Equilibrium Investment Research Articles

Recommenders’ Originals: The Welfare Effects of the Dual Role of Platforms as Producers and Recommender Systems

We study a model of strategic interaction between producers and a monopolist platform that employs a recommendation system. We characterize the consumer welfare implications of the platform’s entry into the production market. Upon entry, the platform biases recommendations to steer consumers towards its own goods, which leads to equilibrium investment adjustments by the producers and lower consumer welfare when the platform’s market size is large. Furthermore, we find that a policy separating recommendation and production or imposing unbiased recommendations is not always welfare improving. Our results highlight the ability of platforms to foreclose competition through the use of biased recommender systems.

Dynamic asset-liability management problem in a continuous-time model with delay

ABSTRACT This paper investigates a dynamic continuous-time asset-liability management (ALM) problem with delay under the mean-variance criterion. The investor allocates her wealth in a financial market consisting of one risk-free asset and one risky asset, and she is subject to a random liability. The historical information of the wealth and liability affects the investor's wealth process, which is then governed by a stochastic differential delay equation. Firstly, a general ALM problem with delay is formulated and the extended Hamilton-Jacobi-Bellman system of equations is obtained. Secondly, we focus on a linear model and derive the closed-form expressions of the equilibrium investment strategy and the corresponding equilibrium value function. Meanwhile, we also derive the pre-commitment strategy for the mean-variance ALM problem with delay using the maximum principle. Finally, some numerical examples and sensitivity analysis are presented to illustrate the equilibrium investment strategies and the efficient frontiers under the equilibrium and pre-commitment frameworks.

Coopetition between B2C E-commerce Companies: Price Competition and Logistics Service Cooperation

This paper studies the impact of logistics cooperation in two competing companies, one of which is equipped with a self-run logistics system while the other is not. The latter outsources logistics services to a third-party logistics company before logistics cooperation, or to its competitor after logistics cooperation with the client’s service quality being in proportion to and no greater than the service provider’s service quality. We find that when the service provider is a price taker, logistics cooperation is beneficial to both firms only when the service quality after logistics cooperation is moderate. Interestingly, under some circumstances, the client’s profit increases even when its service quality decreases after logistics cooperation because logistics cooperation eases the price competition. We also find that all-win situations in which logistics cooperation increases the firms’ profit, consumer surplus and social welfare can be achieved. Finally, when the service price can be chosen by the service provider, we propose a negotiation process in which agreement on logistics cooperation can be reached; when the firm can invest in service quality, logistics cooperation may lower the equilibrium investment level.

Skills, Efficiency, and Timing in a Simple Attack and Defense Model

In this paper, we consider a simple two-player attack and defense model, focusing on the role of players’ abilities and choice timing. Abilities are divided into skills and efficiency, where the former is an absolute notion and the latter a relative notion of ability. Timing is investigated by comparing players’ investments in a simultaneous and a Stackelberg game. In the simultaneous game, the Nash Equilibrium investment level in attack and defense resources is symmetric, increasing in the skills but non-monotonic in the relative efficiency. In the Stackelberg game, the equilibrium investment levels are asymmetric, increasing in the skills, but with their ranking affected only by the relative efficiency. Therefore, interestingly, players’ choice is mostly characterized by players’ relative efficiency rather than by their skills, in regards to timing.

Investment in trade facilitating infrastructure: A political-economy analysis

This paper analyzes public investment in infrastructure that facilitates international trade. It considers a world consisting of small open economies that face transport costs for exporting or importing a particular good. Transport costs can be lowered by an improvement in transport infrastructure. National governments non-cooperatively decide about their respective country's investment level. Governments' preferences are assumed to be biased in favor of producers' interests with consequences for equilibrium investments: Exporting countries, whose producers benefit from a transport cost reduction, spend more for infrastructure than importing countries, whose producers are protected by transport costs from foreign competition. This outcome is inefficient, and governments have an incentive to cooperate internationally. The paper also incorporates bilateral trade with two goods that benefit from infrastructure improvements as well as trade that results from offshoring.

Lumpy Investment in Dynamic General Equilibrium

Microeconomic lumpiness matters for macroeconomics. According to our DSGE model, it explains roughly 60% of the smoothing in the investment response to aggregate shocks. The remaining 40% is explained by general equilibrium forces. The central role played by micro frictions for aggregate dynamics results in important history dependence in business cycles. In particular, booms feed into themselves. The longer an expansion, the larger the response of investment to an additional positive shock. Conversely, a slowdown after a boom can lead to a long lasting investment slump, which is unresponsive to policy stimuli. Such dynamics are consistent with US investment patterns over the last decade. More broadly, over the 1960-2000 sample, the initial response of investment to a productivity shock with responses in the top quartile is 60% higher than the average response in the bottom quartile. Furthermore, the reduction in the relative importance of general equilibrium forces for aggregate investment dynamics also facilitates matching conventional RBC moments for consumption and employment.

Competition Among Proprietary and Open-Source Software Firms: The Role of Licensing in Strategic Contribution

In enterprise software markets, firms are increasingly using services-based business models built on open-source software (OSS) to compete with established, proprietary software firms. Because third-party firms can also strategically contribute to OSS and compete in the services market, the nature of competition between OSS constituents and proprietary software firms can be complex. Moreover, their incentives are likely influenced by the licensing schemes that govern OSS. We study a three-player game and examine how open-source licensing affects competition among an open-source originator, an open-source contributor, and a proprietor competing in an enterprise software market. In this regard, we examine (1) how quality investments and prices are endogenously determined in equilibrium, (2) how license restrictiveness impacts equilibrium investments and the quality of offerings, and (3) how license restrictiveness affects consumer surplus and social welfare. Although some in the open-source community often advocate restrictive licenses such as the GNU General Public License because it is not always in the best interest of the originator for the contributor to invest greater development effort, such licensing can actually be detrimental to both consumer surplus and social welfare when it exacerbates this incentive conflict. We find such an outcome in markets characterized by software providers with similar development capabilities yet cast in favor of the proprietor. In contrast, when these capabilities either become more dispersed or remain similar but tilt in favor of open source, a more restrictive license instead encourages greater effort from the OSS contributor, leads to higher OSS quality, and provides a larger societal benefit. This paper was accepted by Chris Forman, information systems.

Risk shifting and the allocation of capital: A Rationale for macroprudential regulation

Abstract This paper reconsiders the risk-shifting problem of banks and presents a novel rationale for macroprudential regulation. The interplay between this agency problem and equilibrium investment creates a welfare-reducing pecuniary externality that causes capital misallocation and excessive bank risk taking. Therefore, the banking sector tends to be too large, under-capitalized, and inefficiently risky. This distortion is independent of typical frictions like government guarantees or default costs. Macroprudential regulation with capital requirements or deposit rate ceilings corrects misallocation thereby magnifying rent opportunities for banks to reduce risk shifting. Regulation is, however, no Pareto improvement and causes redistribution from households to bank owners.

A Stackelberg reinsurance–investment game with asymmetric information and delay

ABSTRACT This paper investigates a Stackelberg stochastic differential reinsurance–investment game problem, in which the reinsurer is the leader and the insurer is the follower. The unequal status of the reinsurer and the insurer in the financial market is characterized by the asymmetric information model. We consider their wealth processes with delay to characterize bounded memory. The objective of the reinsurer is to find the optimal premium pricing strategy and investment strategy such that its constant absolute risk aversion (CARA) utility of the combination of terminal wealth and average performance wealth is maximized. The objective of the insurer is to find the optimal reinsurance strategy and investment strategy such that its CARA utility of the relative performance is maximized. We derive the equilibrium strategy explicitly for the game by solving corresponding Hamilton–Jacobi–Bellman equations sequentially. Then, we establish the verification theorem. The equilibrium investment strategy indicates that the insurer with less information completely imitates the investment strategy of the reinsurer who has more information on the financial market. Further, we find that the effect of the delay weight on the equilibrium strategy is related to the length of delay time. Finally, we present some numerical examples to demonstrate the findings.

Renewable Energy Power Generation R&D Investment Under Incomplete Information

The incomplete information of the future prospects of new renewable energy power generation technology, which is contained in external random events regarding policy, technology and market, together with the technical uncertainty of R&D success will affect the investment decision of renewable electric power enterprises. The critical beliefs, which are necessary for single enterprise and duopoly renewable energy power enterprises for their investment in new power generation technologies, are obtained respectively by taking into consideration the incomplete information, technical uncertainty and competitiveness and construction of decision-making model based on real options, and the equilibrium type that may generate in market competition of the two symmetric enterprises and the generation conditions are further analyzed in this paper. The result indicated that the winnertake- all privilege granted to the leading innovator and the technical uncertainty to innovative technology by policy will make the following enterprises react in two ways, investment delay or investment advancing. The faster signal arrives, the higher the signal quality is and the higher is the investment belief of the following investor. Moreover, the R&D competition equilibrium among enterprises can result in preemptive equilibrium and simultaneous investment equilibrium.

Coevolution of cognitive abilities and identity signals in individual recognition systems.

Social interactions are mediated by recognition systems, meaning that the cognitive abilities or phenotypic diversity that facilitate recognition may be common targets of social selection. Recognition occurs when a receiver compares the phenotypes produced by a sender with a template. Coevolution between sender and receiver traits has been empirically reported in multiple species and sensory modalities, though the dynamics and relative exaggeration of traits from senders versus receivers have received little attention. Here, we present a coevolutionary dynamic model that examines the conditions under which senders and receivers should invest effort in facilitating individual recognition. The model predicts coevolution of sender and receiver traits, with the equilibrium investment dependent on the relative costs of signal production versus cognition. In order for recognition to evolve, initial sender and receiver trait values must be above a threshold, suggesting that recognition requires some degree of pre-existing diversity and cognitive abilities. The analysis of selection gradients demonstrates that the strength of selection on sender signals and receiver cognition is strongest when the trait values are furthest from the optima. The model provides new insights into the expected strength and dynamics of selection during the origin and elaboration of individual recognition, an important feature of social cognition in many taxa. This article is part of the theme issue 'Signal detection theory in recognition systems: from evolving models to experimental tests'.

Equilibrium and -efficient fertility with increasing returns to population and endogenous mortality

AbstractA general equilibrium model that characterizes the gap between optimal and equilibrium fertility and investment in human capital is developed. The aggregate production function exhibits increasing returns to population arising from specialization, but households face a quantity–quality trade-off when choosing their fertility and how much education these children receive. We show that equilibrium fertility is too low and investment per child is too high, in contrast to a current planner who internalizes the externality of current fertility on the next generation's productivity. We next introduce mortality of young adults in the model and assume that households have a precautionary demand for children. Human capital investment lowers next generation mortality. This model endogenously generates a demographic transition but, since households do not internalize the negative effects of human capital on mortality, the equilibrium demographic transition takes place many years later than the efficient solution. We show that ${\rm {\cal A}}$-efficient fertility and human capital investment pair can switch; in high-mortality regimes, ${\rm {\cal A}}$-efficient fertility is lower than equilibrium fertility, and ${\rm {\cal A}}$-efficient human capital investment is higher than equilibrium investment. In the zero mortality regime, however, ${\rm {\cal A}}$-efficient fertility exceeds equilibrium fertility, and ${\rm {\cal A}}$-efficient human capital investment is lower than the equilibrium choice.

Uniqueness of equilibrium strategies in dynamic mean-variance problems with random coefficients

This paper is concerned with the uniqueness issue of open-loop equilibrium investment strategies of dynamic mean-variance portfolio selection problems with random coefficients. A unified method is developed to treat both the problems with deterministic risk-free return rate, state-dependent risk aversion, and those with full random coefficients, constant risk aversion. To do so, some new necessity conditions for the existence of equilibrium investment strategies are established, which considerably extends the analogue in [9] with distinctive ideas. Some new interesting facts are revealed. For example, if risk-free return rate is random, it is shown that there exists a unique open-loop equilibrium investment strategy relying on initial wealth, even when risk aversion is merely a constant but not state-dependent.

Open-loop equilibrium strategy for mean–variance asset–liability management portfolio selection problem with debt ratio

In this study, we consider a time-consistent mean–variance asset–liability management portfolio selection problem in which the liability is controllable. The objective is to find an equilibrium investment strategy and an equilibrium debt ratio in the financial market consisting of one risk-free asset and one risky asset. By using forward backward stochastic differential equations (FBSDEs), we derive a sufficient condition and a necessary condition for the open-loop equilibrium strategies. The uniqueness of the strategies is also provided. Furthermore, to illustrate our results, we provide numerical examples to show how the parameters impact on the equilibrium strategies and the corresponding efficient frontier.

Complementarity in public and private intellectual property enforcement; implications for international standards

Abstract I examine the relationship between public enforcement of intellectual property (IP) rights and firm strategies to influence entry of non-deceptive counterfeit products: illegal copies of authentic goods purchased consciously by consumers. I assume that private enforcement investment determines the probability that a counterfeit entrant will be detected, while public investment determines the efficacy of the legal institutions responsible for enforcing IP law. Private and public enforcement serve distinct complementary roles, which combine to determine total IP protection in the economy. I show that differences in the investment incentives of the two entities that control enforcement lead to inefficiently low public investment in equilibrium. In this context, international efforts to impose stricter legal penalties against counterfeiters can be counterproductive: further reducing public enforcement and increasing counterfeit prevalence. In contrast, minimum quality standards can be implemented to better align incentives, encourage higher public enforcement, and reduce inefficiency.

University‐firm competition in basic research and university funding policy

AbstractWe characterize equilibrium investments in basic research by the commercial and university sectors contingent on public funding of the university. We find that firms invest in basic research despite the opportunities for free riding and we present conditions under which firms even have incentives to augment the public funding to the university. We characterize the socially optimal volume of public funding for the university sector. Finally, we compare total investments in a mixed duopoly with those of duopolies composed of two universities as well as two profit‐maximizing firms.

Analysis of Optimal Strategies in a Two-Echelon Digital Products Supply Chain Considering Consumer Types

Considering that the consumers are heterogeneous, we analyze pricing and investment strategies in a two-echelon supply chain of digital products which comprises a manufacturer and a retailer. Firstly, we construct demand function of digital product based on the consumer types by introducing product quality. Three different supply chain models are considered: vertical integration model, Cournot model, and manufacturer Stackelberg model. We study the players’ optimal strategies under these three models and focus on analyzing the effects of the players’ power balance on equilibrium optimal pricing and investment. We find the aggregated profits of both sides and investment cost are the highest in vertical integration model. The price of the digital product is the lowest in vertical integration model in most cases, as the customers hope. Finally, we offer managerial implications and direct the further work.

Asymptotic Optimality of a First-Order Approximate Strategy for an Exponential Utility Maximization Problem with a Small Coefficient of Wealth-Dependent Risk Aversion

In Delong [8] we investigate an exponential utility maximization problem for an insurer who faces a stream of non-hedgeable claims. We assume that the insurer’s risk aversion coefficient consists of a constant risk aversion and a small amount of wealth-dependent risk aversion. We apply perturbation theory and expand the equilibrium value function of the optimization problem on the parameter epsilon controlling the degree of the insurer’s risk aversion depending on wealth. We derive a candidate for the first-order approximation to the equilibrium investment strategy. In this paper we formally show that the zeroth-order investment strategy pi _0^* postulated by Delong (Math Methods Oper Res 89:73–113, 2019) performs better than any strategy pi _0 when we compare the asymptotic expansions of the objective functions up to order {mathcal {O}}(1) as epsilon rightarrow 0, and the first-order investment strategy pi _0^*+pi _1^*epsilon postulated by Delong (Math Methods Oper Res 89:73–113, 2019) is the equilibrium strategy in the class of strategies pi ^*_0+pi _1epsilon when we compare the asymptotic expansions of the objective functions up to order {mathcal {O}}(epsilon ^2) as epsilon rightarrow 0, where epsilon denotes the parameter controlling the degree of the insurer’s risk aversion depending on wealth.

Behavioral and Game-Theoretic Security Investments in Interdependent Systems Modeled by Attack Graphs

In this article, we consider a system consisting of multiple interdependent assets, and a set of defenders, each responsible for securing a subset of the assets against an attacker. The interdependencies between the assets are captured by an attack graph, where an edge from one asset to another indicates that if the former asset is compromised, an attack can be launched on the latter asset. Each edge has an associated probability of successful attack, which can be reduced via security investments by the defenders. In such scenarios, we investigate the security investments that arise under certain features of human decision making that have been identified in behavioral economics. In particular, humans have been shown to perceive probabilities in a nonlinear manner, typically overweighting low probabilities and underweighting high probabilities. We show that suboptimal investments can arise under such weighting in certain network topologies. We also show that pure strategy Nash equilibria exist in settings with multiple (behavioral) defenders, and study the inefficiency of the equilibrium investments by behavioral defenders compared to a centralized socially optimal solution.

Contagion Risks and Security Investment in Directed Networks

We develop a model for contagion risks and optimal security investment in a directed network of interconnected agents with heterogeneous degrees, loss functions and security profiles. Our model generalizes much of contagion models in the literature; in particular the independent cascade model and the linear threshold model. We state various limit theorems on the final size of infected agents in the case of random networks with given vertex degrees for finite and infinite variance degree distributions. The results allow us to derive a resilience condition of the network to the infection of a large group of agents and quantify how contagion amplifies small shocks to the network. We show that when the degree distribution has infinite variance and, highly correlated in- and out-degrees, then even when agents have high thresholds, a sub-linear fraction of initially infected agents is enough to trigger the infection of a positive fraction. We also show how these results are sensitive to vertex and edge percolation (immunization). We then study the asymptotic Nash equilibrium and socially optimal security investment. In the asymptotic limit, agents' risk depends on all other agents' investment through an aggregate quantity, that we call network vulnerability. The limit theorems allow us to capture the impact of one class of agents' decision on the overall network vulnerability. Based on our results, the vulnerability is semi-analytic allowing for a tractable Nash equilibrium. We give sufficient conditions for investment in equilibrium to be monotone in the network vulnerability. When investment is monotone, we show that the (asymptotic) Nash equilibrium is unique. In the particular example of two types core-periphery agents, we exhibit a strong effect of the cost heterogeneity and in particular non-monotonous investment as a function of costs.