabolic energy expenditure (MEE) is a critical performance measure of human motion. In this study, a general joint-space numerical model of MEE is derived by integrating the laws of thermodynamics and principles of multibody system dynamics, which can evaluate MEE without the limitations inherent in experimental measurements (phase delays, steady state and task restrictions, and limited range of motion) or muscle-space models (complexities and indeterminacies from excessive DOFs, contacts and wrapping interactions, and reliance on in vitro parameters). Muscle energetic components are mapped to the joint space, in which the MEE model is formulated. A constrained multi-objective optimization algorithm is established to estimate the model parameters from experimental walking data also used for initial validation. The joint-space parameters estimated directly from active subjects provide reliable MEE estimates with a mean absolute error of 3.6 ± 3.6% relative to validation values, which can be used to evaluate MEE for complex non-periodic tasks that may not be experimentally verifiable. This model also enables real-time calculations of instantaneous MEE rate as a function of time for transient evaluations. Although experimental measurements may not be completely replaced by model evaluations, predicted quantities can be used as strong complements to increase reliability of the results and yield unique insights for various applications.

Firm Dynamics and Assortative Matching

I study the relationship between firm growth and the characteristics of newly hired workers. Using Census microdata I obtain a novel empirical result: when a given firm grows faster it hires workers with higher past wages. These results suggest that productive, fast-growing firms tend to hire more productive workers, a form of positive assortative matching. This contrasts with prior research that has found negligible or negative sorting between workers and firms. I present evidence that this difference arises because previous studies have focused on cross-sectional comparisons across firms and industries, while my results condition on firm characteristics (e.g. size, industry, or firm fixed effects). Motivated by the empirical findings I develop a search model with heterogeneous workers and firms. The model is the first to study worker-firm sorting in an environment with worker heterogeneity, firm productivity shocks, multi-worker firms, and search frictions. Despite this richness the model is tractable, allowing me to characterize assortative matching, compositional dynamics and other properties analytically. I show that the model reproduces the positive firm growth-quality of hires correlation when worker and firm types are strong complements in production (i.e. the production function is strictly log-supermodular).

How should process capabilities be combined to leverage supplier relationships competitively?

Two process capabilities have been identified in the operations management literature to leverage supplier relationships for competitive performance: the ability to continuously improve processes with suppliers (process alignment) and the ability to make changes to these relationships (partnering flexibility). While firms may need both capabilities to be successful, it is unclear what strategy should be used to combine these two seemingly contradictory process capabilities. Using data collected from 318 manufacturing firms on a focal firm’s process capabilities to manage supplier relationships, we examine the performance impacts of two dimensions of a particular strategy: balancing (focusing on achieving a close match between the two process capabilities) and complementing (focusing on creating synergy between the two process capabilities). Our results indicate that the balancing dimension has a much stronger effect on a firm’s competitive performance than the complementing dimension. Also, when a firm pursues a high balance and strong complements strategy (combining high levels of both process capabilities), it is able to reduce its competitive performance risks more than when it pursues a high balance and weak complements strategy (combining low levels of both capabilities) or when it implements unbalanced strategies that emphasize either process alignment or partnering flexibility (combining low levels of one capability with high levels of the other). We conclude by discussing the theoretical contributions and practical guidelines.

Outsourcing versus vertical integration: Ethier–Markusen meets the property‐rights approach

AbstractEarly analyses of direct investment versus outsourcing focused on the existence of knowledge‐based assets, knowledge being non‐rivaled and non‐excludable. Ethier was the first to formally model the consequences of non‐excludability for the vertical integration versus outsourcing decision. Later authors took a different approach, modeling physical capital as fully excludable but relationship‐specific. This paper further develops a model with both non‐excludable knowledge capital and fully excludable physical capital. Results show that vertical integration tends to be chosen when (a) the technology is relatively knowledge intensive and/or when (b) knowledge and physical capital are strong complements.

Promises and conventions – An approach to pre-play agreements

I analyze how informal agreements can be sustained by moral emotions with regard to a large class of two-player games. Specifically, I assume that people feel guilty if they breach an agreement and that the guilt increases according to the degree of the harm inflicted on the other. A central insight is that it is easier to sustain efficient informal agreements if actions are strategic complements than if they are strategic substitutes. I complement this general insight by studying two specific cases where negotiators face uncertainty about the breach of the agreement. I show that while the optimal agreement in a game with strategic substitutes must compromise on surplus-maximization and efficiency, the optimal agreement in a game with sufficiently strong strategic complements tends to maximize both the surplus and the probability of compliance especially if the game is symmetric.

Over- and Under-Bidding in Tendering

Consider a government tendering the right to operate, for example, an airport, telecommunication network, or utility. There is an 'incumbent bidder' who owns a complement or substitute facility, and one entering 'new bidder' . With a 'standard auction' on the payment to the government, the incumbent is willing to bid higher than its expected profit from the facility as winning implies that it is a monopolist instead of a duopolist. The incumbent is therefore more likely to win. However, it tends to have a lower expected surplus unless the new bidder can never win, which occurs with 'private values' when the facilities are strong complements or substitutes and always with 'common values'. The 'standard auction' leads to an unregulated outcome which hurts consumers as tendered facilities tend to have limited competition. The government could improve the outcome by endogenously regulating using a 'price auction' on the price to be asked to consumers. Now, it depends who is advantaged: with complements, the incumbent bids below its marginal cost and is more likely to win; with substitutes, it bids above and is less likely to win. The same effects occur in auctions on service quality or number of users. In many settings, the advantaged bidder always wins, and this can greatly affect the competition for the field.

Anticompetitive Exclusion in Related Markets

This paper shows how monopolization of a given market through exclusive contracts can affect the profitability of monopolization of another market in a model with two incumbent firms, each producing a distinct substitute or complementary good and each facing a distinct potential entrant. Externalities between incumbents operate through a scale effect and a profit extraction effect. With linear demand, when both potential entrants have intermediate levels of entry costs there exist multiple equilibria. In particular, when the goods are strong complements there exists an equilibrium with monopolization in both markets and an equilibrium with entry in both markets. When the goods are substitutes or weak complements there exist two asymmetric equilibria, each with a different incumbent monopolizing its market while the other does not. The equilibrium is instead unique when at least one of the two potential entrants has very high or very low entry costs. I discuss implications for antitrust enforcement in markets for complementary inputs and for national antitrust policy-making in the presence of international trade in substitute goods.

Regional competitiveness, university spillovers, and entrepreneurial activity

This study examines the impact of regional competitiveness on the innovative activity of entrepreneurial firms. Based on a unique and hand-collected dataset of publicly listed high-technology start-ups and university regions, this paper tests how regional competitiveness and university spillovers affect the innovation behavior of entrepreneurial firms. The results provide strong evidence that regional competitiveness and university spillovers are strong complements in fostering innovation activity of entrepreneurial firms. However, the results also raise the question whether incentives for universities and their actors might lead to crowding out effects.

Open innovation and systems integration: how and why firms know more than they make

This paper investigates open innovation for the development of complex products. In this context, systems integrators are firms that integrate component innovations into existing product systems and that design entirely new product architectures. To successfully execute these systems integration tasks, these firms need to monitor and absorb the rapid and diverse technological developments that surround them. Systems integration therefore explains why firms know more than they make. Open innovation, on its part, provides the mechanisms that indicate how firms can expand their knowledge boundary. Open innovation and systems integration are strong complements therefore. More specifically, a contingent and a balanced approach to open innovation is suggested: open as far as abundant component knowledge is concerned, and closed with respect to the generation and exploitation of scarce, internally developed architectural knowledge.

Optimal Bundling Strategies in Multiobject Auctions of Complements or Substitutes

We consider a problem at the interface of auctions and bundling. Our revenue-maximizing seller seeking to auction one unit each of two complements or substitutes in the best-of-three formats: the auction of the bundle, separate auctions of the individual items, and a combinatorial auction. We draw on an analytical model to address the following questions: (i) Which of the auctioning strategies is optimal under the second-price, sealed-bid format? (ii) What is the optimal strategy for the bidders? (iii) When the objects are asymmetrically valued (e.g., Super Bowl ticket versus souvenir), what is the optimal auctioning sequence under the pure components strategy? Our results suggest that separate auctions of the two objects are superior to the auction of the bundle for most substitutes and even moderate complements when there are at least four bidders. The auction of the pure bundle is better suited for strong complements or with too few bidders. When the combinatorial auction is an available option, it weakly dominates the auction of the pure bundle but has domains of inferiority relative to the separate auctions. When the objects are asymmetric in value, it is optimal to auction the higher-valued object first.

Welfare‐Worsening Aid Flows To Small Countries: The Role of Nontraded Goods

AbstractThis paper presents the circumstances under which foreign aid can immiserize a small, tariff‐distorted economy, highlighting the role played by the nontraded sector in generating this outcome. An inflow of aid, provided in the form of an increase in the capital stock, can reduce real income of a small, tariff‐distorted economy if: (i) the inflow results in an increase in the price of the nontraded good and the nontraded good and imports are sufficiently strong complements in demand; or (ii) if the inflow leads to a reduction in the price of the nontraded good and the nontraded good and imports are substitutes in demand, provided the degree of substitutability is not too large.

When do creditor rights work?

Creditor-friendly laws are generally associated with more credit to the private sector and deeper financial markets. But laws mean little if not upheld in the courts. We hypothesize that the effectiveness of creditor rights is strongly linked to the efficiency of contract enforcement. This hypothesis is tested using firm level data on 27 European countries in 2002 and 2005. We find that firms have more access to bank credit in countries with better creditor rights, but the association between creditor rights and bank credit is much weaker in countries with inefficient courts. Exploiting the panel dimension of our data and the fact that creditor rights change over time, we show that the effect of a change in creditor rights on change in bank credit increases with court enforcement. In particular, we show that a unit increase in the creditor rights index will increase the share of bank loans in firm investment by 27 percent in a country at the 10th percentile of the enforcement time distribution (Lithuania). However, the increase will be only 7 percent in a country at the 80th percentile of this distribution (Kyrgyzstan). Legal protections of creditors and efficient courts are strong complements. Journal of Comparative Economics 35 (3) (2007) 484–508.

When Do Creditor Rights Work?

Creditor-friendly laws are generally associated with more credit to the private sector, and deeper financial markets. But laws mean little if not upheld in the courts. We hypothesize that the effectiveness of creditor rights is strongly linked to the efficiency of contract enforcement. This hypothesis is tested using firm level data from 27 European countries in 2002 and 2005. We find that firms have more access to bank credit in countries with better creditor rights, but the association between creditor rights and bank credit disappears in countries with inefficient courts. Exploiting the panel dimension of our data and the fact that creditor rights change over time, we show that the effect of a change in creditor rights on change in bank credit increases with court enforcement. In particular, the point estimate of the differential impact of creditor rights implies that a unit increase in the creditor rights index will increase the share of bank loans in firm investment by 27 percent in a country at the 10th percentile of the enforcement time distribution (Lithuania). However, the increase will be only 7 percent in a country at the 80th percentile of this distribution (Kyrgyzstan). Legal protections of creditors and efficient courts are strong complements.

Common and Exclusive Agencies and Partial Delegation

Within the context of common agency, the article examines separation and partial delegation. The first entails breaking the multiple-task agency into smaller single-task agencies, whereas the second allows principals to substitute some of their efforts for the agency's. With respect to the first alternative, it is shown that common agency can be sustained against separation by the presence of strong complements. For the second alternative, principals partially delegate their effort and retain the right to influence agency output at a later stage of the game. Although this tends to weaken agency incentives, principals may prefer this version of common agency than one under full delegation and may prefer it to an exclusive one.