Seth Frey

Cyclic Game Dynamics Driven by Iterated Reasoning

Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated. However, economists have argued that iterated reasoning–what you think I think you think–will suppress complex dynamics by stabilizing or accelerating convergence to Nash equilibrium. We report stable and efficient periodic behavior in human groups playing the Mod Game, a multi-player game similar to Rock-Paper-Scissors. The game rewards subjects for thinking exactly one step ahead of others in their group. Groups that play this game exhibit cycles that are inconsistent with any fixed-point solution concept. These cycles are driven by a “hopping” behavior that is consistent with other accounts of iterated reasoning: agents are constrained to about two steps of iterated reasoning and learn an additional one-half step with each session. If higher-order reasoning can be complicit in complex emergent dynamics, then cyclic and chaotic patterns may be endogenous features of real-world social and economic systems.

Chapter One - Learning Along With Others

Abstract Unlike how most psychology experiments on learning operate, people learning to do a task typically do so in the context of other people learning to do the same task. In these situations, people take advantage of others’ solutions, and may modify and extend these solutions, thereby affecting the solutions available to others. We are interested in the group patterns that emerge when people can see and imitate the solutions, innovations, and choices of their peers over several rounds. In one series of experiments and computer simulations, we find that there is a systematic relation between the difficulty of a problem search space and the optimal social network for transmitting solutions. As the difficulty of finding optimal solutions in a search space increases, communication networks that preserve spatial neighborhoods perform best. Restricting people’s access to others’ solutions can help the group as a whole find good, hard-to-discover solutions. In other experiments with more complex search spaces, we find evidence for several heuristics governing individuals’ decisions to imitate: imitating prevalent options, imitating options that become increasingly prevalent, imitating high-scoring options, imitating during the early stages of a multiround search process, and imitating solutions similar to one’s own solution. Individuals who imitate tend to perform well, and more surprisingly, individuals also perform well when they are in groups with other individuals who imitate frequently. Taken together, our experiments on collective social learning reveal laboratory equivalents of prevalent social phenomena such as bandwagons, strategy convergence, inefficiencies in the collective coverage of a problem space, social dilemmas in exploration/exploitation, and reciprocal imitation.

Reciprocity on the Hardwood: Passing Patterns among Professional Basketball Players

Past theory and research view reciprocal resource sharing as a fundamental building block of human societies. Most studies of reciprocity dynamics have focused on trading among individuals in laboratory settings. But if motivations to engage in these patterns of resource sharing are powerful, then we should observe forms of reciprocity even in highly structured group environments in which reciprocity does not clearly serve individual or group interests. To this end, we investigated whether patterns of reciprocity might emerge among teammates in professional basketball games. Using data from logs of National Basketball Association (NBA) games of the 2008–9 season, we estimated a series of conditional logistic regression models to test the impact of different factors on the probability that a given player would assist another player in scoring a basket. Our analysis found evidence for a direct reciprocity effect in which players who had “received” assists in the past tended to subsequently reciprocate their benefactors. Further, this tendency was time-dependent, with the probability of repayment highest soon after receiving an assist and declining as game time passed. We found no evidence for generalized reciprocity – a tendency to “pay forward” assists – and only very limited evidence for indirect reciprocity – a tendency to reward players who had sent others many assists. These findings highlight the power of reciprocity to shape human behavior, even in a setting characterized by extensive planning, division of labor, quick decision-making, and a focus on inter-group competition.

Mixed human/entity games and the anomalous effects of misattributing strategic agency

People sometimes make better decisions either by treating inanimate objects like strategic reasoners or by treating other reasoners as if they were inanimate objects. I advance “strategic agenthood attribution” as a psychological mechanism for modulating economic behavior. From a design perspective, inducing or suppressing the attribution of strategic abilities can influence aggregate social outcomes. Drawing from experiments in behavioral and institutional economics, developmental and social psychology, and human–robot interaction, I document human strategic reasoning in environments that mix typical adult humans with other kinds of entities. I then discuss anomalous misattributions of strategic agenthood and non-agenthood, with special attention to settings in which two types of error—either attributing strategic reasoning abilities to objects that can’t think, or failing to attribute such abilities to typical human subjects—actually led to better economic outcomes. Because over- and under-mentalizing are endemic to human decision-making processes, game theory can be applied to improve interaction design, whether or not a given interaction is a game. I show that the flexible nature of human agenthood attribution increases the scope of game theory in some places, reduces it elsewhere, and generally introduces behavioral economics as a promising source of theory for human interactions with equivocal agents.

Cognitive mechanisms for human flocking dynamics

Low-level “adaptive” and higher-level “sophisticated” human reasoning processes have been proposed to play opposing roles in the emergence of unpredictable collective behaviors such as crowd panics, traffic jams, and market bubbles. While adaptive processes are widely recognized drivers of emergent social complexity, complementary theories of sophistication predict that incentives, education, and other inducements to rationality will suppress it. We show in a series of multiplayer laboratory experiments that, rather than suppressing complex social dynamics, sophisticated reasoning processes can drive them. Our experiments elicit an endogenous collective behavior and show that it is driven by the human ability to recursively anticipate the reasoning of others. We identify this behavior, “sophisticated flocking”, across three games, the Beauty Contest and the “Mod Game” and “Runway Game”. In supporting our argument, we also present evidence for mental models and social norms constraining how players express their higher-level reasoning abilities. By implicating sophisticated recursive reasoning in the kind of complex dynamic that it has been predicted to suppress, we support interdisciplinary perspectives that emergent complexity is typical of even the most intelligent populations and carefully designed social systems.

Does successful small-scale coordination help or hinder coordination at larger scales?

When we invoke group-level processes like cooperation or coordination, we usually model them as operating either over the set of dyads or at the scale of the whole group. But an individual can interact with the same set of people over many different scales simultaneously. Four people might maintain interactions over any combination of the six possible dyads relating their pairs, the four triads relating their subsets of the three, and the polyad of order four relating them all. What is the relationship between different interaction scales, and how might they interact? The different possible answers to this question reveal conflicting intuitions about group processes.We devised a four-player, multi-strategy experimental paradigm in which participants chose not just whether to coordinate, but with whom, and at what scale. Our results reveal coordination behavior with such a strong preference for dyads that undermining coordination between pairs of participants actually facilitates coordination at the scale of the group. We present these findings as experimental evidence for competition, as opposed to complementarity, between different scales of multi-player coordination. This result undermines a basic premise of approaches in network science that rely on dyad-scale structure as a proxy for group-scale order.