# lgsolve: Equilibrium locations of location game In locationgamer: Identification of Location Game Equilibria in Networks

## Description

Function finds the equilibrium locations of a location game, similar to a hotelling game. Clients choose the location closest to them.

## Usage

 `1` ```lgsolve(edgeMatrix, coordMatrix, nPlayers = 2, demandLoc) ```

## Arguments

 `edgeMatrix` A square matrix consisting of zeros and ones. Has to be zero on the diagonals `coordMatrix` A data frame containing the x and y coordinates of each network vertex `nPlayers` Number of players in the location game. Default is set to 2, which is the only number of players supported right now. `demandLoc` A vector containing the demand or profit at each vertex of the network

## Value

A list with two components. A matrix with zeros and ones, where a one symbolizes a equilibrium location. The row index denotes the location of player 1, and the column index the location chosen by player 2. The second entry is a summary of all equilibrium locations and the payoffs for player 1 and 2.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```edgeMatrix <- matrix(0, nrow = 6, ncol = 6) edgeMatrix[,1] <- c(0,1,0,0,0,0) edgeMatrix[,2] <- c(1,0,1,0,1,0) edgeMatrix[,3] <- c(0,1,0,0,0,0) edgeMatrix[,4] <- c(0,0,0,0,1,0) edgeMatrix[,5] <- c(0,1,0,1,0,1) edgeMatrix[,6] <- c(0,0,0,0,1,0) coordMatrix <- matrix(c(0,3,0,2,0,1,1,3,1,2,1,1), nrow = 6, ncol = 2, byrow = TRUE) demandLoc <- c(100, 100, 100, 100, 100, 100) lgsolve(edgeMatrix, coordMatrix, 2, demandLoc) ```

locationgamer documentation built on Dec. 18, 2020, 5:08 p.m.