When Prisoners Enter Battle: Natural Connections in 2x2 Symmetric Games Public Deposited
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Recently, game theory has gained much interest from many mathematicians as well as economists and psychologists. The simplest and most popular games studied in this field are the 2 X 2 games, which involve two players with two different choices each; each player makes his or her decision individually, but his or her choice will affect the outcome for both that player as well as for the other player. Within these 2 X 2 games, each player has his or her own preference in terms of what outcomes are best for them; for each of the four possible outcomes in these 2 X 2 games, each player also receives a certain payoff, which could be a good or bad payoff. If both players have the same ordering of outcomes, then the game is called symmetric, meaning if the players were switched, the outcomes would be in the same order as initially. In this paper, I show the results I found while researching the connections between these symmetric 2 X 2 games. The twelve total symmetric 2 X 2 games can be shown on a 2D x-y axis; these games can be separated into six different sectors. In each section, the games involved can be manipulated, when transitioning to another game with different payoff preferences, to one common game. When one game is changed to another by simply swapping two of the payoffs, a transition game in between these games appears; by doing a simple operation to these transition games, I was able to find one universal game in each sector. This proves that these are more closely related than mathematicians previously believed. If one has an interest in game theory, wants to learn about an interesting topic in mathematics, or just wants to see what one can do with the power of mathematics, one can read all about the 2 X 2 symmetric games in When Prisoners Enter Battle: Natural Connections in 2 X 2 Symmetric Games.