Spatial competition on 2-dimensional markets and networks when consumers don’t always go to the closest firm

Cahan, Dodge; Chen, Hongjia H.; Christie, Louis; Slinko, Arkadii

doi:10.1007/s00182-021-00776-y

Cited by 2 publications

(2 citation statements)

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“…γ k is the adaptive step size obtained by the application of the Barzilai-Borwein method. γ 0 is set to 0.1, while the other adaptive values are defined in Equation (15). Although the Barzilai-Borwein adaptive step size was developed and used for gradient descent/ascent methods, it is shown numerically that the adaptive step size performs well for the current optimization problem and significantly increases the convergence rate.…”

Section: Iterative Procedures For Nash Equilibrium Solutionsmentioning

confidence: 99%

“…Cahan at al. [15] considered a two-dimensional space competition where firms compete by location, and introduced a probability vector that assigns to the consumers a probability that they will buy from firms other than the nearest one. The authors showed that Nash equilibrium exists in the central region of the marked bounded by hyperbolas computed analytically.…”

Section: Introductionmentioning

confidence: 99%

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Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior

Stoykov

Kostov

2023

Games

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A numerical procedure capable of obtaining the equilibrium states of oligopoly markets under several assumptions is presented. Horizontal and vertical product differentiation were included by taking into account Euclidean distance in a two-dimensional space and quality characteristics of the product. Different quality preferences of consumers were included in the model. Firms implement two strategies in the market: profit maximization and market share maximization. Numerical discretization of a two-dimensional area was performed for computing the equilibrium prices which allows one to consider any market area and any location of the firms. Four scenarios of oligopoly markets were developed by combining both strategies from one side and competitive behavior and a partial cartel agreement from another side. The main differences between the scenarios are outlined. Profits, market shares and equilibrium prices are presented and compared. The influence of collusion, the existence of participants with a market share maximization strategy and consumer preferences on the firm’s profits and equilibrium prices were examined. Cases whereby firms prefer to leave the cartel were investigated. Best locations for the setting of a new store for profit maximization are shown and discussed.

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Section: Iterative Procedures For Nash Equilibrium Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%