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Introduction to Game Theory (Part 1)
Two-player Sequential games — Dominant Strategies, Nash Equilibrium, and Cooperation vs. Defection
Game theory generally refers to the study of mathematical models that describe the behavior of logical decision-makers. It is widely used in many fields such as economics, political science, politics, and computer science, and can be used to model many real-world scenarios. Generally, a game refers to a situation involving a set of players who each have a set of possible choices, in which the outcome for any individual player depends partially on the choices made by other players.
Simultaneous Games
One of the main types of games in game theory is the simultaneous game, in which both players make their moves simultaneously (or if they do not, the later player is unaware of the earlier player’s action, making it effectively simultaneous). Sequential games are often represented in normal form, which, for a game with 2 players and N possible moves for each player, consists of an N x N matrix where each entry is a 2-tuple containing the payoff for each respective player.
To illustrate this, consider the below example. This is a type of sequential game called the Prisoner’s Dilemma, in which each prisoner has the option to either betray…