On Players' Models of Other Players: Theory and Experimental Evidence

On Players' Models of Other Players: Theory and Experimental Evidence

1995 | Dale O. Stahl and Paul W. Wilson
Stahl and Wilson (1994) develop and test a theory of human behavior in 3×3 symmetric games. The theory proposes five boundedly rational archetypes, distinguished by their models of other players and their ability to identify optimal choices. They conduct an experiment to detect these archetypes and estimate parameters defining them. The experimental evidence rejects the rational expectations type but confirms the boundedly rational theory. The authors argue this is a step toward a descriptive and prescriptive theory of games. The theory is based on decision theory, where players form priors about others' behavior and choose best responses given these priors. Players can differ in their priors or their ability to identify best responses. The ability to identify best responses is modeled using a discrete choice model with error, leading to a logit probability function. The precision parameter of the error identifies one member of the family of probabilistic choice functions. Level-0 types have zero precision, leading to uniform choices. Level-1 types believe others are level-0, leading to uniform priors. Level-2 types believe others are level-0 and level-1, leading to a convex combination of uniform and level-1 logit choices. The hierarchy is truncated at level-2 due to diminishing benefits and practical considerations. The authors propose a three-parameter family of boundedly rational types and a rational expectations (RE) type. The RE type has a prior based on expected choices of boundedly rational types and other RE types. The authors develop a formal theory of these types, including parameter specifications. Each type is identified by a parameter triplet, and the model generates predicted probability distributions of choices. The authors design an experiment with 12 symmetric 3×3 games to estimate parameters and test for the presence of boundedly rational types and RE types. The experiment involves 48 participants, each playing each game once with no feedback. The data allow the authors to estimate parameters and test for the presence of types. The statistical analysis confirms the boundedly rational theory but rejects the RE type. The authors compute semi-parametric Bayesian posteriors for each participant's type, finding that most have high probability of being one type. The authors present results of robustness exercises, finding that behavioral predictions and posterior type identifications are remarkably robust. The findings suggest that human behavior in games is better explained by boundedly rational types than by rational expectations. The results indicate that participants' behavior arises from one "model of other players" for all games. The authors conclude that the boundedly rational theory provides a descriptive and prescriptive framework for understanding human behavior in games.Stahl and Wilson (1994) develop and test a theory of human behavior in 3×3 symmetric games. The theory proposes five boundedly rational archetypes, distinguished by their models of other players and their ability to identify optimal choices. They conduct an experiment to detect these archetypes and estimate parameters defining them. The experimental evidence rejects the rational expectations type but confirms the boundedly rational theory. The authors argue this is a step toward a descriptive and prescriptive theory of games. The theory is based on decision theory, where players form priors about others' behavior and choose best responses given these priors. Players can differ in their priors or their ability to identify best responses. The ability to identify best responses is modeled using a discrete choice model with error, leading to a logit probability function. The precision parameter of the error identifies one member of the family of probabilistic choice functions. Level-0 types have zero precision, leading to uniform choices. Level-1 types believe others are level-0, leading to uniform priors. Level-2 types believe others are level-0 and level-1, leading to a convex combination of uniform and level-1 logit choices. The hierarchy is truncated at level-2 due to diminishing benefits and practical considerations. The authors propose a three-parameter family of boundedly rational types and a rational expectations (RE) type. The RE type has a prior based on expected choices of boundedly rational types and other RE types. The authors develop a formal theory of these types, including parameter specifications. Each type is identified by a parameter triplet, and the model generates predicted probability distributions of choices. The authors design an experiment with 12 symmetric 3×3 games to estimate parameters and test for the presence of boundedly rational types and RE types. The experiment involves 48 participants, each playing each game once with no feedback. The data allow the authors to estimate parameters and test for the presence of types. The statistical analysis confirms the boundedly rational theory but rejects the RE type. The authors compute semi-parametric Bayesian posteriors for each participant's type, finding that most have high probability of being one type. The authors present results of robustness exercises, finding that behavioral predictions and posterior type identifications are remarkably robust. The findings suggest that human behavior in games is better explained by boundedly rational types than by rational expectations. The results indicate that participants' behavior arises from one "model of other players" for all games. The authors conclude that the boundedly rational theory provides a descriptive and prescriptive framework for understanding human behavior in games.
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