An Extension of Two Species Lotka-Volterra Competition Model

Limiting resource is a angular stone of the interactions between species in ecosystems such as competition, prey-predators and food chain systems. In this paper, we propose a planar system as an extension of Lotka-Voterra competition model. This describes? two competitive species for a single resource? which are affected by intra and inter-specific interference. We give its complete analysis for the existence and local stability of all equlibria and some conditions of global stability. The model exhibits a rich set of behaviors with a multiplicity of coexistence equilibria, bi-stability, tri-stability and occurrence of global stability of the exclusion of one species and the coexistence? equilibrium. The asymptotic behavior and the number of coexistence equilibria are shown by a saddle-node bifurcation of the level of resource under conditions on competitive effects relatively to associated growth rate per unit of resource.Moreover, we determine the competition outcome in the situations of Balanced and Unbalanced intra-inter species competition effects. Finally, we illustrate results by numerical simulations.

Content and Access Provision in a Discrete Competition Model

The non-rival, non-excludable and infinitely expansible characteristics of digital goods with marginal cost of zero strongly favours the use of bundling strategies. Theoretical tractability requires most models in the current literature to make highly stylized assumptions, rarely observed or anticipated in the real-life situations, motivating inquiry. This paper considers a competition model in which: * the firms, consumers and differentiated products are finite in number; * prices are discrete and not continuous; * consumers may purchase multiple items in a single product category where the degree of complementarity or substitutability of the product categories can also vary across consumers; and * where consumer-specific cost savings are obtained when purchasing multiple items from the same firm. Approximate solutions are obtained through numerical simulation. Firms act in concert to maximise the total firm revenue. Our main finding is that the interplay between maximal firm revenue, consumer surplus and prices is very complex and that high firm revenue and high consumer surplus are not antithetic. It suggests also that consumer surplus and market concentration are not necessarily related. Many market outcomes that are observed may be due to chance rather than design as diverse outcomes can accompany situations that are, to the firms, difficult to distinguish.

Traveling waves and spreading properties for a reaction-diffusion competition model with seasonal succession*

In this paper, we investigate the propagation dynamics of a reaction–diffusion competition model with seasonal succession in the whole space. Under the weak competition condition, the corresponding kinetic system admits a globally stable positive periodic solution ( u ^ ( t ) , v ^ ( t ) ) . By the method of upper and lower solutions and the Schauder fixed point theorem, we first obtain the existence and nonexistence of traveling wave solutions connecting (0, 0) to ( u ^ ( t ) , v ^ ( t ) ) . Then we use the comparison arguments to establish the spreading properties for a large class of solutions.

Exchange Competition, Entry, and Welfare

We assess the consequences for market quality and welfare of different entry regimes and exchange pricing policies. To do so, we integrate a microstructure model with a free-entry, exchange competition model where exchanges have market power in technological services. Free-entry delivers superior liquidity and welfare outcomes vis-`a-vis an unregulated monopoly, but entry can be excessive or insufficient. Depending on the extent of the monopolist's technological services undersupply compared to the first best, a planner can achieve a higher welfare controlling entry or platform fees.