This paper introduces the concept of Quantal Response Equilibrium (QRE) in normal form games, where players choose strategies based on relative expected utility and assume others do the same. QRE is defined as a fixed point of this process and is shown to exist. For a logit specification of the error structure, QRE approaches a subset of Nash equilibria as the error variance goes to zero, and it implies a unique selection from the set of Nash equilibria in generic games. The model is fitted to experimental data using maximum likelihood estimation. The paper also explores the relationship between QRE and traditional game theory concepts, demonstrating an equivalence between QRE and Bayesian equilibrium in an incomplete information version of the game. Additionally, it investigates the learning effects in QRE, showing that the precision of players' estimates of expected payoffs increases with experience. The findings suggest that QRE can account for systematic deviations from Nash equilibrium in experimental data, providing a statistical framework for understanding strategic behavior in games.This paper introduces the concept of Quantal Response Equilibrium (QRE) in normal form games, where players choose strategies based on relative expected utility and assume others do the same. QRE is defined as a fixed point of this process and is shown to exist. For a logit specification of the error structure, QRE approaches a subset of Nash equilibria as the error variance goes to zero, and it implies a unique selection from the set of Nash equilibria in generic games. The model is fitted to experimental data using maximum likelihood estimation. The paper also explores the relationship between QRE and traditional game theory concepts, demonstrating an equivalence between QRE and Bayesian equilibrium in an incomplete information version of the game. Additionally, it investigates the learning effects in QRE, showing that the precision of players' estimates of expected payoffs increases with experience. The findings suggest that QRE can account for systematic deviations from Nash equilibrium in experimental data, providing a statistical framework for understanding strategic behavior in games.