The paper by Faruk Gul and Wolfgang Pesendorfer explores a two-period model where individuals face the temptation of choosing inferior options in the second period. The authors introduce the concepts of commitment and self-control, defining these as preferences over sets of alternatives. They develop axioms that characterize the individual's commitment ranking, temptation ranking, and the cost of self-control. The main findings include: 1. **Representation Theorems**: The authors derive representation theorems that identify the individual's preferences over sets of alternatives in terms of utility functions \( u \) and \( v \). The function \( U(A) \) represents the individual's preferences, where \( U(A) = \max_{x \in A} u(x) + v(x) - \max_{y \in A} v(y) \). 2. **Set Betweenness Axiom**: This axiom captures the idea that the presence of additional options can affect an individual's utility, leading to a preference for commitment. It states that if \( A \succeq B \), then \( A \cup B \) is "between" \( A \) and \( B \). 3. **Self-Control**: An individual has self-control if they resist temptation and choose an option with higher ex ante utility. The cost of self-control is determined by the relative magnitudes of \( u \) and \( v \). 4. **Temptation Without Self-Control**: The authors also consider the case where self-control is prohibitively costly, leading to preferences that maximize the temptation ranking \( v \) while evaluating choices using \( u \). 5. **Comparative Measures**: The paper introduces measures to compare preferences for commitment and self-control. A preference relation has greater preference for commitment than another if it benefits from commitment more often. 6. **Application to Decision-Making**: The authors apply their theoretical framework to analyze real-world decision-making scenarios, such as choosing lunch options, to illustrate the concepts of commitment and self-control. The paper provides a comprehensive framework for understanding how individuals make choices in the presence of temptation and the role of self-control in these decisions.The paper by Faruk Gul and Wolfgang Pesendorfer explores a two-period model where individuals face the temptation of choosing inferior options in the second period. The authors introduce the concepts of commitment and self-control, defining these as preferences over sets of alternatives. They develop axioms that characterize the individual's commitment ranking, temptation ranking, and the cost of self-control. The main findings include: 1. **Representation Theorems**: The authors derive representation theorems that identify the individual's preferences over sets of alternatives in terms of utility functions \( u \) and \( v \). The function \( U(A) \) represents the individual's preferences, where \( U(A) = \max_{x \in A} u(x) + v(x) - \max_{y \in A} v(y) \). 2. **Set Betweenness Axiom**: This axiom captures the idea that the presence of additional options can affect an individual's utility, leading to a preference for commitment. It states that if \( A \succeq B \), then \( A \cup B \) is "between" \( A \) and \( B \). 3. **Self-Control**: An individual has self-control if they resist temptation and choose an option with higher ex ante utility. The cost of self-control is determined by the relative magnitudes of \( u \) and \( v \). 4. **Temptation Without Self-Control**: The authors also consider the case where self-control is prohibitively costly, leading to preferences that maximize the temptation ranking \( v \) while evaluating choices using \( u \). 5. **Comparative Measures**: The paper introduces measures to compare preferences for commitment and self-control. A preference relation has greater preference for commitment than another if it benefits from commitment more often. 6. **Application to Decision-Making**: The authors apply their theoretical framework to analyze real-world decision-making scenarios, such as choosing lunch options, to illustrate the concepts of commitment and self-control. The paper provides a comprehensive framework for understanding how individuals make choices in the presence of temptation and the role of self-control in these decisions.