Game Theory
This paper will explore game theory in the branch combinatorial games through a broad view through the aid of the game Pick-Up-Bricks and game trees, and introduce the MEX Principle by analysing the game Nim.
Abstract
Combinatorial games, a branch of game theory, allows us to further understand the topic of decision making and uses simple games to work out different strategies that result in various outcomes. It introduces rational thinking where a player makes decisions based on the outcomes it will bring them. This method of thinking can be applied to larger fields such as economics and finance for parties to maximize their own income. In this paper, we will explore game theory in the branch combinatorial games through a broad view. This will be done through the aid of the game Pick-Up-Bricks and game trees. We will then take a deeper look into a category of combinatorial games, Normal-Play Games. To understand how they work, we will look at the example of Cut-cake. We will continue on to talk about the four different types of games, sum of games, and the properties of positions in normal play games. Afterwards, we will discuss impartial games and introduce the MEX Principle by analysing the game Nim. Lastly, we will apply the MEX Principle to the game of Shade.