Comparing Behavioral Models Using Data From Experimental Centipede Games

Abstract

The centipede game posits one of the most well‐known paradoxes of backward induction in the literature of experimental game theory. Given that deviations from the unique subgame perfect Nash equilibrium generates a Pareto improvement, several theoretical models have been employed in order to rationalize this kind of behavior in this social dilemma. The available explanations range from social preferences including fairness, altruism or cooperation motives, errors in playing, inability to perform backward induction or different depths of reasoning. In the present study, we use the Blavatskyy's theoretical contribution, and relax the assumptions of Expected Utility maximization and risk‐neutral attitudes, to test an alternative explanation. We compare various probabilistic decision theory models in terms of their descriptive (in‐sample) and predictive (out‐of‐sample fit) performance, using data from experimental centipede games. We find that introducing non‐Expected Utility preferences to the Quantal Response Equilibrium model, along with a nonlinear utility function, provides a better explanation compared to alternative specifications such as the Level‐k or the Quantal Response Equilibrium model with altruistic motives. (JEL C72, C92, D81, D82)

Belief and higher‐order belief in the centipede games: An experimental investigation

“…The author estimates the variance of uncertainties about players' payoff types, which could fit all qualitative features of the existing experimental results. Georgalos (2019) compares several parametric models and finds that, combining a non‐expected utility model with the quantal response equilibrium provides a better prediction of subjects' behaviour than the cognitive hierarchy models or the altruistic preference model of McKelvey and Palfrey (1992).…”

Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making

“…However, this is a poor predictor of what happens experimentally (Ho and Su, 2013), where players are shown to "grow" the money pile by playing for several rounds before taking (Ke, 2019). Again, there are multiple reasons proposed to explain players deviation from the predicted unique (subgame) Nash equilibrium, ranging from playing errors, cooperation, altruism or various reasoning depths (Georgalos, 2020). For example, when the length of the game is known, increasing game length lead to higher cooperation levels, whereas unknown lengths lead to less cooperation (Krockow et al, 2018).…”