With the material contained in this chapter, we are entering the realm of non-price competition. To be more precise, I should rather say that we are about to extend the models reviewed in Chapter 3 to variables complementing price, quantity and capacity competition. Yet, it is true that the models appearing in the previous chapter boil down to the determination of outputs and prices.

The relevance of non-price instruments is well understood in industrial economics. In particular, the predatory nature of advertising has been recognised at least since Braithwaite (1928), and its impact on market power since Kaldor (1950).

Quite intuitively in view of its intrinsically dynamic nature, advertising is probably the most debated topic in the tradition of optimal control and differential game theory. In fact, understanding advertising campaigns has been the driver of some of the earliest applications of differential game theory to IO and management, in Friedman (1958), Dhrymes (1962), Clemhout et al. (1971) and Leitmann and Schmitendorf (1978). Interestingly, the views on the nature of advertising commonly accepted in IO (see, e.g., Tirole, 1988; Bagwell, 2007) significantly differ from the taxonomy of advertising acquired in the literature dealing with dynamic formulations of the same problems.

Industrial economists stress that advertising is aimed at enhancing a brand's reputation by altering consumer tastes, thereby preventing any welfare assessment. We are aware of this since Dorfman and Steiner (1954) and many others (Dixit and Norman, 1978). Advertising campaigns can be informative, persuasive or complementary (Stigler and Becker, 1977; Becker and Murphy, 1993), the latter property indicating that advertising contributes to define the overall features of a product, and therefore complements it. In a sense, complementary advertising can be seen as an extension or reinforcement of the concept of persuasive advertising. In the applications of dynamic techniques to this subject, the attention is focussed on the specific state variable affected by advertising efforts (which are controls), or on the impact of advertising along the product life cycle, in such a way that the taxonomy of advertising commonly used in the applications of differential game theory is somewhat different in terms of both terminology and interpretation.

Introduction

It is a fact of life that the preferences, information, and choices – hence the behavior – of an agent affect and are affected by the behavior of the agents she interacts with. In fact, there is a two-way feedback between individual and aggregate behavior: agents’ interaction affects the evolution of the system as a whole; at the same time, the collective dynamics that shape the social structure of the economy affect individual behavior.

For example, consider the case of the adoption of a new technology by initially uninformed consumers. Each agent, based on her preferences, may have some ex-ante evaluation about the quality of new products introduced in the market. However, by interacting with their peers, agents may gather fresh information about the new product and, eventually, they may decide whether to buy it or not. This influences the adoption rate of the product, which can be in turn exploited by other consumers as a parameter to be employed when subsequently considering whether to buy the product or not. Therefore, individual decisions may be affected by agent interactions, then impact on the aggregate state of the system, which can in turn feed back to individual behaviors.

Traditionally, economic theory has largely overlooked the importance of interactions among economic agents. In standard economic theory, interactions are treated as externalities or spillovers. In general equilibrium theory (GET), the presence of externalities is often treated as a pathology of the model, leading to possible nonexistence of equilibria. Therefore, in the model it is often assumed that externalities do not simply exist – i.e., that agents only interact indirectly through a nonagent – that is prices, whose role is to aggregate individual information. Hence, in GET, agents are totally disconnected, dots living in a vacuum without any connections (links) between them.

To appreciate the importance of externalities in mainstream economics, one has to resort to game theoretic models. In this setup, agents interact directly with all the other agents in the game. Interactions are captured via strategic complementarities: the payoff of any single agent depends directly on the choices made in the game by all the N − 1 other agents. This configures a scenario completely at odds with the one portrayed in GET, namely one where agents live in a fully connected world, where they are linked with anyone else.

Introduction

A rather common misunderstanding about simulations is that they are not as sound as mathematical models. Computer simulations are, according to a popular view, characterised by an intermediate level of abstraction: they are more abstract than verbal descriptions but less abstract than ‘pure’ mathematics. This is nonsense. Simulations do consist of a well-defined (although not concise) set of functions, which relate inputs to outputs. These functions describe a fully recursive system and unambiguously define its macro dynamics. In this respect, AB models are no different from any other model: they are logical theorems saying that, given the environment and the rules described by the model, outputs necessarily follow from inputs. As in any other model, they provide sufficiency theorems: the environment and the rules are sufficient conditions to obtain the results, given the inputs. The resort to computer simulations is only an efficient way – given some conditions – to obtain the results.

In this chapter we offer a characterisation of AB models as recursive models. The chapter has a simple structure: Section 3.2 places AB modelling in the wider context of simulation models; Section 3.3 introduces the notation and the key concepts; finally, Section 3.4 concludes elaborating on what constitutes a proof in an AB setting.

Discrete-Event vs. Continuous Simulations and the Management of Time

Computer-based simulations face the problem of reproducing real-life phenomena, many of which are temporally continuous processes, using discrete microprocessors. The abstract representation of a continuous phenomenon in a simulation model requires that all events be presented in discrete terms. However, there are different ways of simulating a discrete system.

In Discrete Event Simulations (DES) entities are thought of as moving between different states as time passes. The entities enter the system and visit some of the states (not necessarily only once) before leaving the system. This can be contrasted with System Dynamics (SD), or continuous simulation modelling, a technique created during the mid-1950s by Jay Forrester at the Massachusetts Institute of Technology (Forrester, 1971), which characterises a system in terms of ordinary differential equations (ODEs). SD takes a slightly different approach to DES, focusing more on flows around networks than on the individual behaviour of entities. In SD, three main objects are considered: stocks, flows and delays. Stocks are basic stores of objects, as the number of unemployed workers.