Comparing theories of one-shot play out of treatment

The collective wisdom of behavioral game theory

“…The first data set, reported by Stahl and Wilson (1995), consists of the strategy choices of 48 subjects who each played a set of 12 3×3 symmetric games, including three games with unique mixed-strategy Nash equilibria and nine games with unique pure-strategy symmetric equilibria, some (but not all) of which being dominance solvable. The second data set, reported by Külpmann and Kuzmics (2022), consists of the strategy choices of 147 subjects who each played a set of 20 2 × 2 games of the hawk-dove and matching-pennies forms. The third data set, also reported by Külpmann and Kuzmics (2022), consists of the strategy choices of 166 subjects who each played a set of 20 3 × 3 games, half of them of a hawk-dove variety with an additional strategy available and half of them of a rock-paper-scissors variety.…”

“…The second data set, reported by Külpmann and Kuzmics (2022), consists of the strategy choices of 147 subjects who each played a set of 20 2 × 2 games of the hawk-dove and matching-pennies forms. The third data set, also reported by Külpmann and Kuzmics (2022), consists of the strategy choices of 166 subjects who each played a set of 20 3 × 3 games, half of them of a hawk-dove variety with an additional strategy available and half of them of a rock-paper-scissors variety. 3 In each dataset we know each individual subject's choice in each game, so we can fit the models at the individual-subject level.…”

“…The weights (or lack thereof) on these models cannot be viewed in isolation. In both Külpmann and Kuzmics (2022) datasets the level-k reasoning model and the cognitive hierarchy model always make the same predictions, so they share weight equally; but in the Stahl and Wilson (1995) there. If the cognitive hierarchy model and the noisy level-k model were omitted from the analysis, then the pure level-k model would get positive weight for this dataset as well.…”

Revisiting the Asymmetric Matching Pennies Contradiction in China

“…Belot et al [ 21 ] find that in matching pennies games, subjects who can observe their opponents gestures have a tendency to automatically imitate their opponents’ action. Brocas and Carrillo [ 22 ] had children and adolescents play a hide-and-seek game and found that most participants favor the high-value location, even though only the seeker in theory can maximize payoffs in this way Külpmann and Kuzmics [ 23 ] propose a new method to compare theories under mixed-strategy predictions. They find that although Nash equilibrium with risk aversion is among the best predictors, it cannot correctly predict the behavior of the own-payoff-seeking player in asymmetric matching pennies and rock–scissors–paper games.…”