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4 I N N O VAT I O N S I N T R AV E L D E M A N D M O D E L I N G , V O L U M E 2 · The solution point can have certain properties that tages and disadvantages vary according to theoretical allow theoretical extensions or reinterpretation of perspective and modeling context more generally. In results, such as socially desirable allocations of resources essence, the equilibrium approach facilitates a more in welfare economics analysis, pricing strategies and wide-ranging theoretical consideration of the cross- second-best approaches, non-Walresian or reduced sectional tendencies of the system, whereas the process assumptions, contestable markets, and the property that simulation approach allows a more empirical explo- all used paths have the same minimum cost with trans- ration of the actual dynamic behavior of the system. port networks in certain forms of equilibrium; Two common misconceptions (among many potential · The solution point can have certain properties that ones) are that make it relatively easy (or quick) to find (such as with the FrankWolfe algorithm); 1. The iterations used in a calculation process to find · The defined equilibrium state generally does not the equilibrium solution in some way mimic the real- exist in reality for most systems of interest, except with world behavior of the system, which would be the case more generalized and extended (perhaps sometimes even only by coincidence, and tortured) definitions of equilibrium, such as spatially or 2. The simulation error in some way mimics the vari- temporally dynamic equilibrium that may also give up ation in system behavior even when the random elements something related to the benefits of the properties involved in the calculation process reflect analyst uncer- already listed, including the potential instability and tainty rather than variation in system behavior, which nonuniqueness of equilibrium points; and again would be the case only by coincidence. · Failure to reach the defined equilibrium point within a sufficient tolerance can lead to difficulties when results are being interpreted, particularly when results DEGREE OF AGGREGATE CONSTRAINT are being compared for different input conditions, lead- AND LEVEL OF DISAGGREGATION ing to the potential for large calculation burdens such that iteration "recipes" are a poor compromise. The equilibrium approach and the process simulation approach are two points (or perhaps regions) on a con- For the process simulation approach, tinuum of the degree of aggregate constraint on the mod- eling system. At one end is a complete lack of any · It provides a more direct match with actual system aggregate constraints or restrictions on the system, and at mechanics; the other is a full set of such constraints. Specific model- · It generally can draw on a wider range of under- ing approaches can be placed along this continuum, with standing and appreciation of the elements of behavior the recognition of a range of levels of such constraints involved; and even of types of equilibrium as different forms of · It does not require the definition of an equilibrium such constraint. There is a similar continuum in relation state or even rely on the concept of equilibrium; to the level of representation of the individual behavioral · It incorporates path dependencies that complicate agents in the system and the distributions of their interac- understanding and evaluation; tions, from the explicit treatment of each agent as a · It can display emergent aggregate behavior, leading unique object to the handling of aggregate quantities rep- to a greater appreciation of system dynamics; resenting groups or flows of agents as specific entities. · It typically involves random elements in its calcula- Specific modeling approaches can be placed jointly tion processes (by using Monte Carlo techniques) with along these two continua in a two-dimensional plane. the implication that the calculated output values also Figure 1 shows these placements for a selection of mod- have random components (sometimes called simulation eling approaches. error or microsimulation error) with distributions that Figure 1 also shows regions with aggregate behavior vary with level of aggregation and often are not well that is chaotic, emergent, or both. This representation is understood; and based on the recognition that chaotic behavior tends to · The calculation of expectations for outputs in gen- arise when there are comparatively fewer agents-- eral requires multiple simulation runs, leading to the consistent with the idea that a larger number of individ- potential for large calculation burdens. ual objects with a comparatively wide distribution of responses results in a dissipation of impact that dampens These two approaches have their proponents, and the the system. It is also based on the recognition that emer- debates that arise about the approaches' relative merits gent aggregate behavior arises in a meaningful sense only can sometimes be heated. This is hardly surprising, as when there are enough individual agents to allow for the these two approaches arise from different viewpoints, interactions among the agents to develop into something and the strength and even the relevance of the advan- beyond what they explicitly specify.