Subject-specific performance information can worsen the tragedy of the commons: Experimental evidence

Abstract

The main aim of this article is to investigate the behavioral consequences of the provision of subject-specific information in the group effort levels chosen by players in an experimental CPR game. We examine two basic treatments, one with incomplete information and the other with complete information. In the former, subjects are informed only about their own individual payoffs and the aggregate extraction effort level of the group, and in the latter they are also informed about the individual effort levels and payoffs of each subject. Given this setting, the basic question we attempt to answer is: Will the provision of subject-specific performance information (i.e. individual’s effort levels and payoffs) improve or worsen the tragedy of the commons (i.e. an exploitation effort level greater than the socially optimum level)? In order to motivate our hypotheses and explain our experimental results at the individual level, we make use of the theory of learning in games, which goes beyond standard non-cooperative game theory, allowing us to explore the three basic benchmarks in the commons context: Nash equilibrium, Pareto efficient, and open access outcomes. We use several learning and imitation theoretical models that are based on contrasting assumptions about the level of rationality and the information available to subjects, namely: best response, imitate the average, mix of best response and imitate the average, imitate the best and follow the exemplary learning rules. Finally, in order to econometrically test the hypotheses formulated from the theoretical predictions we use a random-effects model to assess the explanatory power of the different selected behavioral learning and imitation rules.

Introduction

The standard economic theory on common property resource (henceforth CPR) exploitation predicts a non-cooperative result in the commons implying the economic overexploitation of the resource. In a non-cooperative game theoretic context, this implies that the Nash equilibrium (henceforth NE) of the CPR game is inefficient, entailing an exploitation effort level greater than the Pareto efficient (henceforth PE), i.e. where marginal revenue equals marginal cost.¹ This economic prediction about CPR use has been empirically tested in practice with field studies and experimental works recreating the commons setting.²

In particular, the experimental literature on the commons has received increasing attention from social scientists in the last two decades.³ Some laboratory experiments have been mainly designed to investigate whether experimental results conform to the economic predictions on CPR exploitation. These studies have concluded that at the aggregate level behavior does approximate the NE level, being therefore consistent with the basic non-cooperative game theoretic prediction (Ostrom et al., 1994, Walker et al., 1990: 209). Some studies have also examined what happens with this basic result when face-to-face communication is allowed, by having, at some point, an open group discussion before each round of the experiment. These works have shown that repeated face-to-face communication can be extremely successful in increasing group returns as well as subjects’ overall performance (Cardenas, 2000, Cardenas, 2003, Ostrom and Walker, 1991, Ostrom et al., 1994, Sally, 1995). In addition to allowing cheap talk, some works have also investigated the impact of sanctioning in CPR experiments by giving subjects the opportunity to pay a fee in order to impose a fine on the payoffs received by another player (Casari and Plott, 2003, Ostrom et al., 1992, Ostrom et al., 1994). These studies have found that in contrast to what economic theory predicts (no costly sanctioning in a finitely repeated game), players do sanction, reacting both to the cost of sanctioning and to the fee-to-fine relationships, and that in general a sanctioning system greatly improves the efficiency of resource use. Finally, some papers have also assessed the willingness and ability of subjects to look for and adopt different institutional arrangements designed to improve social outcomes in a CPR setting (Cardenas et al., 2000, Rodriguez-Sickert et al., 2008, Walker et al., 2000). These papers point the importance of collective choice, showing that giving participants the opportunity of proposing allocation rules can significantly increase efficiency and that the imposition of external regulatory rules, including external enforcement, can imply a poorer performance in terms of group returns, as it can crowd out group regarding behavior in favor of greater self interest.

Specifically, this paper relates to a recent experimental work by Apesteguia (2006), who analyses the impact of information on players’ decisions regarding the exploitation of a commonly shared resource, asking the question: Does information matter in the commons? In that article the author specially investigates the effects of the provision of information about the payoff structure in the context of a CPR game. He runs two treatments, one with complete information on the payoff structure and the other with none, the main result of the paper being that aggregate behavior is not significantly different between the two treatments. In both cases the aggregate effort levels converge to the NE.

In this work we want to add to the experimental literature on the commons by building upon and complementing the work of Apesteguia. Particularly, we examine the behavioral consequences of the provision of subject-specific information on the aggregate effort levels chosen by players in an experimental CPR game. As did Apesteguia (2006), we consider two basic scenarios, one with incomplete information, henceforth treatment ‘incomplete’, and another with complete information, henceforth treatment ‘complete’. In the former, subjects are informed only about their own individual payoffs and the aggregate extraction effort level of the group, while in the latter they are also informed about the individual effort levels and payoffs of each subject. Given this setting, the basic question we attempt to answer is: Will the provision of subject-specific performance information (i.e. individuals’ effort levels and payoffs) improve or worsen the tragedy of the commons (i.e. an exploitation effort level greater than the socially optimum level)?

Our paper adds to and complements Apesteguia’s and previous experimental works on the commons in several respects. First, although the provision of information regarding the payoff structure is quite relevant in the commons, the information about subject-specific performance, such as other individuals’ effort levels and payoffs, is also crucial in the decision-making process frequently faced in the commons, adding a different perspective to the problem. Indeed, additional information about other players’ actions and profits adds a potential strategic and psychological component to the analysis, which may well change Apesteguia’s basic result in terms of whether or not information matters in the commons. In fact, while the results of Apesteguia’s work show that aggregate behavior is not significantly different between the two treatments, converging in both cases to the NE effort level, we postulate as a main hypothesis of our paper that in treatment ‘incomplete’ the average aggregate use level will match the NE outcome, but in treatment ‘complete’ the average group effort level will be significantly higher than the NE. In other words, we expect to prove that more information in the commons can make a difference in terms of aggregate results.

Second, in order to motivate our hypotheses and explain our experimental results at the individual level, we make use of the theory of learning in games (see, e.g., Fudenberg & Levine, 1999), which goes beyond standard game theory, allowing us to explore three basic benchmarks in the commons context: NE, PE and Open Access (henceforth OA) outcomes. The rationality behind using learning and imitation models to motivate these benchmarks is that decision costs may imply that although agents have the required information to, for instance, derive best response strategies, they prefer not doing so because it is too costly. In fact, it can be assumed that agents try to find strategies, such as imitation rules, that save on cognitive effort and decision costs (Offerman, Potters, & Sonnemans, 2002). In particular, unlike Apesteguia (2006), who considers mainly best response dynamics to explain individual behavior in both treatments, we use several learning and imitation theoretical models, which are based on contrasting assumptions about the level of rationality and the information available to subjects, namely: ‘best response’, ‘imitate the average’, mix of ‘best response’ and ‘imitate the average’, ‘imitate the best’ and ‘follow the exemplary’ learning rules.⁴

Given the informational requirements of these rules, in treatment ‘incomplete’ agents could not apply ‘imitate the best’ or ‘follow the exemplary’, thus we would expect that in this treatment players use ‘best response’ or ‘imitate the average’ rules, or a mix of both. As we will show, the mix of ‘best response’ and ‘imitate the average’ leads towards an aggregate effort level converging globally to the NE of the constituent CPR game. Furthermore, since the cognitive efforts to apply ‘best response’ are relatively higher than those needed to apply ‘imitate the average’, we would also expect that the latter is employed more frequently than the former on average.

In treatment ‘complete’, players can also apply ‘best response’ and ‘imitate the average’ rules, or the mix of both, and besides, since subject-specific performance information from all subjects is now provided, players can also use ‘imitate the best’ and ‘follow the exemplary’. Hence, for this treatment we could expect that players can be influenced to some extent by the experience of others when deciding their effort levels. As shown by Vega-Redondo, 1997, Alós-Ferrer and Ania, 2005, if all subjects follow ‘imitate the best’, the unique stochastically stable state of the process is the OA outcome of the constituent CPR game, and, as proved by Offerman et al. (2002) if all subjects use the ‘follow the exemplary’ rule, the unique stochastically stable state of the process is the PE outcome of the constituent CPR game. Moreover, the ‘imitate the best’ rule can be used at minimal decision costs in comparison to ‘follow the exemplary’, since subjects receive the information processed in such a way that the comparison of payoffs across agents and the identification of the associated use level are straightforward. Hence, we would expect that the former is employed more frequently than the latter on average.

Finally, in order to econometrically test the hypotheses formulated from the theoretical predictions we use a random-effects model (see, e.g., Skrondal & Rabe-Hesketh, 2004), to assess the explanatory power of the different selected behavioral learning and imitation rules. One of the main reasons to use this technique is that each subject repeatedly interacts with the same group of players throughout the experiment, and therefore, in principle, we need to control within-subject dependence in effort decisions that may be introduced by unobserved between-subject heterogeneity. A random-effects model for analyzing subjects’ effort adjustment decisions is further justified given that the target of inference is the population of players and the interest is in analyzing potential subject heterogeneity in the employment of the learning and imitation rules.

The paper is structured as follows: Section 2 describes the experimental environment and the theoretical predictions are introduced in Section 3. In Section 4, we set forward the hypotheses of the work, and Section 5 presents the experimental results. Finally, a summary of conclusions is put forward.