Cooperation in an Overlapping Generations Experiment

Recent theoretical work shows that folk theorems can be developed for infinite overlapping generations games. Cooperation in such games can be sustained as a Nash equilibrium. But, of course, there are other equilibria. This paper investigates experimentally whether cooperation actually occurs in a simple overlapping generations game. Subjects both play the game and formulate strategies. Our main finding is that subjects fail to exploit the intertemporal structure of the game. Even when we provided subjects with a recommendation to play the grim trigger strategy, most of the subjects still employed safe history-independent strategies. Journal of Economic Literature Classification Numbers: C72, C92, D90.     

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.     

Existence of equilibria in countable games: An algebraic approach

Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Waldʼs pick-the-larger-integer game. Several authors have provided conditions for the existence of equilibria in infinite games. These conditions are typically of topological nature and are rarely applicable to countable games. Here we establish an existence result for the equilibrium of countable games when the strategy sets are a countable group, the payoffs are functions of the group operation, and mixed strategies are not requested to be σ-additive. As a byproduct we show that if finitely additive mixed strategies are allowed, then Waldʼs game admits an equilibrium. Finally we extend the main results to uncountable games.     

Mental processes and strategic equilibration: An fMRI study of selling strategies in second price auctions

This study is the first to attempt to isolate a relationship between cognitive activity and equilibration to a Nash Equilibrium. Subjects, while undergoing fMRI scans of brain activity, participated in second price auctions against a single competitor following predetermined strategy that was unknown to the subject. For this auction there is a unique strategy that will maximize the subjects’ earnings, which is also a Nash equilibrium of the associated game theoretic model of the auction. As is the case with all games, the bidding strategies of subjects participating in second price auctions most often do not reflect the equilibrium bidding strategy at first but with experience, typically exhibit a process of equilibration, or convergence toward the equilibrium. This research is focused on the process of convergence.In the data reported here subjects participated in sixteen auctions, after which all subjects were told the strategy that will maximize their revenues, the theoretical equilibrium. Following that announcement, sixteen more auctions were performed. The question posed by the research concerns the mental activity that might accompany equilibration as it is observed in the bidding behavior. Does brain activation differ between being equilibrated and non-equilibrated in the sense of a bidding strategy? If so, are their differences in the location of activation during and after equilibration? We found significant activation in the frontal pole especially in Brodmann’s area 10, the anterior cingulate cortex, the amygdala and the basal forebrain. There was significantly more activation in the basal forebrain and the anterior cingulate cortex during the first sixteen auctions than in the second sixteen. The activity in the amygdala shifted from the right side to the left after the solution was given.     

Strategic complexity in repeated extensive games

This paper studies a machine (finite automaton) playing a two-player repeated game of a simple extensive-form game with perfect information. We introduce a new complexity measure called multiple complexity which incorporates a strategyʼs responsiveness to information in the stage game as well as the number of states of the machine. We completely characterize the Nash equilibrium of the machine game. In the sequential-move prisonerʼs dilemma, cooperation can be sustained as an equilibrium.     

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.     

Representing equilibrium aggregates in aggregate games with applications to common agency

An aggregate game is a normal-form game with the property that each playerʼs payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without requiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self-generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggregates of the original n-player game. We illustrate the value of this approach in common-agency games where the playersʼ strategy space is an infinite-dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral hazard versions of these games.     

Do cheaters in the lab also cheat in the field?

In this paper, we study the correlation between cheating in the lab and cheating in the field. We conduct a laboratory experiment using a variant of the Mind game (Jiang, 2013). Payoffs above a certain threshold are indicative of cheating behavior. Subjects are paid their earnings by bank transfer. A fraction of the subjects is deliberately paid more than their earnings. We send subjects a reminder e-mail stating their earnings and asking them if they have received their payment. We find a significant correlation of 0.31 between cheating in the lab and in the field. Subjects with higher payoffs in the Mind game are also less likely to report the overpayment. Our results speak to the lab-field generalizability of cheating behavior.     

Information sharing between vertical hierarchies

When do principals independently choose to share the information obtained from their privately informed agents? Information sharing affects contracting within competing organizations and induces agentsʼ strategies to be correlated through the distortions imposed by principals to obtain information. We show that the incentives to share information depend on the nature of upstream externalities between principals and the correlation of agentsʼ information. With small externalities, principals share information when externalities and correlation have opposite signs, and do not share information when externalities and correlation have the same sign. In this second case, principals face a prisonersʼ dilemma since they obtain higher profits by sharing information.     

Trade Liberalization and Cartel Stability

Can reduced trade barriers promote a collusive understanding about not exporting into each others domestic markets? Reduced trade costs increase the short‐run gains from starting exporting, but can also make the long‐run punishment of such a strategy harsher. If collusion on prices is supported by a trigger strategy, a reduction in trade costs weakens competition in the sense that collusion is easier to sustain. In a corresponding model with collusion on quantities, this conclusion is reversed. The authors also discuss how results change if grim trigger strategies are replaced by stick‐and‐carrot punishments.     

Career length: Effects of curvature of earnings profiles,earnings shocks,taxes, and social security

The same high labor supply elasticity that characterizes a representative family model with indivisible labor and employment lotteries also emerges without lotteries when self-insuring individuals choose interior solutions for their career lengths. Off corners, the more elastic is an earnings profile to accumulated working time, the longer is a workerʼs career. Negative (positive) unanticipated earnings shocks reduce (increase) the career length of a worker holding positive assets, while the effects are the opposite for a worker with negative assets. By inducing a worker to retire at an official retirement age, government provided social security can attenuate responses of career lengths to earnings profile slopes, earnings shocks, and taxes.     

Individual characteristics and behavior in repeated games: an experimental study

Using a laboratory experiment, we investigate whether a variety of behaviors in repeated games are related to an array of individual characteristics that are popular in economics: risk attitude, time preference, trust, trustworthiness, altruism, strategic skills in one-shot matrix games, compliance with first-order stochastic dominance, ability to plan ahead, and gender. We do find some systematic relationships. A subject’s compliance with first-order stochastic dominance as well as, possibly, patience, gender, and altruism have some systematic effects on her behavior in repeated games. At the level of a pair of subjects who are playing a repeated game, each subject’s gender as well as, possibly, patience and ability to choose an available dominant strategy in a one-shot matrix game systematically affect the frequency of the cooperate–cooperate outcome. However, overall, the number of systematic relationships is surprisingly small.     

Resuscitating businessman risk: A rationale for familiarity-based portfolios

This paper studies two frequently observed portfolio behaviors that are seemingly inconsistent with rational portfolio choice. The first is the tendency of workers and entrepreneurs to hold their companyʼs stock. The second is the propensity of workers to limit their equity holdings through time. The explanation offered here for both of these behaviors lies in the option to switch jobs when oneʼs company does poorly. This is equivalent to holding put options on oneʼs own company stock and call options on the other companyʼs stock, where both options must be exercised at the same time. Given these initial undiversified implicit financial holdings, workers need to allocate a relatively large share of their regular financial assets to their own companyʼs stock and a relatively small share to the stock of their alternative employment simply to restore overall portfolio balance. Although this effect can only create some hedging demand for companyʼs stock, it is a factor of potentially major import for assessing the suitability of workersʼ financial decisions. I find that, under certain conditions, workers optimally hold almost 40% of their financial wealth in their companyʼs stock.     

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.     

Bargaining with random implementation: An experimental study

We use a laboratory experiment to study bargaining with random implementation. We modify the standard Nash demand game so that incompatible demands do not necessarily lead to the disagreement outcome. Rather, with exogenous probability q, one bargainer receives his/her demand, with the other getting the remainder. We use an asymmetric bargaining set (favouring one bargainer) and disagreement payoffs of zero, and we vary q over several values.Our results mostly support game theoryʼs directional predictions. As with conventional arbitration, we observe a strong chilling effect on bargaining for q near one: extreme demands and low agreement rates. Increasing q reinforces the gameʼs built-in asymmetry – giving the favoured player an increasingly large share of payoffs – but also raising efficiency. These effects are non-uniform: over sizable ranges, increases in q have minimal effect, but for some q, small additional increases lead to sharp changes in results.     

Exploring Ambiguity and Familiarity Effects in The “Earnings Game” Between Managers and Investors

Prior evidence suggests that managers and investors play an earnings game in which managers bias their earnings forecasts downward as the earnings announcement date approaches. Knowing managers’ incentives to provide biased guidance, investors still revise their expectations downward helping to create “positive earnings surprises.” Using a 2 (ambiguity) × 2 (familiarity) between subject randomized experimental design where MBA students playing the roles of manager and investor answer a series of questions related to earnings guidance, we investigate whether earnings environment ambiguity and manager-investor familiarity influence behavior during the “earnings game.” In general, results from this study suggest that ambiguity contributes to managers’ propensity to mislead and investors’ propensity to follow, and a false sense of familiarity may amplify investors’ reliance on managers’ guidance.     

The minimum approval mechanism implements the efficient public good allocation theoretically and experimentally

We propose the minimum approval mechanism (MAM) for a standard linear public good environment with two players. Players simultaneously and privately choose their contributions to the public good in the first stage. In the second stage, they simultaneously decide whether to approve the otherʼs choice. Both contribute what they choose in the first stage if both players approve; otherwise, both contribute the minimum of the two choices in the first stage. The MAM implements the Pareto-efficient allocation in multiple solution concepts including backward elimination of weakly dominated strategies (BEWDS), limit logit agent quantal response equilibrium, subgame perfect minimax regret equilibrium, level-k thinking, and diagonalization heuristics. Moreover, the MAM is unique under plausible conditions. Overall, contributions in the MAM experiment averaged 94.9%. Quantifying subjectsʼ responses to the questionnaire reveal heterogeneous reasoning processes and highlight the importance of developing mechanisms that implement the desired social choice outcome in multiple solution concepts.     

Internet cautions: Experimental games with internet partners

We report the results of experiments conducted over the internet between two different laboratories. Each subject at one site is matched with a subject at another site in a trust game experiment. We investigate whether subjects believe they are really matched with another person, and suggest a methodology for ensuring that subjects’ beliefs are accurate. Results show that skepticism can lead to misleading results. If subjects do not believe they are matched with a real person, they trust too much: i.e., they trust the experimenter rather than their partner. JEL Classification C9     

Behavior in one-shot traveler’s dilemma games: model and experiments with advice

We report results of one-shot traveler’s dilemma game experiments to test the predictions of a model of introspection. The model describes a noisy out-of-equilibrium process by which players reach a decision of what to do in one-shot games. To test the robustness of the model and to compare it to other models of introspection without noise, we introduce non-binding advice. Advice has the effect of coordinating all players’ beliefs onto a common strategy. Experimentally, advice is implemented by asking subjects who participated in a repeated traveler’s dilemma game to recommend an action to subjects playing one-shot games with identical parameters. In contrast to observations, models based on best-response dynamics would predict lower claims than the advised. We show that our model’s predictions with and without advice are consistent with the data.