The paper explores psychological games, where players' payoffs depend not only on their actions but also on their beliefs, beliefs about others' beliefs, and so on. Unlike conventional game theory, psychological games allow for the modeling of belief-dependent emotions such as anger and surprise. The authors show that while backward induction cannot be applied and "perfect" psychological equilibria may not exist, subgame perfect and sequential equilibria always do exist. The paper introduces the concept of psychological games in both normal form and extensive form. In normal form games, players' payoffs depend on their beliefs, and the authors define a "summary form" that captures the necessary information to compute Nash equilibria. They show that psychological Nash equilibria exist under relatively modest assumptions. In extensive form games, the authors demonstrate that the failure of backward induction is due to the fact that when a node is reached, it does not capture adequately the state of the game: the node identifies a history of play, but not the players' beliefs. The authors show that psychological games always have equilibria analogous to subgame perfect equilibria and sequential equilibria, respectively. The paper presents several examples, including the Bravery Game and the Confidence Game, which illustrate the unique properties of psychological games. In the Bravery Game, players' payoffs depend on their beliefs about their opponents' beliefs, leading to multiple equilibria. In the Confidence Game, players' payoffs depend on their expectations of others' expectations, leading to different equilibria based on these expectations. The authors also discuss the existence of subgame perfect and sequential equilibria in psychological games. They show that while trembling hand perfect equilibria may not exist, subgame perfect and sequential equilibria always do. The paper concludes that psychological games provide a framework for the formal analysis of strategic settings in which expectations and emotions play a role.The paper explores psychological games, where players' payoffs depend not only on their actions but also on their beliefs, beliefs about others' beliefs, and so on. Unlike conventional game theory, psychological games allow for the modeling of belief-dependent emotions such as anger and surprise. The authors show that while backward induction cannot be applied and "perfect" psychological equilibria may not exist, subgame perfect and sequential equilibria always do exist. The paper introduces the concept of psychological games in both normal form and extensive form. In normal form games, players' payoffs depend on their beliefs, and the authors define a "summary form" that captures the necessary information to compute Nash equilibria. They show that psychological Nash equilibria exist under relatively modest assumptions. In extensive form games, the authors demonstrate that the failure of backward induction is due to the fact that when a node is reached, it does not capture adequately the state of the game: the node identifies a history of play, but not the players' beliefs. The authors show that psychological games always have equilibria analogous to subgame perfect equilibria and sequential equilibria, respectively. The paper presents several examples, including the Bravery Game and the Confidence Game, which illustrate the unique properties of psychological games. In the Bravery Game, players' payoffs depend on their beliefs about their opponents' beliefs, leading to multiple equilibria. In the Confidence Game, players' payoffs depend on their expectations of others' expectations, leading to different equilibria based on these expectations. The authors also discuss the existence of subgame perfect and sequential equilibria in psychological games. They show that while trembling hand perfect equilibria may not exist, subgame perfect and sequential equilibria always do. The paper concludes that psychological games provide a framework for the formal analysis of strategic settings in which expectations and emotions play a role.