In 1954, O.G. Haywood used game theory to analyze the military decisions used in the Battle of the Bismarck Sea, a battle fought during the World War II. Haywood analyzed the Battle of the Bismarck Sea by using a two-person zero-sum game [1]. This paper discusses the fundamental concepts of the two-person zero-sum game and some Nash Equilibrium dominance ideas as well as the strategies applied ...

W present a diagrammatic method that allows the determination of all Nash equilibria of 2×M nonzero sum games, extending thus the well known diagrammatic techniques for 2 × M zero sum and 2 × 2 nonzero sum games. We show its appropriateness for teaching purposes by analyzing modified versions of the prisoners’ dilemma, the battle of the sexes, as well as of the zero sum game of matching pennies...

There are two complementary approaches to playing sums of combinatorial games. They can be characterized as local analysis and global search. Algorithms from combinatorial game theory such as Hotstrat and Thermostrat [2] exploit summary information about each subgame such as its temperature or its thermograph. These algorithms can achieve good play, with a bounded error. Their runtime depends m...

In this section, we will first prove that any 2-player zero-sum finite game has a Nash equilibrium of mixed strategies (a special case of Nash’s theorem), and a Nash equilibrium can be found through solving linear programs. We will further show how to prove lower bounds on randomized complexity of Las Vegas algorithms using this result. A 2-player game is a zero-sum game if the sum of the payof...