Scott E. Page

Path dependence and the validation of agent-based spatial models of land use

In this paper, we identify two distinct notions of accuracy of land‐use models and highlight a tension between them. A model can have predictive accuracy: its predicted land‐use pattern can be highly correlated with the actual land‐use pattern. A model can also have process accuracy: the process by which locations or land‐use patterns are determined can be consistent with real world processes. To balance these two potentially conflicting motivations, we introduce the concept of the invariant region, i.e., the area where land‐use type is almost certain, and thus path independent; and the variant region, i.e., the area where land use depends on a particular series of events, and is thus path dependent. We demonstrate our methods using an agent‐based land‐use model and using multi‐temporal land‐use data collected for Washtenaw County, Michigan, USA. The results indicate that, using the methods we describe, researchers can improve their ability to communicate how well their model performs, the situations or instances in which it does not perform well, and the cases in which it is relatively unlikely to predict well because of either path dependence or stochastic uncertainty.

Problem Solving by Heterogeneous Agents

A substantial amount of economic activity involves problem solving, yet economics has few, if any, formal models to address how agents of limited abilities find good solutions to difficult problems. In this paper, we construct a model of heterogeneous agents of bounded abilities and analyze their individual and collective performance. By heterogeneity, we mean differences in how individuals represent problems internally, their perspectives, and in the algorithms they use to generate solutions, their heuristics. We find that while a collection of bounded but diverse agents can locate optimal solutions to difficult problems, problem solving firms can exhibit arbitrary marginal returns to problem solvers and that the order that problem solvers are applied to a problem can matter, so that the standard story of decreasing returns to scale may not apply to problem solving firms. Journal of Economic Literature Classification Numbers: C6, D2.

Making the Difference: Applying a Logic of Diversity

Executive Overview Each year, corporations spend billions of dollars on diversity training, education, and outreach. In this article, I explain why these efforts make good business sense and why organizations with diverse employees often perform best. I do this by describing a logic of diversity that relies on simple frameworks. Within these frameworks, I demonstrate how collections of individuals with diverse tools can outperform collections of high “ability” individuals at problem solving and predictive tasks. In problem solving, these benefits come not through portfolio effects but from superadditivity: Combinations of tools can be more powerful than the tools themselves. In predictive tasks, diversity in predictive models reduces collective error. Its a mathematical fact that diversity matters just as much as highly accurate models when making collective predictions. This logic of diversity provides a foundation on which to construct practices that leverage differences to improve performance.

Can Game(s) Theory Explain Culture? The Emergence of Cultural Behavior within Multiple Games

The hallmarks of cultural behavior include consistency within and across individuals, variance between populations, behavioral stickiness, and possibly suboptimal performance. In this article, we build a formal framework within which these behavioral attributes emerge from the interactions of purposive agents. We then derive mathematical results showing these behaviors are optimal given our assumptions. Our framework rests on two primary assumptions: (1) agents play ensembles of games, not just single games as is traditionally the case in evolutionary game theory models; and (2) agents have finite cognitive capacity. Our analysis combines agent-based techniques and mathematics, enabling us to explore dynamics and to prove when the behaviors produced by the agents are equilibria. Our results provide game theoretic foundations for cultural diversity and agent-based support for how cultural behavior might emerge.

Behavioral spillovers and cognitive load in multiple games: An experimental study

We present evidence from laboratory experiments of behavioral spillovers and cognitive load that spread across strategic contexts. In the experiments, subjects play two distinct games simultaneously with different opponents. We find that the strategies chosen and the efficiency of outcomes in one game depends on the other game that the subject plays, and that play is altered in predictable directions. We develop a measure of behavioral variation in a normal form game, outcome entropy, and find that prevalent strategies in games with low outcome entropy are more likely to be used in the games with high outcome entropy, but not vice versa. Taken together, these findings suggest that people do not treat strategic situations in isolation, but may instead develop heuristics that they apply across games.

The standing ovation problem

Over the last decade, research topics such as learning, heterogeneity, networks, diffusion, and externalities, have moved from the fringe to the frontier in the social sciences. In large part this new research agenda has been driven by key tools and ideas emerging from the study of complex adaptive systems. Research is often inspired by simple models that provide a rich domain from which to explore the world. Indeed, in complex systems, Bak’s (1996) sand pile, Arthur’s (1994) El Farol bar, and Kauffman’s (1989) NK system have provided such inspirations. Here we introduce another model that offers similar potential—the Standing Ovation Problem (SOP). This model is especially appropriate given the focus of this special issue on complex adaptive social systems. The SOP has much to offer as it (1) is easily explained and part of everyone’s common experience; (2) simultaneously emphasizes some of the key themes that arise in social systems, such as learning, heterogeneity, incentives, and networks; and (3) is amenable to research efforts across a variety of fields. These features make it an ideal platform from which to explore the power, promise, and pitfalls of complexity modeling in the social sciences. The basic SOP can be stated as: A brilliant economics lecture ends and the audience begins to applaud. The applause builds and tentatively, a few audience members may or may not decide to stand. Does a standing ovation ensue or does the enthusiasm fizzle? Inspired by the seminal work of Schelling (1978), the SOP possesses sufficient structure to generate nontrivial dynamics without imposing too many a priori modeling constraints. Like Schelling’s work, it focuses on the macro-behavior that emerges from micro-motives, and relies on models that emphasize agents driven by simple behavioral algorithms placed in interesting spatial contexts. Though ostensibly simple, the social dynamics responsible for a standing ovation are complex. As the performance ends, each audience member must decide whether or not to stand. Of course, if the decision to stand is simply a personal choice based on the individual’s own assessment of the worth of the performance, the problem becomes trivial. However, people do not stand solely based upon their own impressions of the performance. A seated audience member surrounded by people standing might be enticed to stand, even if he hated the performance. This behavioral mimicry could be strategic (the agents wants to send the

Two Measures of Difficulty

SummaryThe paper constructs two measures of difficulty for functions defined over binary strings. The first of these measures,cover size, captures the difficulty of solving a problem in parallel. The second measure,ascent size, captures the difficulty of solving a problem sequentially. We show how these measures can help us to better understand the performance of genetic algorithms and simulated annealing, two widely used search algorithms. We also show how disparities in these two measures may shed light on the organizational structure of firms.

Uncertainty, Difficulty, and Complexity

In this article I clarify the often muddled distinctions between uncertainty, difficulty, and complexity and show that all three can enhance our understanding of institutional performance and design. To cope with uncertainty, institutions align incentives for information revelation; to handle difficult problems, institutions create incentives for diverse problem-solving approaches; and to harness complexity, institutions adjust selection criteria, rates of variation, and the level of connectedness. The distinction between complex systems and equilibrium systems also necessitates a discussion of the differences between the existence, stability, and attainment of equilibria and why, despite often being neglected, the latter two concepts are important to our understanding of institutions.

Complex Adaptive Systems: An Introduction to Computational Models of Social Life: An Introduction to Computational Models of Social Life

Theoretical physics is replete with models. When equations of motion are not available, or not amenable to perturbation theory, or just too hard from which to extract useful information, then physicists turn to models and computation. The Ising model of ferromagnetism is a classic example. A simple nearest neighbor temperature dependent interaction, in two or more dimensions, leads to long-range order and a phase transition at a finite temperature. This model has many locally interacting parts and an emergent behavior (ferromagnetism) at a critical temperature. However, the system never adapts. It does not change the phase transition to a higher temperature or avoid a phase transition altogether. Social systems are always adapting, and this interesting twist produces a vast array of possibilities and forms the basis of much of the discussion in Miller and Page’s book. This book is not a textbook, but rather an essay on complex adaptive systems. The discussions and insights will be better appreciated by readers who have already tried their hand at investigating complex adaptive systems. These systems can be so complex that the best method to discover their properties is to dispatch many computer agents to experience the system’s possibilities. The study becomes more interesting when the agents can alter their actions and the rules of the game. Miller and Page give the simple, but instructive example of forest growth and lightning induced forest fires. If trees grow too rapidly they will cover the allowable space and a fire started anywhere in the forest will spread and destroy the entire forest. A very slow growth will only produce a sparse forest. The authors find a tree growth rate to achieve an optimal stable high forest coverage. Their solution is trumped when altruistic agents are introduced, one for each tree. Some of the agents adapt by not growing a tree in their plot of land (to their personal disadvantage) but the overall global organization is one of firebreaks preventing large scale fires. Adaptation wins! Another model discussed is what physicists call the minority game, that is, making a choice that puts you in the minority. This is perhaps best known through the El Faro example of choosing whether or not to go to Santa Fe’s El Faro bar tonight based on whether it was

Interpreted and generated signals

Private information is typically modeled as signals. A joint probability distribution captures relationships between signals and between signals and relevant variables. In this paper, we define and contrast two types of signals: generated and interpreted. We demonstrate that even though the standard assumption of conditional independence is a reasonable benchmark assumption for generated signals, it imposes a specific, and unlikely structure on interpreted signals. We also show that independent interpreted signals are negatively correlated in their correctness, but generated signals can be independent. Our findings may limit the contexts in which many models of information aggregation and strategic choices in auctions, markets, and voting apply.