Fast or fair? A study of response times

This paper uses a modified dictator game to investigate the relationship between response times and social preferences. We find that faster subjects more often chose the option with the highest payoff for themselves. Moreover, our within-analysis reveals that, for a given individual, payoff maximizing choices are reached quicker than choices expressing social preferences.     

Nonparametric learning rules from bandit experiments: The eyes have it!

How do people learn? We assess, in a model-free manner, subjectsʼ belief dynamics in a two-armed bandit learning experiment. A novel feature of our approach is to supplement the choice and reward data with subjectsʼ eye movements during the experiment to pin down estimates of subjectsʼ beliefs. Estimates show that subjects are more reluctant to “update down” following unsuccessful choices, than “update up” following successful choices. The profits from following the estimated learning and decision rules are smaller (by about 25% of average earnings by subjects in this experiment) than what would be obtained from a fully-rational Bayesian learning model, but comparable to the profits from alternative non-Bayesian learning models, including reinforcement learning and a simple “win-stay” choice heuristic.     

Competition and coordination in experimental minority games

This work presents experimental results on a coordination game in which agents must repeatedly choose between two sides, and a positive fixed payoff is assigned only to agents who pick the minoritarian side. We conduct laboratory experiments in which stationary groups of five players play the game for 100 periods, and manipulate two treatment variables: the amount of information about other players’ past choices and the salience of information regarding the game history (i.e., the length of the string of past outcomes that players can see on the screen while choosing). Our main findings can be summarized as follows: aggregate efficiency in the game is in most cases significantly higher than the level corresponding to the symmetric mixed strategy Nash equilibrium. In addition, providing players with information about individual choices in the group does not improve aggregate efficiency with respect to when such information is absent. Displaying information about more rounds than just the previous one, on the other hand, seems to have a positive effect on aggregate efficiency. At the individual level, we find a stronger statistical relation between players’ current choices and their own past choices than between players’ choices and previous aggregate outcomes. In addition, the depth of the relation between present and past choices seems to be affected by the prompt availability of information about the game history. Finally, we detect evidence of a mutual co-adaptation between players’ choices over time that is partly responsible for the high level of efficiency observed.      

The control of game form recognition in experiments: understanding dominant strategy failures in a simple two person “guessing” game

This paper focuses on instructions and procedures as the reasons that subjects fail to behave according to the predictions of game theory in two-person “guessing game” (beauty contest game) experiments. In this game, two individuals simultaneously choose a number between 0 and 100. The winner is the person whose chosen number is the closest to 2/3 of the average of the two numbers. The weakly dominant strategy is zero. Because of the simplicity of the game, the widespread failure of subjects to choose the weakly dominant strategy has been interpreted as evidence of some fundamental inability to behave strategically. By contrast, we find that subjects’ behavior reflects a lack of understanding of the game form, which we define as the relationships between possible choices, outcomes and payoffs. To a surprising degree, subjects seem to have little understanding of the experimental environment in which they are participating. If subjects do not understand the game form, the experimental control needed for testing game theory is lost. The experiments reported here demonstrate that the failure to act strategically is related to how the game is presented. We test how well subjects are able to recognize the game under a variety of different presentations of the game. Some subjects fail to recognize the game form when it is presented abstractly. When the game is transformed into a simple isomorphic game and presented in a familiar context, subjects do choose weakly dominant strategies. While our results confirm the ability of subjects to make strategic decisions, they also emphasize the need to understand the limitations of experimental subjects’ ability to grasp the game as the experimenter intends. Given these limitations, we provide suggestions for better experimental control.     

Lab and framed lab versus natural experiments: Evidence from a risky choice experiment

Some recent papers have studied data from TV game shows to examine the behaviour of individuals towards risk. It is generally agreed that data from these shows are useful in detecting individual risk aversion in the field, with both “real life” subjects and incentives. Field experiments also include some interesting reality features that could affect individuals’ behaviour and possibly lead to different findings. This paper aims at investigating lab versus field evidence in risk taking attitudes, especially controlling for framing effects. To assess whether the behaviour of subjects in the field is consistent with that of experimental subjects, we designed an experiment to mimic (with experimental rewards and subjects) the rules of a well-known Italian TV game show, Affari Tuoi, in two different settings: a traditional lab setting, where the game was played individually (109 subjects) (Treatment 1); and a framed lab, in which the experiment was replicated in the Italian public television (RAI) studio where the show was actually recorded, with a smaller sample of undergraduate students (33) and in the presence of an audience (Treatment 2). Our comparison between the two different settings aims at establishing whether the presence of an audience, or of a situation that reproduces the stress that contestants must experience in the TV studio, can affect experimental subjects’ choices. We did not find any significant evidence of framing effects: students behave in a similar way in the two lab settings, responding essentially to incentives. Comparing the risk attitudes shown by experimental subjects in the two lab treatments with those exhibited by the contestants in the field, we found that contestants in the TV show are generally more risk averse than students in the lab.     

Conditional cooperation in a sequential move game

Cooperation is a pervasive social phenomenon, but more often than not economic theories have little to say about its causes and consequences. In this paper, we explore the hypothesis that cooperative behaviour might be motivated by pure self-interest when the “social” payoff in a game is increasing. We report the results of a series of experiments on the Centipede game. The experiments are organised in two subsequent steps. Subjects first participate in a 2-period trust game, randomly matched with unknown partners. We apply the strategy method in order to elicit their social preferences. On the basis of their pre-game behaviour, individuals are divided into three main social groups: selfish individuals, pure altruists and reciprocators. At the second step of the experiment, subjects play a repeated 6-move Centipede game with an increasing final payoff. Each subject plays twice, in a low and in a high-stake Centipede game, and he/she is informed about his/her co-player social preferences. We provide statistical evidence to identify the origin of cooperation within homogeneous and heterogeneous social groups. We construct a Poisson regression model to assess the determinants of the duration of conditional cooperation in the Centipede.     

Experimental study of cursed equilibrium in a signaling game

The laboratory experiment described in this paper provides evidence on play in signaling games in the context of electoral competition. In this game, voters must infer the preferred policy of each candidate from the candidate’s choice of whether to announce (truthfully) his preferred policy or to take no position. Bayesian voters would put high probability on a candidate having an extreme policy preference after observing him take no position, but cursed voters would not fully appreciate the informational content of the decision to take no position. Stated beliefs reveal substantial uncertainty about other players’ strategies. Based on estimates of a structural model of cursed equilibrium allowing for heterogeneity in the degree of cursedness, 32% of choices between candidates are consistent with Bayesian updating, 32% imply no inferences about others’ types after observing their actions, and the remainder indicate partial updating. Though the experiment also includes treatments with subjects in both roles, these estimates are based on interactions with programmed candidates, implying that uncertainty about others’ rationality and strategic sophistication is not driving the result. We also find that the quantal response error structure in which errors depend on payoff differences cannot explain the pattern of errors that subjects make.     

Toward a “constitution” for behavioral policy-making

Behavioral policy interventions aimed at redirecting individuals’ behavior toward optimal choices are characterized by an important issue which is often overlooked: the lack of an instrument to define what “optimal” means. If agents are subject to behavioral biases leading them to make “wrong” choices, the policy-maker can no longer rely on the revealed preferences approach (e.g., what people choose is what people prefer) for defining a welfare criterion. In this article, we reiterate the argument put forward by some scholars that choosing a suitable welfare criterion once the link between observed choices and individuals’ preferences is broken becomes a problematic task. We review the state of the art in the literature and the possible approaches proposed to overcome the problem, concluding that a solution has not yet been reached. Moreover, we argue that the lack of an established welfare criterion characterizing behavioral policy-making could pave the way to government wanting to restrict individual freedom. In the absence of any legislative constraint for the executive, stating that what individuals choose is not what they prefer in principle justifies any freedom-reducing government intervention, since choices can be arbitrarily labeled “sub-optimal” or “welfare-reducing.” To avoid this risk without turning down the potential of behavioral policy-making, we propose that an independent committee establishes ex ante procedural rules and domains where behavioral policy-making can be implemented. The article suggests some possible examples of normative provisions characterizing this constitution-type document, such as the selective identification of the only sectors where behavioral policies could be effectively applied, the periodic evaluation of policy effects, and the use of sunset clauses.     

Social norms and trust among strangers

We study the development of a social norm of trust and reciprocity among a group of strangers via the “contagious strategy” as defined in Kandori (1992). Over an infinite horizon, the players anonymously and randomly meet each other and play a binary trust game. In order to provide the investors with proper incentives to follow the contagious strategy, there is a sufficient condition that requires that there exists an outside option for the investors. Moreover, the investorsʼ payoff from the outside option must converge to the payoff from trust and reciprocity as the group size goes to infinity. We show that this sufficient condition is also a necessary condition to sustain any sequential equilibrium in which the trustees adopt the contagious strategy. Our results imply that a contagious equilibrium only supports trust if trust contributes almost nothing to the investorsʼ payoffs.     

PREFERENCES UNDER IGNORANCE

A decision maker (DM) makes choices from different sets of alternatives. The DM is initially ignorant of the payoff associated with each alternative and learns these payoffs only after a large number of choices have been made. We show that, in the presence of an outside option, once payoffs are learned, the optimal choice rule from sets of alternatives can be rationalized by a DM with strict preferences over all alternatives. Under this model, the DM has preferences for preferences while being ignorant of what preferences are “right.”     

Technology adoption in markets with network effects: Theory and experimental evidence

We examine a technology-adoption game with network effects in which coordination on either technology A or technology B constitutes a Nash equilibrium. Coordination on technology B is assumed to be payoff dominant. We define a technology’s critical mass as the minimal share of users, which is necessary to make the choice of this technology the best response for any remaining user. We show that the technology with the lower critical mass implies risk dominance and selection by the maximin criterion. We present experimental evidence that both payoff dominance and risk dominance explain participants’ choices in the technology-adoption game. The relative riskiness of a technology can be proxied using either technologies’ critical masses or stand-alone values absent any network effects.     

A model of boundedly rational “neuro” agents

We consider a model in which each agent in a population chooses one of two options. Each agent does not know what the available options are and can choose an option only after observing another agent who has already chosen that option. In addition, the agents’ preferences over the two options are correlated. An agent can either imitate an observed agent or wait until he meets two agents who made different choices, in which case he can compare their choices and choose accordingly. A novel feature of the model is that agents observe not only the choices made by others, but also some information about the process that led them to those choices. We study two cases: In the first, an agent notes whether the observed agent imitated others or whether he actually compared the available alternatives. In the second, an agent notes whether the observed agent’s decision was hasty or not. It is shown that in equilibrium the probability of making a mistake is higher in the second case and that the existence of these nonstandard “neuro” observations systematically biases the equilibrium distribution of choices.     

On choosing which game to play when ignorant of the rules

This paper suggests a theory of choice among strategic situations when the rules of play are not properly specified. We take the view that a “strategic situation” is adequately described by a TU game since it specifies what is feasible for each coalition but is silent on the procedures that are used to allocate the surplus. We model the choice problem facing a decision maker (DM) as having to choose from finitely many “actions”. The known “consequence” of the ith action is a coalition from game f _i over a fixed set of players \(N_i\cup\{d\}\) (where d stands for the DM). Axioms are imposed on her choice as the list of consequences (f ₁,..., f _m ) from the m actions varies. We characterize choice rules that are based on marginal contributions of the DM in general and on the Shapley Value in particular.     

Unobserved heterogeneity and equilibrium: an experimental study of Bayesian and adaptive learning in normal form games

We describe an experiment based on a simple two-person game designed so that different learning models make different predictions. Econometric analysis of the experimental data reveals clear heterogeneity in the subjects’ learning behavior. But the subjects follow only a few decision rules for basing their play on their information, and these rules have simple cognitive interpretations. There is a unique equilibrium in pure strategies, and many equilibria in mixed strategies. We find that the only equilibrium consistent with the data is one of the mixed strategy equilibria. This equilibrium is shown, surprisingly, to be consistent with Jordan's Bayesian model.     

Who knows it is a game? On strategic awareness and cognitive ability

We examine strategic awareness in experimental games, that is, the question of whether subjects realize they are playing a game and thus have to form beliefs about others’ actions. We conduct a beauty contest game and elicit measures of cognitive ability and beliefs about others’ cognitive ability. We show that the effect of cognitive ability is highly non-linear. Subjects below a certain threshold choose numbers in the whole interval and their behavior does not correlate with beliefs about others’ ability. In contrast, subjects who exceed the threshold avoid choices above 50 and react very sensitively to beliefs about the cognitive ability of others.     

The minority game unpacked:

We conduct an experiment on a minority-of-three game in which each player is a team composed of three subjects. Each team can freely discuss its strategies in the game and decisions must be made via majority rule. Team discussions are recorded and their content analyzed to detect evidence of strategy co-evolution among teams playing together. Our main results show no evidence supporting the mixed strategy Nash equilibrium solution, and provide evidence more consistent with reinforcement learning models than with belief-based models. Exhibiting level-2 rationality (i.e., reasoning about others’ beliefs) is positively and significantly correlated with higher than average earnings in the game. In addition, teams that are more successful tend to become more self-centered over time, paying more attention to their own past successes than to the behavior of other teams. Finally, we find evidence of mutual adaptation over time, as teams that are more strategic induce competing teams to be more self-centered instead. Our results contribute to the understanding of coordination dynamics resting on heterogeneity and co-evolution of decision rules. In addition, they provide support at the decision process level to the validity of modeling behavior using reinforcement learning models.     

How sensitive are bargaining outcomes to changes in disagreement payoffs?

We use a human-subjects experiment to investigate how bargaining outcomes are affected by changes in bargainers’ disagreement payoffs. Subjects bargain against changing opponents, with randomly drawn asymmetric disagreement outcomes that vary over plays of the game, and with complete information about disagreement payoffs and the cake size. We find that subjects only respond about half as much as theoretically predicted to changes in their own disagreement payoff and to changes in their opponent’s disagreement payoff. This effect is observed in a standard Nash demand game and a related unstructured bargaining game, in both early and late rounds, and is robust to moderate changes in stake sizes. We show theoretically that standard models of expected utility maximisation are unable to account for this under-responsiveness, even when generalised to allow for risk aversion. We also show that quantal-response equilibrium has, at best, mixed success in characterising our results. However, a simple model of other-regarding preferences can explain our main results.     

Learning to collude: An experiment in convergence and equilibrium selection in oligopoly

The paper considers a simple oligopoly model where firms know their own and the average pay-off in the industry. Firms choose decision rules for trading. The theory predicts that there are three types of Nash equilibria in this game (collusive, Cournot and Stackelberg). Our experiments test the selection process. We find that there is clear evidence of convergence to an equilibrium, and whilst both Cournot and collusive outcomes were selected, the collusive equilibrium is more common. The experimental results also give insights into the process of individual learning, confirming that subjects follow aspiration rules rather than reinforcement rules.     

When less information is good enough: experiments with global stag hunt games

There is mixed evidence on whether subjects coordinate on the efficient equilibrium in experimental stag hunt games under complete information. A design that generates an anomalously high level of coordination, Rankin et al. (Games Econo Behav 32(2):315–337, 2000), varies payoffs each period in repeated play rather than holding them constant. These payoff “perturbations” are eerily similar to those used to motivate the theory of global games, except the theory operates under incomplete information. Interestingly, that equilibrium selection concept is known to coincide with risk dominance, rather than payoff dominance. Thus, in theory, a small change in experimental design should produce a different equilibrium outcome. We examine this prediction in two treatments. In one, we use public signals to match Rankin et al. (2000)’s design; in the other, we use private signals to match the canonical example of global games theory. We find little difference between treatments, in both cases, subject play approaches payoff dominance. Our literature review reveals this result may have more to do with the idiosyncrasies of our complete information framework than the superiority of payoff dominance as an equilibrium selection principle.     

Endogenous Move Structure and Voluntary Provision of Public Goods: Theory and Experiment

In this paper, we examine voluntary contributions to a public good, embedding Varian's (1994) voluntary contribution game in extended games that allow players to choose the timing of their contributions. We show that predicted outcomes are sensitive to the structure of the extended game, and also to the extent to which players care about payoff inequalities. We then report a laboratory experiment based on these extended games. We find that behavior is similar in the two extended games: subjects avoid the detrimental move order of Varian's model, where a person with a high value of the public good commits to a low contribution, and instead players tend to delay contributions. These results suggest that commitment opportunities may be less damaging to public good provision than previously thought.