Simple Competition Model Research Articles

Regulating Digital Piracy Consumption

Regulators across the globe have imposed penalties on consumers for digital piracy consumption. Contrary to expectations, however, digital piracy consumption has continued to grow. The authors develop a simple model of competition between a copyright holder and a pirate firm to offer a plausible account for this observation as well as actionable guidelines for optimal regulation design. The core of this idea is to endogenize the pirate firm's strategic investment in antitracking technologies that help consumers evade a regulator's penalty. The authors find that as the penalty rises, piracy consumption can surprisingly increase after decreasing first; relatedly, the copyright holder and the society may suffer from tighter regulation. Depending on the cost of antitracking technologies of the pirate firm, the regulator optimally sets the penalty to operate in two different regimes. When the technology is available at a low cost, the regulator can achieve the goals of maximizing social welfare and minimizing piracy consumption simultaneously by setting a moderate penalty that maximizes consumers’ expected penalty and tolerates some level of piracy consumption. In contrast, when the technology is costly, the regulator should set a relatively high penalty to completely impede piracy supply. Additionally, the authors show that supply-side regulation does not substitute away demand-side regulation, and educating consumers about copyright protection may unintentionally lead to an increase in piracy consumption. Last, the authors identify complex nonmonotonic long-run effects of piracy consumption regulation on the copyright holder's incentives for content creation and copyright protection.

Food policies: balancing health and market in the era of ubiquitous ultra-processed foods

As the development of modern food systems continues to reshape dietary habits, the need for effective food policies to counter the rise of ultra-processed foods (UPFs) becomes increasingly urgent. UPFs are industrial formulations of several highly refined ingredients and additives with little or no nutritional value but potentially harmful health effects. In this paper, we develop a simple model of duopolistic competition in which food manufacturers compete by choosing the degree of food sophistication of their products (i.e., the degree of food formulation and processing). We show that when firms compete for market shares, an unhealthy degree of food sophistication is a strategically stable Nash–Bertrand equilibrium outcome. Furthermore, we compare the effectiveness of alternative health-related food policies. Our model highlights the shortcomings of nutrient-to-limit regulations and suggests that policy interventions should prioritize whole-food reformulation-based approaches within an 'ecological' regulatory framework.

Interspecific competition models and resource inequality between individuals.

Most classical discrete-time population models of interspecific competition have emerged as population-level phenomenological models with no evident basis at the individual level. This study shows that the Hassell-Comins model, a widely used discrete-time model of interspecific competition, can be derived in a bottom-up manner from a simple model of random resource competition between individuals of two species as an expression of expected population sizes in the next generation. The random competition leads to inequalities in resource allocation between individuals, which are related to the key parameters of the Hassell-Comins model that determine the density dependence of each species. The relationship between population-level parameters, such as intra- and interspecific competition coefficients, and individual-level parameters is discussed in detail, as is how the derived competition equations depend on the degree of inequality within each species. By considering limits of maximum or minimum resource inequality within each species, the derived model can describe interspecific competition for various combinations of two species exhibiting ideal scramble or ideal contest intraspecific competition.

A Simple Model of Corporate Tax Incidence

We analyze the incidence of a linear corporate tax using a simple and portable competitive general equilibrium model in which capital owners choose to invest either in domestic production or a foreign investment opportunity and workers make extensive margin labor supply decisions. Our analysis explores the effect of corporate taxation on wages, employment, domestic profits, and domestic investment. Analytical results and numerical simulations generate insights in line with recent empirical evidence on corporate tax incidence: the burden of the corporate tax is shared between workers and firms, with larger responses among more capital-intensive firms.

Resource competition predicts assembly of gut bacterial communities in vitro.

Microbial community dynamics arise through interspecies interactions, including resource competition, cross-feeding and pH modulation. The individual contributions of these mechanisms to community structure are challenging to untangle. Here we develop a framework to estimate multispecies niche overlaps by combining metabolomics data of individual species, growth measurements in spent media and mathematical models. We applied our framework to an in vitro model system comprising 15 human gut commensals in complex media and showed that a simple model of resource competition accounted for most pairwise interactions. Next, we built a coarse-grained consumer-resource model by grouping metabolomic features depleted by the same set of species and showed that this model predicted the composition of 2-member to 15-member communities with reasonable accuracy. Furthermore, we found that incorporation of cross-feeding and pH-mediated interactions improved model predictions of species coexistence. Our theoretical model and experimental framework can be applied to characterize interspecies interactions in bacterial communities in vitro.

Eco-evolutionary feedbacks in the human gut microbiome

Gut microbiota can evolve within their hosts on human-relevant timescales, but little is known about how these changes influence (or are influenced by) the composition of their local community. Here, by combining ecological and evolutionary analyses of a large cohort of human gut metagenomes, we show that the short-term evolution of the microbiota is linked with shifts in its ecological structure. These correlations are not simply explained by expansions of the evolving species, and often involve additional fluctuations in distantly related taxa. We show that similar feedbacks naturally emerge in simple resource competition models, even in the absence of cross-feeding or predation. These results suggest that the structure and function of host microbiota may be shaped by their local evolutionary history, which could have important implications for personalized medicine and microbiome engineering.

Economic spillovers and political payoffs in government competition for firms: Evidence from the Kansas City Border War

When jurisdictions use business incentives to compete for firms, the political payoffs of winning firms are privately derived by the politicians of the winning jurisdictions, but the economic payoffs, such as new jobs, can spill over to the residents of non-winning jurisdictions. I study how potential political payoffs shape government competition for firms using a simple model of government competition and firm location choice. I use the model to propose an empirical approach of deriving lower bounds on political payoffs with data on accepted incentives. Applying this approach to the recent state competition between Kansas and Missouri for firm relocation within Kansas City, I find that the two states derived sizable political payoffs.

Competition in a system of Brownian particles: Encouraging achievers.

We introduce and analytically and numerically study a simple model of interagent competition, where underachievement is strongly discouraged. We consider N≫1 particles performing independent Brownian motions on the line. Two particles are selected at random and at random times, and the particle closest to the origin is reset to it. We show that, in the limit of N→∞, the dynamics of the coarse-grained particle density field can be described by a nonlocal hydrodynamic theory which was encountered in a study of the spatial extent of epidemics in a critical regime. The hydrodynamic theory predicts relaxation of the system toward a stationary density profile of the "swarm" of particles, which exhibits a power-law decay at large distances. An interesting feature of this relaxation is a nonstationary "halo" around the stationary solution, which continues to expand in a self-similar manner. The expansion is ultimately arrested by finite-N effects at a distance of order sqrt[N] from the origin, which gives an estimate of the average radius of the swarm. The hydrodynamic theory does not capture the behavior of the particle farthest from the origin-the current leader. We suggest a simple scenario for typical fluctuations of the leader's distance from the origin and show that the mean distance continues to grow indefinitely as sqrt[t]. Finally, we extend the inter-agent competition from n=2 to an arbitrary number n of competing Brownian particles (n≪N). Our analytical predictions are supported by Monte Carlo simulations.

Taxing mobile and overconfident top earners

We set up a simple model of tax competition for mobile, highly-skilled and overconfident managers. Firms endogenously choose the compensation scheme for managers, which consists of a fixed wage and a bonus payment in the high state. Managers are overconfident about the probability of the high state and hence of receiving the bonus, whereas firms and governments are not. When governments maximize tax revenues, we show that overconfidence unambiguously reduces the bonus tax rate that governments set in the non-cooperative tax equilibrium, while increasing tax revenues. When the government objective incorporates the welfare of resident managers, however, bonus taxes also serve a corrective role and may rise in equilibrium when overconfidence is increased.

Stability of cycling behaviour near a heteroclinic network model of Rock–Paper–Scissors–Lizard–Spock

The well-known game of Rock–Paper–Scissors can be used as a simple model of competition between three species. When modelled in continuous time using differential equations, the resulting system contains a heteroclinic cycle between the three equilibrium solutions representing the existence of only a single species. The game can be extended in a symmetric fashion by the addition of two further strategies (‘Lizard’ and ‘Spock’): now each strategy is dominant over two of the remaining four strategies, and is dominated by the remaining two. The differential equation model contains a set of coupled heteroclinic cycles forming a heteroclinic network. In this paper we carefully consider the dynamics near this heteroclinic network. We develop a technique to use a previously defined definition of stability (known as fragmentary asymptotic stability) in numerical continuation software. We are able to identify regions of parameter space in which arbitrarily long periodic sequences of visits are made to the neighbourhoods of the equilibria, which form a complicated pattern in parameter space.

Growing Oligopolies, Prices, Output, and Productivity

American industries have grown more concentrated over the last 40 years. In the absence of productivity innovation, this should lead to price hikes and output reductions, decreasing consumer welfare. With US census data from 1972 to 2012, I use price data to disentangle revenue from output. Industry-level estimates show that concentration increases are positively correlated to productivity and real output growth, uncorrelated with price changes and overall payroll, and negatively correlated with labor’s revenue share. I rationalize these results in a simple model of competition. Productive industries (with growing oligopolists) expand real output and hold down prices, raising consumer welfare, while maintaining or reducing their workforces, lowering labor’s share of output. (JEL D43, L13, D24, D33, D21, D42)

Analysis of the Droop Model with Wall Growth in a Chemostat

In this paper, we construct a simple chemostat-based variable yield model of competition between two bacterial strains, one of which is capable of wall growth [14]. In this model we prove the boundedness of solutions, analyze the local stability of equilibria and establish the global stability for the locally stable extinction equilibrium. Furthermore, when the extinction equilibrium becomes unstable, we prove the existence and uniqueness of the positive equilibrium and the uniform persistence of the system.

Negotiating exclusion: Regulatory barriers in preferential trade agreements

AbstractTrade negotiations now center on regulations. This paper argues that these negotiations can raise uncertainty over fixed costs. We develop a simple model of exporter competition to show how uncertainty generated by negotiations redistributes profits across firms. We show that regulatory uncertainty reduces competition by deterring entry on the part of less productive firms and shifting market share toward top producers. Empirically, we show that this negotiation‐driven uncertainty can help explain the economically concentrating effects of preferential agreements. Preferential trade agreements combine tariff concessions with regulatory changes that ensure the benefits of the agreement are limited to member states. Using novel data covering firm‐level export activity and public investment decisions in the automotive and automotive parts sectors during NAFTA, we find that negotiation‐driven uncertainty deterred non‐North American producers while benefiting the top American auto manufacturers.

Identifying robust strategies for assisted migration in a competitive stochastic metacommunity.

Assisted migration (AM) is the translocation of species beyond their historical range to locations that are expected to be more suitable under future climate change. However, a relocated population may fail to establish in its donor community if there is high uncertainty in decision‐making, climate, and interactions with the recipient ecological community. To quantify the benefit to persistence and risk of establishment failure of AM under different management scenarios (e.g., choosing target species, proportion of population to relocate, and optimal location to relocate), we built a stochastic metacommunity model to simulate several species reproducing, dispersing, and competing on a temperature gradient as temperature increases over time. Without AM, the species were vulnerable to climate change when they had low population sizes, short dispersal, and strong poleward competition. When relocating species that exemplified these traits, AM increased the long‐term persistence of the species most when relocating a fraction of the donor population, even if the remaining population was very small or rapidly declining. This suggests that leaving behind a fraction of the population could be a robust approach, allowing managers to repeat AM in case they move the species to the wrong place and at the wrong time, especially when it is difficult to identify a species’ optimal climate. We found that AM most benefitted species with low dispersal ability and least benefited species with narrow thermal tolerances, for which AM increased extinction risk on average. Although relocation did not affect the persistence of nontarget species in our simple competitive model, researchers will need to consider a more complete set of community interactions to comprehensively understand invasion potential.

Physical Interactions between Heme Oxygenase‐1 and the Cytochromes P450 Lead to Complex Changes in Enzyme Activity

The cytochromes P450 (P450s) catalyze the oxygenation of endogenous and exogenous organic substrates, including most prescribed drugs. Heme oxygenase-1 (HO-1) is an inducible enzyme responsible for the rate-limiting step of heme catabolism. HO-1 and the P450s are membrane-bound proteins expressed on the cytosolic face of the endoplasmic reticulum where they must interact with NADPH-cytochrome P450 reductase (POR) for activity. Because POR levels are often limiting, HO-1 and the P450s must compete for POR binding in order to function. However, simple competition for POR is often complicated by homomeric and heteromeric P450•P450 interactions. We hypothesized that HO-1 might participate with the P450s in their competition for POR and that this competition might lead to changes in P450 and/or HO-1 activity. We were also interested in determining whether HO-1 could physically interact with P450s and measuring what functional effects any P450•HO-1 complex might have. Using bioluminescence resonance energy transfer (BRET), we were able to establish that HO-1 formed physical complexes with CYP1A1, CYP1A2, and CYP2D6 in transiently transfected HEK293T cells. The stability of these complexes was determined by measuring the BRET signal generated by GFP- and Renilla luciferase-tagged P450 and HO-1 in the presence and absence of untagged POR. The presence of POR did not have a significant effect on the interactions of HO-1 with CYP1A2 and CYP2D6 but caused an increase in the BRET signal generated by the HO-1/CYP1A1 pair. Further BRET studies of these three P450s showed that the presence of HO-1 inhibited the formation of POR•P450 complexes, while, conversely, the presence of untagged P450 caused marginal disruption of POR•HO-1 complex formation. The differences in the response of the HO-1•CYP1A1 complex and the HO-1•CYP1A2 complex to POR indicated the possibility of different functional consequences of these P450/HO-1 interactions. Activity measurements of purified enzymes in lipid reconstituted systems confirmed that this was the case. CYP1A1 and HO-1 had large inhibitory effects on each other over a large range of POR concentrations. HO-1 activity in the presence of CYP1A1 approached that of HO-1 alone only in the presence of a large excess of POR. The parallel experiments with HO-1 and CYP1A2 yielded results that differed both qualitatively and quantitatively from those seen with CYP1A1. Like CYP1A1, CYP1A2 caused inhibition of HO-1 activity, though the effect of CYP1A2 was much milder. The effect of HO-1 on CYP1A2 was also smaller in magnitude than was observed with CYP1A1, but CYP1A2 activity increased in the presence of HO-1 and subsaturating POR. In the presence of HO-1 and excess POR, CYP1A2 activity was slightly inhibited. Kinetic analysis of these results showed that they were inconsistent with a simple model of competition between HO-1 and P450 for POR.

Complex dynamics of some models of antimicrobial resistance on complex networks

Studying the spread of epidemics and diseases is a worldwide problem especially during the current time where the whole world is suffering from COVID‐19 pandemic. Antimicrobial resistance (AMR) and waning vaccination are classified as worldwide problems. Both depend on the exposure time to antibiotic and vaccination. Here, a simple model for competition between drug‐resistant and drug‐sensitive bacteria is given. Conditions for local stability are investigated, which agree with observation. Existence of positive solution in the AMR complex networks is proved. Dynamics of the identical AMR models are explored with different topologies of complex networks such as global, star, line, and unidirectional line networks coupled through their susceptible states. Chaotic attractors are shown to exist as the AMR models are located on all these topologies of complex networks. Thus, it is found that the dynamics of the AMR model become more complicated as it is located on either integer‐order or fractional‐order complex networks. Furthermore, a discretized version of the fractional AMR model is presented. Complex dynamics such as existence of Neimark–Sacker, flip bifurcations, coexistence of multiple attractors, homoclinic connections, and multiple closed invariant curves are investigated. Basin sets of attraction are also computed. Finally, the discretized system is located on complex networks with different topologies which show rich variety of complex dynamics. Also, 0–1 test is used to verify the existence of unpredictable dynamics. So, studying the dynamics of AMR models on complex networks is very helpful to understand the mechanism of spread of diseases.

Entry, Size Expansion, and Gains from Trade with Heterogeneous Firms

This paper presents a simple model of monopolistic competition that features a general class of additively separable preferences without any fixed costs. While trade always crowds out less productive firms as long as countries are symmetric, we show that the impact is independent of entry/exit a la Hopenhayn, and is different from the effect of market size expansion, which may crowd in less productive firms. Our analysis pin-points the source of gains from trade in the presence of heterogeneous firms as bringing about new varieties from foreign countries by expanding more productive firms at home.

A simple model of a money-management market with rational and extrapolative investors

I analyze a simple model of competition in fees among mutual funds. The funds are vertically differentiated in terms of the expected return they can generate for investors. Following Berk and Green (2004), I assume that a fund’s net return is decreasing in the amount of capital it manages, and that there is an infinite supply of capital by rational investors. Unlike the Berk-Green model, I assume there is also a finite supply of capital by non-rational investors who naively chase recent net returns. Investor behavior and the funds’ fee profile induce a long-run average amount of managed capital for each fund. I analyze Nash equilibrium in the game played by the funds, focusing on the implications of fund skill on fees, capital flows and net performance.

Labor Share, Foreign Demand and Superstar Exporters

This paper proposes a new determinant of labor share changes. Using micro-data on the universe of French manufacturing exporters over 1995-2007, I show that a measure of export demand growth exogenous to firm-level outcomes drives down the manufacturing labor share through two effects. First, foreign demand shocks allow low-labor share, highly internationalized “superstar” exporters to grow disproportionately more. Second, foreign demand growth decreases the labor share of exporters and this effect is stronger for larger exporters. Both effects explain 12% of the labor share decline over 1995-2000 and led to a 1.2 percentage point drop over 2000-2007. A simple model of endogenous competition with heterogeneous firms rationalizes the findings. A market size increase allows exporters to expand, which decreases their share of fixed labor cost in value-added, and increases competition on international markets. Fiercer competition favors superstar exporters, further decreasing their labor share through the fixed cost channel. Overall, these findings provide direct causal evidence of a “winner take most” phenomenon induced by trade globalization.

Interspecific competition between two self-fertile and one related sexual species of tadpole shrimp Triops (Branchiopoda, Notostraca) with reproductive interference, Allee effect and environmental fluctuation

Invasive alien species of tadpole shrimp Triops, originated from America, were first introduced into rice fields of Japan in the 1910s and have spread around Japan. In the 1950s, a European species of Triops also seems to have entered Japan. Originally, Japanese paddy fields had Asian Triops species as a prehistoric naturalised animal. A new invasive Triops from Western Australia has been reported in the south part of Japan, occasionally forming mixed populations. The expansion of Triops has resulted in negative ecological and potential economic impact. Longhursts revision did not contain any specimens of the richest collection in the world, i.e., Daday Collection in the Hungarian Natural History Museum. And therefore, Naganawa surveyed at least 20 times as many samples as those by Longhurst, and number the named Triops granarius s.l. species group from Africa-India to Siberia-Asia at eight species, organised in the same genus. As for the establishment or extinction patterns, based on Tilmans competition model, we built a simple mathematical competition model between two self-fertile and one related sexual species of Japan, incorporating reproductive interference. To make the mathematical model more natural, we also assumed environmental fluctuation and Allee effect, which reduces the population growth rate of sexual species with low density. Intense reproductive interference drove the competition to sexual exclusion of self-fertile species. However, even under intense reproductive interference, Allee effect allowed self-fertile species to survive when the competition started with the lower densities; contrary to the survival of sexual species when the competition started with the higher densities.