Cognitive Economics

As the standard theory of rational choice under uncertainty, expected utility represents a key building block of the economic theory. This rational choice theory has the advantage of resting on solid axiomatic foundations. The present chapter reviews these foundations from normative and descriptive point of views. Then, some of the most promising generalizations of expected utility are reviewed.

In this chapter we discuss the meaning of general equilibrium in eco­nomics. We explain the proof of the existence of equilibria in a simple case, that of an exchange economy and describe how this context may be generalised to an economy with production. We show that equilibria are efficient in the sense of Pareto. We show how the problems of stability and uniqueness of equilibria have posed major difficulties for standard economic theory. We conclude by examining the problems that arise when one considers the nature of equilibria in more general economic settings.

This chapter recalls the main principles of non-cooperative game theory and especially its main equilibrium concepts. It proceeds by progressively introducing more and more complexity into the basic interaction model between rational players. The basic model is static with complete and perfect information and introduces the concept of Nash equilibrium as a fixed point of players’ best responses. Then, sequential action is explicitly introduced and leads to the concept of subgame perfect equilibrium, usually obtained by a backward induction procedure. Coming back to a static framework, structural uncertainty is embedded in the Bayesian equilibrium concept, where beliefs about others’ types are confirmed. Finally, combining temporality and factual uncertainty, one obtains the Bayesian Nash equilibrium concept, grounded on a fixed point between players’ beliefs about others’ past moves and their own future actions.

A survey of the results obtained during the past three decades in some of the most widely used tasks and paradigms in the experimental study of reasoning is presented. It is shown that, at first sight, human performance suffers from serious shortcomings. However, after the problems of communication between experimenter and subject are taken into account, which makes it possible to clarify the subject’s representation of the tasks, one observes a better performance, although still far from perfect. Current theories of reasoning, of which the two most prominent are very briefly outlined, agree in identifying the load in working memory as the main source of limitation in performance. Finally, a recent view on human rationality prompted by the foregoing results is described.

A logic is said to be supraclassical if it permits us to infer more from a set of premises than classical logic authorizes. It is called nonmonotonic if increasing the premises available for inference can lead to loss, as well as gain, of conclusions.

Probabilistic inference is a well-known kind of nonmonotonic supraclassical reasoning, and is familiar to many economists. But there are qualitative kinds as well, little known outside circles of logicians and computer scientists. They allow us to conclude more than classical logic permits, without appeal to probability distributions. Like probabilistic inference, they are also nonmonotonic.

The purpose of this chapter is to take some of the mystery out of these systems, by showing that they are not as unfamiliar as may at first sight appear. In fact, they are easily accessible to anybody with a background in classical propositional logic.

Cognitive modeling can be derived from expert knowledge integration or experimental data analysis. This Chapter introduces these two main ways of modeling and concentrates on the latter aspect and the related numerical tools together with their possible role. More precisely, the evolutionary approach is presented for optimization and tuning, artificial neural networks for associative reasoning and the stochastic approach for planning. We then conclude on the need for a modular framework, integrating these numerical and other symbolic tools.

In this lecture we introduce the concepts and tools of Statistical Mechanics using the Ising model of condensed matter physics, proposed about one century ago to explain magnetism, as a paradigm. The evocative power of this model brought the techniques of Statistical Mechanics to other fields, like brain models in Cognitive Science, Machine Learning Theory, and more recently to the analysis of models in Game Theory, Economy and Sociology.

A brief review of disorder systems in Statistical Physics is presented using the framework of the Ising model. Associated properties are described in terms of a social metaphor with a collection of people wearing either red or green shirts. Firstly, the ferromagnetic case is studied in detail to present both mechanisms of spontaneous symmetry-breaking and continuous order-disorder transition. The concept of phase diagram is explained as well as the role of thermal fluctuations in the universal properties associated with a critical phenomenon.The effect of an external uniform field is also presented together with the notion of first order phase transition. Then various disorder systems are reviewed, such as having competing exchange interactions leading to spin glasses, and random local fields leading to the random field model.

We propose a stochastic generalization of the Lotka-Volterra-Eigen-Schuster systems. In the generalized system, the set of dynamical variables is divided into several subsets, such that the variables within each subset interact with each other more strongly than with those in other subsets. It is shown that the size distribution of the dynamical variables within each subset approach a power-law form, while the exponents that characterize these distributions are different in different subsets. The exponent for each subset is found to depend only on the ratio between the stochastic term and the deterministic additive term. The model can be applied in the context of international trade, where the dynamical variables represent the revenues of firms or income/wealth of individuals.

This chapter presents the main topics which can be subsumed under the label “cognitive economics” and which correspond to current work. It first presents the cognitive processes carried out by an individual agent concerning the structure and revision of his beliefs and the mental deliberation preceding his choice. It then presents the mechanisms of interaction between several agents in the strategic and face-to-face form of game theory or in the more parametric and indirect form of economic theory. Each of the four successive themes is treated from two points of view, an epistemic one where hyper-intelligent agents act and coordinate instantaneously through sophisticated reasoning and an evolutionary one where boundedly rational agents adapt reciprocally through dynamic learning processes. Concluding remarks concern the ontological and epistemological positions of cognitive economics.

This Chapter proposes a new definition of the collective belief of a group, namely what the majority of the members of the group think the collective belief is. Consequently, for an individual i, to determine what the group believes leads him to reflect on how the other members of the group approach this very same question. This definition is very different from the usual definition, whereby “the group G believes P” means simply that the majority of the members of G believe P. Three points are demonstrated. Firstly, the notion of salience or focal point developed by Shelling fits this new definition. Secondly, thus defined, group belief is closely dependent on the cultural and historical context that shapes the identity of the group. Thirdly, and this is our main result, group belief defined in this way is disconnected from what agents really believe. Each individual can believe P and, at the same time, believe that the group believes Q. This is what we call “the autonomy of group belief”.

In this brief overview, we describe some of the main kinds of conditional assertion to be found in common language and scientific discourse, and how logicians have sought to model them.

In this Chapter, we deal with the consistency of dynamic individual choices. We impose that a decision maker should value information as a consistency requirement and show that this is compatible with a relaxation of Hammond’s consequentialism. More precisely we show that an axiom that we dub “selection of optimal strategies” is enough to entail a positive value for information. This axiom does not imply the sure thing principle and therefore leaves room for alternatives to the expected utility model. We illustrate this through a decision theoretic model that is not based on probabilistic beliefs but possesses the property of positive value of information.

The main purpose of viability theory is to explain the evolution of the state of a control system, governed by nondeterministic dynamics and subjected to viability constraints, to reveal the concealed feedbacks which allow the system to be regulated and provide selection mechanisms for implementing them.

It assumes implicitly an “opportunistic” and “conservative” behavior of the system: a behavior which enables the system to keep viable solutions as long as its potential for exploration (or its lack of determinism) — described by the availability of several evolutions — makes possible its regulation.

Examples of viability constraints are provided by architectures of networks imposing constraints described by connectionist tensors operating on coalitions of actors linked by the network. The question raised is how to modify a given dynamic system governing the evolution of the signals, the connectionist tensors and the coalitions in such a way that the architecture remains viable.

This chapter first gives an overview of some developments in the area of adaptive learning in games. Next, we present a general framework to model adaptive learning processes with persistent noise, and define the notion of stochastic stability. We provide several leading examples.

This Chapter describes what Evolutionary Game Theory has contributed to the study of communication in its investigations of games of signaling and cheap-talk. Two examples are proposed. In a simple Sender-Receiver game, no common knowledge is needed for Sender’s and Receiver’s behavior to be in equilibrium and informative. In cheap-talk games for inefficient equilibria to be unstable it may be necessary for the message space to be large.

Economists do not like the idea of comparing the economy to an ants’ nest or to a bee-hive. They are no doubt convinced that such organizations are in some sense optimal but they are not convinced that the optimality is achieved in the same way as it is in an economy or market. Thus, if you ask most economists what is the basic question that concerns them they will probably answer that it is to understand what the equilibrium of the economy or market that interests them is like, and whether it entails an efficient use of resources. Yet there is a prior problem that intrigues many people when they first come to economics and which is posed by the behavior of social insects. It is that of explaining how the myriad of disparate individual economic activities, in a modern economy, come to be coordinated. Economic agents constantly interact with each other in different ways and for different purposes and somehow out of these individual interactions a certain coherence at the aggregate level develops. Disappointingly economics has rather little to say about this. The reason is that the basic paradigm in economic theory is one in which individuals take decisions in isolation, using only the information received through some general market signals, such as prices, to make their decisions. The standard model does not deny that agents interact but, as Samuelson said, they only do so through the price system. Indeed, a way of characterizing the efficient markets hypothesis so pervasive in the financial markets literature is to say that all information private and public is aggregated in the price system. Thus no agent has any interest in searching for information other than from prices. Direct interaction is not an integral part of market behavior according to this view.

Economic experiments can provide data of interest to cognitive economists. Likewise, cognitive economics is well-suited to the explanation of some types of experimental data. In this Chapter, we survey the principal results that have been obtained from experimental research on markets. The contrast in behavior between service and asset markets is presented as a phenomenon that might be investigated by cognitive economists. We also describe some recent developments in the experimental study of games and summarize some of the principal general ideas that have emerged.

This Chapter extends some economic models that take advantage of a formalism inspired from statistical mechanics to account for social influence in individual decisions. Starting with a framework suggested by Durlauf, Blume and Brock, we introduce three classes of models shifting progressively from rational towards adaptive expectations. We discuss the risk and opportunity of transposing the tools, methods and concepts from statistical mechanics to economics. We also analyze some issues seldom addressed, such as a comparison between two models of heterogeneous idiosyncratic preferences, corresponding to cases with quenched and annealed disorder in statistical physics, respectively.

We discuss the influence of information contagion on the dynamics of choices in social networks of heterogeneous buyers. Starting from an inhomogeneous cellular automata model of buyers dynamics, we show that when agents try to adjust their reservation price, the tatonement process does not converge to equilibrium at some intermediate market share and that large amplitude fluctuations are actually observed. When the tatonnement dynamics is slow with respect to the contagion dynamics, large periodic oscillations reminiscent of business cycles appear.

This Chapter provides a short introduction to Agent-based Computational Economics (ACE), in order to underline the interest of such an approach in cognitive economics. Section 22.2 provides a brief bird’s eye view of ACE. In section 22.3, some interesting features of the Santa-Fe Approach to complexity are then introduced by taking simple examples using the Moduleco computational laboratory. Section 22.4 underlines the interest of ACE for modelling and exploring dynamic features of markets viewed as cognitive and complex social interactive systems. Simple examples of simulations based on two cognitive economics models are briefly discussed. The first one, deals with the so-called exploration-exploitation compromise, while the second deal with social influence and dynamics over social networks.

The object of this chapter is to stress the role of networks as support of economic dynamics and more particularly of cognitive dynamics, focusing on the impact of the topological structures of networks. In a first section we present the remarkable properties of small-world networks in terms of accessibility and connectivity and their consequences in the context of a knowledge-based economy. Then we turn our attention to the larger category of influence networks and their applications to diffusion processes. We introduce social learning in randomly drawn networks, agents modifying the intensity of their links according to the degree of concordance of their state at each period of time. The network structure thus evolves to a critical state where a small number of individuals is capable of triggering large “avalanches” over the network.

This Chapter presents recent strategic models of coalition and network formation, with two applications to industrial organization: the formation of cartels and strategic alliances.

Given an individually used standard on a territory we study the conditions for total spreading of a new emergent better fitted competing standard. The associated dynamics is monitored by local competing updating which occurs at random among a few individuals. The analysis is done using a cellular automata model within a two-dimensional lattice with synchronous random walk. Starting from an initial density of the new standard the associated density evolution is studied using groups of four individuals each. For each local update the outcome goes along the local majority within the group. However in case of a tie, the better fitted standard wins. Updates may happen at each diffusive step according to some fixed probability. For every value of that probability a critical threshold, in the initial new emergent standard density, is found to determine its total either disappearance or spreading making the process a threshold phenomenon. Nevertheless it turns out that even at a zero density measure of the new emergent standard there exits some peculiar killer clusters of it which have a non zero probability to grow and invade the whole system. At the same time the occurrence of such killer clusters is a very rare event and is a function of the system size. Application of the model to a large spectrum of competing dynamics is discussed. It includes the smoker-non smoker fight, opinion forming, diffusion of innovation, species evolution, epidemic spreading and cancer growth.

This Chapter deals with the issue of cognitive efficiency on the Internet. Cognitive efficiency refers here to the creation of chatrooms that gather individuals with homogenous preferences (but unable to recognize each other in the “real world”) and that provide relevant consumption advice on experience goods. Hence, we raise the question of the ability for individuals initially scattered on the Net to meet in homogenous chatrooms (according to taste and consumption decisions) in order to ensure informational relevance. We show that, in the simple model we propose, cognitive efficiency depends on (i) individuals’ preference patterns (especially on relative utilities between the various varieties of goods), (ii) on their requirement concerning the quality of advice they receive, and, though not specifically modelized, (iii) on the entry process in chatrooms (simultaneous or sequential, with or without mimetic behavior).