Horiztonal and Vertical Lines

Often in game theory, we wish to add vertical or horizontal lines to our graphics, for example, when we find the players’ security levels.

## Do not change this cell, only execute it. 
## This cell initializes Python so that pandas, numpy and scipy packages are ready to use.

%matplotlib inline
import matplotlib.pyplot as plots
plots.style.use('fivethirtyeight')
import numpy as np
import scipy as sp
from scipy.optimize import linprog

Vertical Lines

The function we use to create vertical lines is in the matplotlib package which have imported above as plots. The correct function title is shown below:

plots.axvline()

The correct function call is shown first with its options shown below:

plots.axvline(x=1, color='blue', linestyle='--', label='x = 1')

• With \(x=1\), we place the vertical line through the desired point on the \(x\)-axis.

• We can specify the color as needed.

• With linestyle, we can specify a dashed line.

Horizontal Lines

The function plots.axhline() works in exactly the same way to create a horizontal line.

Putting it All Together

The command cell below includes the XY-axis and graphing window options from the previous section. You should note that we have added a title to the graph, labels for the \(x\)-axis and \(y\)-axis, and a legend.

# Create the plot with overall size specified
plots.figure(figsize=(5, 5))
plots.xlim(-0.5, 3)
plots.ylim(-0.5, 3)
plots.axhline(0, color='black', linewidth=1)
plots.axvline(0, color='black', linewidth=1)

# Draw a dotted vertical line at x = 2
plots.axvline(x=2, color='blue', linestyle='--', label='x = 2')

# Adding labels and a grid for clarity
plots.xlabel('Row Player')
plots.ylabel('Column Player')
plots.title('XY-Axis with Vertical Line x=2')
plots.grid(True, linestyle=':', alpha=0.6)
plots.legend()

plots.show()