This paper provides an introduction to game theory for economists and social scientists, focusing on fundamental concepts rather than surveying all major results. It begins with a review of decision theory, emphasizing the importance of subjective probability and utility in rational decision-making. The paper then introduces game theory as the study of mathematical models of conflict and cooperation between intelligent, rational decision-makers. It discusses various models of games, including dynamic models and strategic form games, and explains how to analyze these models to predict player behavior. The paper delves into Nash equilibria, explaining that a Nash equilibrium is a set of strategies where no player can benefit by unilaterally changing their strategy. It also explores refinements of the Nash equilibrium concept, such as sequential equilibria, which consider the rationality of players' actions in all information states, including those with probability zero. These refinements aim to identify more reasonable equilibria that are stable under small perturbations of the game. Additionally, the paper discusses extensions of the equilibrium set, including the use of joint contracts, repetition, and communication. Joint contracts allow players to commit to specific actions, repetition can enforce correlated strategies through punishment, and communication can enable players to coordinate on better outcomes without binding contracts. The paper concludes by highlighting the importance of game theory in understanding and predicting behavior in economic and social contexts.This paper provides an introduction to game theory for economists and social scientists, focusing on fundamental concepts rather than surveying all major results. It begins with a review of decision theory, emphasizing the importance of subjective probability and utility in rational decision-making. The paper then introduces game theory as the study of mathematical models of conflict and cooperation between intelligent, rational decision-makers. It discusses various models of games, including dynamic models and strategic form games, and explains how to analyze these models to predict player behavior. The paper delves into Nash equilibria, explaining that a Nash equilibrium is a set of strategies where no player can benefit by unilaterally changing their strategy. It also explores refinements of the Nash equilibrium concept, such as sequential equilibria, which consider the rationality of players' actions in all information states, including those with probability zero. These refinements aim to identify more reasonable equilibria that are stable under small perturbations of the game. Additionally, the paper discusses extensions of the equilibrium set, including the use of joint contracts, repetition, and communication. Joint contracts allow players to commit to specific actions, repetition can enforce correlated strategies through punishment, and communication can enable players to coordinate on better outcomes without binding contracts. The paper concludes by highlighting the importance of game theory in understanding and predicting behavior in economic and social contexts.