Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

Using the Logit quantal response form as the response function in each step, the original definition of static quantal response equilibrium (QRE) is extended into an iterative evolution process. QREs remain as the fixed points of the dynamic process. However, depending on whether such fixed points are the long-term solutions of the dynamic process, they can be classified into stable (SQREs) and unstable (USQREs) equilibriums. This extension resembles the extension from static Nash equilibriums (NEs) to evolutionary stable solutions in the framework of evolutionary game theory. The relation between SQREs and other solution concepts of games, including NEs and QREs, is discussed. Using experimental data from other published papers, we perform a preliminary comparison between SQREs, NEs, QREs and the observed behavioral outcomes of those experiments. For certain games, we determine that SQREs have better predictive power than QREs and NEs

How do people play against Nash opponents in games which have a mixed strategy equilibrium?

We examine experimentally how humans behave when they, unbeknownst to them, play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects’ play was consistent with their Nash equilibrium strategy. But a larger percentage of subjects’ play was more consistent with different models of play: equiprobable play for the zero-sum game, and the minimax strategy in the non-profitable game

Learning about Learning in Games through Experimental Control of Strategic Interdependence

We report experiments in which humans repeatedly play one of two games against a computer program that follows either a reinforcement learning or an Experience Weighted Attraction algorithm. Our experiments show these learning algorithms detect exploitable opportunities more sensitively than humans. Also, learning algorithms respond to detected payoff-increasing opportunities systematically; however, the responses are too weak to improve the algorithms’ payoffs. Human play against various decision maker types doesn’t vary significantly. These factors lead to a strong linear relationship between the humans’ and algorithms’ action choice proportions that is suggestive of the algorithm’s best response correspondence. These properties are revealed only by our human versus com

Man versus Nash An experiment on the self-enforcing nature of mixed strategy equilibrium

We examine experimentally how humans behave when they play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects’ play was consistent with their Nash equilibrium strategy, while a larger percentage of subjects’ play was more consistent with different models of play: equiprobable play for the zero-sum game, and the minimax strategy in the unprofitable game. We estimate the heterogeneity and dynamics of the subjects’ latent mixed strategy sequences via a hidden Markov model. This provides clear results on the identification of the use of pure and mixed strategies and the limiting distribution over strategies. The mixed strategy Nash equilibrium is not self-enforcing except when it coincides with the equal probability mixed strategy, and there is surprising amounts of pure strategy play and clear cycling between the pure strategy states

A hidden Markov model for the detection of pure and mixed strategy play in games

We propose a statistical model to assess whether individuals strategically use mixed strategies in repeated games. We formulate a hidden Markov model in which the latent state space contains both pure and mixed strategies, and allows switching between these states. We apply the model to data from an experiment in which human subjects repeatedly play a normal form game against a computer that always follows its part of the unique mixed strategy Nash equilibrium profile. Estimated results show significant mixed strategy play and non-stationary dynamics. We also explore the ability of the model to forecast action choice.   JEL classiffication: C92; C72; C10

Man Versus Nash: An Experiment on the Self-enforcing Nature of Mixed Strategy Equilibrium

We examine experimentally how humans behave when they play against a computer which implements its part of a mixed strategy Nash equilibrium. We consider two games, one zero-sum and another unprofitable with a pure minimax strategy. A minority of subjects' play was consistent with their Nash equilibrium strategy, while a larger percentage of subjects' play was more consistent with different models of play: equiprobable play for the zero-sum game, and the minimax strategy in the unprofitable game. We estimate the heterogeneity and dynamics of the subjects' latent mixed strategy sequences via a hidden Markov model. This provides clear results on the identification of the use of pure and mixed strategies and the limiting distribution over strategies. The mixed strategy Nash equilibrium is not self-enforcing except when it coincides with the equal probability mixed strategy, and there is surprising amounts of pure strategy play and clear cycling between the pure strategy states

Three essays on behavioral game theory

176 p.Esta tesis presenta tres estudios sobre teoría de juegos del comportamiento, estudiando las desviaciones del comportamiento racional, utilizando técnicas experimentales y econométricas.El primer capítulo estudia el comportamiento en el juego del ciempiés, juego con gran interés y tradición en economía. Para ello tiene en cuenta múltiples modelos de comportamiento y gracias a un novedoso diseño intenta discernir cuál es el más relevante a la hora de explicar y predecir el comportamiento. El estudio concluye que mayoritariamente el comportamiento es explicado por el fallo del conocimiento común de la racionalidad, y que además no hay uno si no varios modelos que explican distintas proporciones de la población, lo cual explica la literatura.El segundo capítulo evalúa la capacidad predictiva de exitosos modelos de comportamiento basados en evitar el arrepentimiento. Los compara de forma teórica y en la literatura con otro modelo exitoso basado en el fallo del conocimiento común de la racionalidad, y concluye este último es el que explica mejor comportamiento atribuido originalmente a los modelos basados en arrepentimiento.El tercer capítulo compara el comportamiento en el juego del ciempiés jugando de forma simultanea o secuencial. Las diferencias se dan o no dependiendo de las características particulares del juego