Wolfgang Balzer, Karl R. Brendel and Solveig Hofmann (2001)
Bad Arguments in the Comparison of Game Theory and Simulation in Social Studies
Journal of Artificial Societies and Social Simulation
vol. 4, no. 2,
<http://jasss.soc.surrey.ac.uk/4/2/1.html>
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Received: 17-Jul-00 Accepted: 01-Feb-01 Published: 31-Mar-01
Yet there are game theoretic models from which empirical implications can be obtained on a qualitative, macroscopic level. The spatial theory of voting, for instance, has models yielding realistic percentages of equilibrium numbers of voters who abstain, numbers that can be compared with empirical data. Applications of the 'folk theorems' on repeated games yield predictions about stable outcomes based on data about the initial distribution of strategies in the population. This would be an argument in favour of game theory if simulation studies were not able to provide similar predictions. Nevertheless, simulation studies can be used in the same way. There are simulations about spatial movements of actors in the spirit of Schelling's original model that can be fitted with actual data.^{[13]} The percentages of cooperation in PD simulations including whole neighbourhoods can be compared with experimental data from laboratory experiments,^{[14]} and distributions of producers/predators/protectors resulting from 3P simulations can be compared with actual such distributions in existing societies.^{[15]}
It is difficult to find an asymmetry here. Even if a greater number of studies with empirical implications could be found in the game theoretic approach, one still might counterbalance this by pointing to its history being 3 or 4 decades longer than that of the discrete simulation approach.
Obviously, it makes little sense to say that one of the two approaches is simpler than the other tout court. In order to compare for simplicity we have to refer to a common application. The question is whether in view of some particular, or all, applications that can be, or have been, treated both in game theoretic terms and by means of simulation, there is a difference in simplicity. A priori, the area of overlap of possible applications should be very big, due to the unrestricted nature of game theoretic models which, in principle, can be applied to almost everything. In practice, however, it is difficult to find examples. One example are the PD tournaments which after Axelrod (1984) were studied more carefully both with paper and pencil and with simulations. Without closer inspection it is difficult to claim that one of the two approaches is simpler in this area would require closer inspection, but this is difficult because of the lack of acknowledged criteria.
Without closer inspection, two things can be said. First, simulation is simpler when the application aims at exploring a space of possibilities to find new, interesting ones. Conversely, game theoretic study is simpler when the goal lies in the consolidation and integration of many possibilities in one homogenous picture. These points can be perceived in the PD studies. New, stable strategy combinations were found in the simulation results,^{[16]} but integrating all of them into a neat model required the cumulated game theoretical knowledge available in the form of its theorems.
There is one more aspect to simplicity that, though hardly relevant at the group level, can be very important at the level of a single individual researcher. In order to write a discrete, social simulation program the essential task is to formulate some rules for the individual behaviour of the simulated agents in a computer language. Often these rules can be integrated in simulation tools or shells. The simulation then can be run by taking a ready made simulation environment and just plugging in the rules one has formulated. In this way, one can in fact generate very complicated and complex systems by very simple rules.^{[17]} A game theoretic study of the same rules would involve the build-up of a full game theoretical model. Assuming that the researcher is a social scientist who initially does not know game theory nor any programming language we can ask which way is easier and in that sense simpler: learning game theory or learning a programming language? Though this also is an involved matter, it seems to me that learning game theory so far as to be able to construct the particular model one is after is harder than learning a programming language to the extent that one can formulate the rules of behaviour and run a program. This difference will become more salient with the development of further tools for computer simulation, which has already begun.
^{2} A typical example is Gilbert and Doran (1994).
^{3} See, for instance, Scheibe (1997, 1999).
^{4} For example: "Complex adaptive systems are so intricate that there is little hope of a coherent theory without the controlled experiments that a massively parallel computer makes possible", Holland (1992, p. 27/28). It should be mentioned that in the same paper the author also stresses the need of theory.
^{5} For example Binmore (1998) ends his review of Axelrod (1997) saying that Axelrod's "conjectures can only be evaluated in a scientific manner by running properly controlled robustness tests that have been designed using a knowledge of the underlying theory".
^{6} A cluster law H with just two terms can be conjunctively separated if it is equivalent to a sentence A B where A and B each contain only one of the two terms, see Balzer et al. (1987).
^{7} In the following, we will use the terms 'data' and 'observation sentences' interchangeably. An initial condition is just a (sub)set of the set of data or observation sentences.
^{8} Whereby we can assume that models of the latter kind have the same type as the models of H.
^{9} As just explained, one can as well consider the intersection of two such classes, and have a theory consisting of at least one class of models in which also certain observation sentences are true. The observation sentences may be 'distributed' over different models.
^{10} To get an idea of such a rule based simulation system, see Balzer (1999).
^{11} The theory's data are 'distributed' over different models.
^{12} 'Intermediate' levels are discussed in philosophy of science under the labels of 'theory net' and 'theory evolution', see Balzer et al. (1987).
^{13} See e.g. Nowak and Vallacher (1994).
^{14} See Liebrand and Messick (1996).
^{15} See Albert and Balzer (2000).
^{16} Though the folk theorems assure that these combinations are stable, this does not mean that we 'knew' these combinations just because we knew the theorems. These theorems, see e.g. Osborne and Rubinstein (1994), cover a huge set of possibilities. To see the point, consider an analogous situation in quantum physics. We would not say we know the energy operator just because we know the standard theorems about (unbounded) operator algebras.
^{17} In SMASS, for instance, which uses Prolog, the formulation of a rule can be a very simple matter of a couple of hours, since Prolog syntax is almost like that of natural language, see Balzer (1999).
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