Endogenous Barriers to Learning

Motivated by the idea that lack of experience is a source of errors but that experience should reduce them, we model agents' behavior using a stochastic choice model, leaving endogenous the accuracy of their choice. In some games, increased accuracy is conducive to unstable best-response dynamics. We define the barrier to learning as the minimum level of noise which keeps the best-response dynamic stable. Using logit Quantal Response, this defines a limitQR Equilibrium. We apply the concept to centipede, travelers' dilemma, and 11-20 money-request games and to first-price and all-pay auctions, and discuss the role of strategy restrictions in reducing or amplifying barriers to learning.Comment: 26 pages, 15 figure

"Test two, choose the better" leads to high cooperation in the Centipede game

Explaining cooperative experimental evidence in the Centipede game constitutes a challenge for rational game theory. Traditional analyses of Centipede based on backward induction predict uncooperative behavior. Furthermore, analyses based on learning or adaptation under the assumption that those strategies that are more successful in a population tend to spread at a higher rate usually make the same prediction. In this paper we consider an adaptation model in which agents in a finite population do adopt those strategies that turn out to be most successful, according to their own experience. However, this behavior leads to an equilibrium with high levels of cooperation and whose qualitative features are consistent with experimental evidence.Financial support from the Spanish State Research Agency (PID2020-118906GB-I00 / AEI / 10.13039/501100011033), from “Junta de Castilla y León - Consejería de Educación” through BDNS 425389, from the Spanish Ministry of Science, Innovation and Universities (PRX18-00182, PRX19/00113), and from the Fulbright Program (PRX19/00113), is gratefully acknowledged

IMPLEMENTATION, ELIMINATION OF WEAKLY DOMINATED STRATEGIES AND EVOLUTIONARY DYNAMICS

This paper studies convergence and stability properties of Sjöström's (1994) mechanism, under the assumption that boundedly rational players find their way to equilibrium using monotonic learning dynamics and best-reply dynamics. This mechanism implements most social choice functions in economic environments using as a solution concept one round of deletion of weakly dominated strategies and one round of deletion of strictly dominated strategies. However, there are other sets of Nash equilibria, whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics, all these sets of equilibria contain limit points of the learning dynamics. Furthermore, even if the dynamics converge to the "right" set of equilibria (i.e. the one which contains the solution of the mechanism), it may converge to an equilibrium which is worse in welfare terms. In contrast with this result, any interior solution of the best-reply dynamics converges to the equilibrium whose outcome the planner desires.Implementation Theory, Evolutionary Dynamics

Best experienced payoff dynamics and cooperation in the centipede game

We study population game dynamics under which each revising agent tests each of his strategies a fixed number of times, with each play of each strategy being against a newly drawn opponent, and chooses the strategy whose total payoff was highest. In the centipede game, these best experienced payoff dynamics lead to cooperative play. When strategies are tested once, play at the almost globally stable state is concentrated on the last few nodes of the game, with the proportions of agents playing each strategy being largely independent of the length of the game. Testing strategies many times leads to cyclical play.U.S. National Science Foundation (Grants SES-1458992 and SES- 1728853), the U.S. Army Research Office (Grants W911NF-17-1-0134 MSN201957), Project ECO2017-83147- C2-2-P (MINECO/AEI/FEDER, UE), and the Spanish Ministerio de Educación, Cultura, y Deporte (Grants PRX15/00362 and PRX16/00048

A Behavioral Approach to Learning in Economics - Towards an Economic Theory of Contingent Learning

In economics, adjustment of behavior has traditionally been treated as a "black box." Recent approaches that focus on learning behavior try to model, test, and simulate specific adjustment mechanisms in specific environments (mostly in games). Results often critically depend on distinctive assumptions, and are not easy to generalize. This paper proposes a different approach that aims to allow for more general conclusions in a methodologically more compatible way. It is argued that the introduction of the main determinants of learning behavior as situational restrictions into the standard economic model may be a fruitful way to capture some important aspects of human behavior that have often been omitted in economic theory. Based on a simple model of learning behavior (learning loop), robust findings from psychology are used to explain behavior adjustment, and to identify its determinants (contingent learning). An integrative methodology is proposed where the "black box" is not opened, but instead the factors that determine what happens inside, and the limits imposed by theses factors can be analyzed and used for model building. The paper concludes with testable hypotheses about learning behavior in the context of economics.microeconomics, game theory, learning theory, experiments

Transparency, Efficiency and the Distribution of Economic Welfare in Pass-Through Investment Trust Games

We design an experiment to examine welfare and behavior in a multi-level trust game representing a pass through investment in an intermediated market. In a repeated game, an Investor invests via an Intermediary who lends to a Borrower. A pre-experiment one-shot version of the game serves as a baseline and to type each subject. We alter the transparency of exchanges between non-adjacent parties. We find transparency of the exchanges between the investor and intermediary does not significantly affect welfare. However, transparency regarding exchanges between the intermediary and borrower promotes trust on the part of the investor, increasing welfare. Further, this has asymmetric effects: borrowers and intermediaries achieve greater welfare benefits than investors. We discuss implications for what specific aspects of financial market transparency may facilitate more efficiency.financial intermediation, financial market transparency, pass through securities, multi-level trust games, experiments

Co-operation in the finitely repeated prisoner’s dilemma

More than half a century after the first experiment on the finitely repeated prisoner’s dilemma, evidence on whether cooperation decreases with experience–as suggested by backward induction–remains inconclusive. This paper provides a meta-analysis of prior experimental research and reports the results of a new experiment to elucidate how cooperation varies with the environment in this canonical game. We describe forces that affect initial play (formation of cooperation) and unraveling (breakdown of cooperation). First, contrary to the backward induction prediction, the parameters of the repeated game have a significant effect on initial cooperation. We identify how these parameters impact the value of cooperation–as captured by the size of the basin of attraction of Always Defect–to account for an important part of this effect. Second, despite these initial differences, the evolution of behavior is consistent with the unraveling logic of backward induction for all parameter combinations. Importantly, despite the seemingly contradictory results across studies, this paper establishes a systematic pattern of behavior: subjects converge to use threshold strategies that conditionally cooperate until a threshold round; and conditional on establishing cooperation, the first defection round moves earlier with experience. Simulation results generated from a learning model estimated at the subject level provide insights into the long-term dynamics and the forces that slow down the unraveling of cooperation