Exploring Games

It is fun to play games, but with their eyes on issues of studying patterns in whatever environment a pattern may appear, mathematicians, notably John Nash (1928‑2015) and Lloyd Shapley (1923‑2016), have explored the world of games from a mathematical perspective. We will take a brief look at some research investigations that can be explored at a variety of grade levels involving games that are played using entries in a 2 X 2 matrix or array (Figure 1). I will use examples to show you the basics about playing matrix games of “perfect information." Luck plays no “direct” part in playing such games. The players know the rules and payoffs before they begin play, and the rules and payoffs don’t change as the game is played. I will also discuss ways to classify games as to whether they are fair or not, and if they are not fair, what to “do.” In these games, players want to “play” in the best way they can even if their opponent has an "advantage" that is built into the game itself.