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Full-Text Articles in Physical Sciences and Mathematics
Evolutionary Dynamics Of Bertrand Duopoly, Julian Killingback, Timothy Killingback
Evolutionary Dynamics Of Bertrand Duopoly, Julian Killingback, Timothy Killingback
Computer Science Department Faculty Publication Series
Duopolies are one of the simplest economic situations where interactions between firms determine market behavior. The standard model of a price-setting duopoly is the Bertrand model, which has the unique solution that both firms set their prices equal to their costs-a paradoxical result where both firms obtain zero profit, which is generally not observed in real market duopolies. Here we propose a new game theory model for a price-setting duopoly, which we show resolves the paradoxical behavior of the Bertrand model and provides a consistent general model for duopolies.
Generalized Catalan Numbers From Hypergraphs, Paul E. Gunnells
Generalized Catalan Numbers From Hypergraphs, Paul E. Gunnells
Mathematics and Statistics Department Faculty Publication Series
The Catalan numbers Cn ∈ {1,1,2,5,14,42,…} form one of the most venerable sequences in combinatorics. They have many combinatorial interpretations, from counting bracketings of products in non-associative algebra to counting plane trees and noncrossing set partitions. They also arise in the GUE matrix model as the leading coefficient of certain polynomials, a connection closely related to the plane trees and noncrossing set partitions interpretations. In this paper we defi ne a generalization of the Catalan numbers. In fact we defi ne an infinite collection of generalizations Cn(m) , m >= 1, with m = 1 giving the …