Matteo Richiardi, Roberto Leombruni, Nicole Saam and Michele Sonnessa (2006)
A Common Protocol for Agent-Based Social Simulation
Journal of Artificial Societies and Social Simulation
vol. 9, no. 1
<http://jasss.soc.surrey.ac.uk/9/1/15.html>
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Received: 12-Dec-2005 Accepted: 15-Dec-2005 Published: 31-Jan-2006
x_{i,t+1} = f_{i}(x_{i,t}, x_{-i,t}, &alpha_{i}) | (1) |
where x_{-i} is the state of all individuals other than i and α are some structural parameters.
Y_{t} = s(x_{1,t} …, x_{n,t}) | (2) |
Y_{i} = g_{t}(x_{1,0}, …, x_{n}_{,0}; α_{1}, … &alpha_{n}) | (3) |
(4) |
(5) |
on the artificial data, where β are some coefficients to be estimated in the artificial data. Note that this is nothing else than a sensitivity analysis on all the parameters together.
the distinction drawn between calibrating and estimating the parameters of a model is artificial at best. Moreover, the justification for what is called "calibration" is vague and confusing. In a profession that is already too segmented, the construction of such artificial distinctions is counterproductive.
Figure 1. An example of a Class diagram |
In particular Class diagrams can be used to show three types of relationships:
Figure 2. An example of a Time-Sequence diagram |
^{2}(Arifovic 1995; Arifovic 1996; Andreoni 1995; Arthur 1991; Arthur 1994; Gode and Sunder 1993; Weisbuch 2000)
^{3}We looked for journal articles containing the words "agent-based", "multi-agent", "computer simulation", "computer experiment", "microsimulation", "genetic algorithm", "complex systems", "El Farol", "evolutionary prisoner's dilemma", "prisoner's dilemma AND simulation" and variations in their title, keywords or abstract in the EconLit database, the American Economic Association electronic bibliography of world economics literature. Note however that EconLit sometimes does not report keywords and abstracts. We have thus integrated the resulting list with the references cited in the review articles cited above. The ranking is provided in Kalaitzidakis et al. (2003).
^{4}Schelling 1969; Tullock and Campbell 1970.
^{5}Clarkson and Simon 1960; Cohen 1960; Cohen and Cyert 1961; Orcutt 1960; Shubik 1960 .
. ^{6}JEDC has a section devoted to computational methods in economics and finance.
^{7}We looked for journal articles containing the words "simulation", "agent-based", "multi-agent" and variations in their title, keywords or abstract in the Sociological Abstracts database. All abstracts have been checked for subject matter dealing with ABM. We used the 2001 Citation Impact Factors (CIF) ranking for Sociology journals (93 journals).
^{8}for a brief account of the analogies and differences between agent-based simulations and traditional analytical modelling see Leombruni and Richiardi (2005)
^{9}There is some confusion in the literature to this regard, and it should be an aim of the methodological clarification we are calling for to address it. For discrete-time simulation social scientists generally mean that the state of the system is updated (i.e. observed) only at discrete (generally constant) time intervals. No reference is made to the timing of events within a period - see, for example, Allison and Leinhardt (1982). Conversely, a model is said to be continuous-time event-driven when the state of the system is updated every time a new event occurs (Lancaster 1990; Lawless 1982). In this case it is necessary to isolate all the events and define their exact timing. Note that discrete-time simulation is a natural option when continuous, flow variables are modelled, and the definition of an event becomes more arbitrary. For this reason (and mainly in the Computer Science literature) the definitions above are sometimes reversed.
^{10}Examples of centralized coordination mechanisms other than the usual, unrealistic Walrasian auctioneer (the hypothetical market-maker who matches supply and demand to get a single price for a good) generally assumed by traditional analytical models include real auctions, stock exchange books, etc. Examples of decentralized coordination mechanisms include bargaining, barter, etc.
^{11}Note that this is not equivalent to saying that simulations are an inductive way of doing science: induction comes at the moment of explaining the behaviour of the model (Axelrod 1997). Epstein qualifies the agent-based simulation approach as 'generative' (Epstein 1999), while the logic behind it refers to abduction (Leombruni 2002).
^{12}These statistics can either be a macro aggregate, or a micro indicator, as in the case of individual strategies. In both cases, as a general rule all individual actions, which in turn depend on individual states, matter.
^{13}Sometimes we are interested in the relationship between different (aggregate) statistics: e.g. the unemployment rate and the inflation rate in a model with individuals searching on the job market and firms setting prices. The analysis proposed here is still valid however: once the dynamics of each statistics is known over time, the relationship between them is univocally determined.
^{14}This definition applies both to the traditional homo sociologicus and the traditional homo oeconomicus. In the first paradigm individuals follow social norms and hence never change their behaviour. In the latter, individuals with rational expectations maximize their utility.
^{15}Or even not dependent on the initial conditions
^{16}Here, the distinction between in-sample and out-of-sample values, and the objection that two formulations may fit equally well the first, but not the latter, is not meaningful. Any value in the relevant range can be included in the artificial experiments.
^{17}Ergodicity means that a time average is indeed representative of the full ensemble. So, if the system is ergodic, each simulation run gives a good description of the overall behavior of the system.
^{18}For an overview on the discussion see Dawkins et al. 2001, pp. 3661ff.
^{19}Homomorphism is used as the criterion for validity rather than isomorphism, because the goal of abstraction is to map an n-dimensional system onto an m-dimensional system, where m < n. If m and n are equal, the systems are isomorphic.
^{20}For a discussion on the confusion that surrounds the basic definition of validity, see Bailey (1988).
^{21}The Object Management Group (OMG) is an open membership, not-for-profit consortium that produces and maintains computer industry specifications for interoperable enterprise applications. Among its members are the leading companies in the computer industry (see http://www.omg.org).
^{22}For an agent based modeller the concept of an actor may create some confusion. According to the UML symbolism, each object or class defined within the software architecture is represented by squared boxes (the class notation), while each external element (like human operators, hardware equipment) interacting with the software is represented by a stylized human symbol (the actor).
^{23}JAS ( http://jaslibrary.sourceforge.net); RePast ( http://repast.sourceforge.net)
^{24}The state of the system is updated (i.e. observed) only at discrete (generally constant) time intervals. No reference is made to the timing of events within a period.
^{25}The state of the system is updated every time a new event occurs. All events are isolated and their exact timing defined.
^{26}auction, book, etc.
^{27}bargaining, etc.
^{28}The behaviour of all meaningful individual and aggregate variables is explored, with reference to the results currently available in the literature. For instance, in a model of labour participation, if firm production is defined, aggregate production (business cycles, etc.) is also investigated.
^{29}The model is investigated only with respect to the behaviour of some variables of interest
^{30}defined as a state where individual strategies do not change anymore.
^{31}defined as a state where some relevant (aggregate) statistics of the system becomes stationary.
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