In this article, I exploit a new station-level, twelve-hourly price dataset to examine the strong retail price cycles in the Toronto gasoline market. The cycles are visually similar to the theoretical Edgeworth Cycles of Maskin & Tirole [1988]: strongly asymmetric, tall, rapid, and highly synchronous across stations. I test a series of predictions made by the theory about how firm behaviors would differentially evolve over the path of a cycle. The evidence is consistent with the existence of Edgeworth Cycles and inconsistent with competing hypotheses. One finding is that smaller firms are more likely than larger firms to initiate rounds of price undercutting but the reverse is true for rounds of price increases. While the cycles are an interesting phenomenon for study in their own right, the evidence has important implications for understanding market power in both cycling and non-cycling gasoline markets.

/pdf/edgeworth-price-cycles-evidence-from-the-toronto-retail-4ydu5k2ery.pdf

Edgeworth Price Cycles: Evidence from the Toronto Retail Gasoline Market - eScholarship

Systems of differential equations

An extension of the results of hirsch on systems of differential equations which are competitive or cooperative

For a class of flows on polytopes, including many examples from evolutionary game theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertices and edges. This piecewise linear flow is easy to compute, even in higher dimensions, allowing the usage of numeric algorithms to detect robust invariant dynamical structures such as periodic, homoclinic and heteroclinic orbits. We apply this method to prove the existence of chaotic behaviour in some Hamiltonian replicator systems on the five dimensional simplex.

https://iopscience.iop.org/article/10.1088/1361-6544/ab49e6/pdf

Asymptotic Poincaré maps along the edges of polytopes

In this paper we address a class of replicator dynamics, referred as polymatrix replicators,
that contains well known classes of evolutionary game dynamics, such as
the symmetric and asymmetric (or bimatrix) replicator equations, and some replicator equations for $n$-person games. Polymatrix replicators form a simple class of
algebraic o.d.e.'s on prisms (products of simplexes), which describe the evolution of strategical behaviours within a population stratified in $p\geq 1$ social groups.
 &nbsp
In the 80's Raymond Redheffer et al. developed a theory on the class of stably dissipative Lotka-Volterra systems.
This theory is built around a reduction algorithm that ``infers'' the localization of the system' s attractor in some affine subspace.
It was later proven that the dynamics on the attractor of such systems is always embeddable in a Hamiltonian Lotka-Volterra system.
 &nbsp
In this paper we extend these results to polymatrix replicators.

Conservative and Dissipative Polymatrix Replicators

Rank of stably dissipative graphs

In this paper we address a class of replicator dynamics, referred as polymatrix replicators, that contains well known classes of evolutionary game dynamics, such as the symmetric and asymmetric (or bimatrix) replicator equations, and some replicator equations for $n$-person games. Polymatrix replicators form a simple class of algebraic o.d.e.'s on prisms (products of simplexes), which describe the evolution of strategical behaviours within a po\-pu\-lation stratified in $n\geq 1$ social groups. 
In the 80's Raymond Redheffer et al. developed a theory on the class of stably dissipative Lotka-Volterra systems. This theory is built around a reduction algorithm that "infers" the localization of the system' s attractor in some affine subspace. It was later proven that the dynamics on the attractor of such systems is always embeddable in a Hamiltonian Lotka-Volterra system. 
In this paper we extend these results to polymatrix replicators.

Lotka-Volterra systems were introduced in the 1920s by Lotka and Volterra independently of one another when they began to publish studies on systems of differential equations in areas of chemistry and interaction of populations, respectively. These systems are generally classified into three groups: competitive (or cooperative) systems, conservative systems and dissipative systems. Within the class of dissipative systems can be considered the stably dissipative systems, which are characterized by being dissipative systems that maintain their properties even when disturbed. The present work focuses mainly on dissipative systems, namely in the study of properties and examples of stably dissipative systems. We attempt to explore an algorithm developed in 1980 by Redheffer et al. acting in the graph of the interaction matrix system. Finally we discuss some ideas related to the dynamics of such systems and present some examples. Key-words: Lotka-Volterra system, differential equation, dynamical system, conservative system, dissipative system, stably dissipative system, attractor.

/pdf/sistemas-lotka-volterra-dissipativos-3fpp8h3kvh.pdf

Telmo Peixe

Papers

Asymptotic Poincaré maps along the edges of polytopes

Rank of stably dissipative graphs

Conservative and Dissipative Polymatrix Replicators

Conservative and Dissipative Polymatrix Replicators

Sistemas Lotka-Volterra dissipativos