saddle-point

Project is inspired by course by prof. Marek Szopa from University of Silesia in Katowice about Game Theory and allows finding and asserting if saddle points exists in given payoff matrix. More about saddle points you cand find here (PL): https://www.youtube.com/watch?v=NjVSltkCA0E&t=3863s

Main algorithm (to find saddle points) works as follow:

Let A be the payoff matrix.

1. Find minimal values in every row and return their indexes.
2. Transpose A and find maximal values in every row, return their indexes and reverse it.
3. Intersect sets from steps 1. and 2.

Examples

Library contains two functions.

First one has-saddle-points? allows you to assert if saddle points exists in given matrix:

(deftest has-saddle-points-returns-true-test
    (testing "If true is returned when saddle points exist"
        (def matrix [[8 -8 -1 0] [4 2 1 3] [3 -1 0 2] [6 0 -2 10]])
        (is (= (has-saddle-points? matrix) true))))

The secont one find-saddle-points allows you to find saddle points in given matrix:

(deftest find-saddle-points-test
    (testing "If saddle points are returned when exist"
        (def matrix [[8 -8 -1 0] [4 2 1 3] [3 -1 0 2] [6 0 -2 10]])
        (is (= (find-saddle-points matrix) #{'(1 2)}))))