This paper introduces a statistical model for quantal response equilibria (QRE) in normal form games. The model assumes that players choose strategies based on relative expected utility, but with random errors. A QRE is defined as a fixed point of this process, where players' strategies are determined by the probability of selecting a particular action based on expected payoffs and random errors. The model is shown to approach Nash equilibria as the error term approaches zero and to uniquely select a Nash equilibrium in generic games. For a logit specification of the error structure, the model is shown to fit experimental data well. The model is estimated using maximum likelihood methods, and the results suggest that players' estimates of expected payoffs from different actions influence the statistical predictions of the model. The model also accounts for learning effects, where players' experience with the game leads to more accurate estimates of expected payoffs and, consequently, more accurate strategy choices. The paper compares the QRE model to other equilibrium concepts in traditional game theory and establishes a formal connection between the QRE model and Bayesian equilibrium in incomplete information games. The QRE model is shown to be a natural extension of well-established statistical models of choice and is able to account for systematic deviations from Nash equilibrium in experimental data. The paper presents results from several experiments on normal form games, including the Lieberman, O'Neill, Rapoport and Boebel, and Ochs experiments. The results show that the QRE model fits the data well and provides a more accurate prediction of player behavior than the Nash model. The model also suggests that learning is taking place, as players' estimates of expected payoffs improve over time, leading to more accurate strategy choices. The paper concludes that the QRE model provides a useful framework for understanding equilibrium in normal form games, as it accounts for systematic deviations from Nash equilibrium and provides a statistical structure for estimation. The model is able to capture the learning process and the role of random errors in decision-making, making it a valuable tool for analyzing experimental data in game theory.This paper introduces a statistical model for quantal response equilibria (QRE) in normal form games. The model assumes that players choose strategies based on relative expected utility, but with random errors. A QRE is defined as a fixed point of this process, where players' strategies are determined by the probability of selecting a particular action based on expected payoffs and random errors. The model is shown to approach Nash equilibria as the error term approaches zero and to uniquely select a Nash equilibrium in generic games. For a logit specification of the error structure, the model is shown to fit experimental data well. The model is estimated using maximum likelihood methods, and the results suggest that players' estimates of expected payoffs from different actions influence the statistical predictions of the model. The model also accounts for learning effects, where players' experience with the game leads to more accurate estimates of expected payoffs and, consequently, more accurate strategy choices. The paper compares the QRE model to other equilibrium concepts in traditional game theory and establishes a formal connection between the QRE model and Bayesian equilibrium in incomplete information games. The QRE model is shown to be a natural extension of well-established statistical models of choice and is able to account for systematic deviations from Nash equilibrium in experimental data. The paper presents results from several experiments on normal form games, including the Lieberman, O'Neill, Rapoport and Boebel, and Ochs experiments. The results show that the QRE model fits the data well and provides a more accurate prediction of player behavior than the Nash model. The model also suggests that learning is taking place, as players' estimates of expected payoffs improve over time, leading to more accurate strategy choices. The paper concludes that the QRE model provides a useful framework for understanding equilibrium in normal form games, as it accounts for systematic deviations from Nash equilibrium and provides a statistical structure for estimation. The model is able to capture the learning process and the role of random errors in decision-making, making it a valuable tool for analyzing experimental data in game theory.