Complex Systems and Society by Giulia Ajmone Marsan Nicola Bellomo & Andrea Tosin

Author:Giulia Ajmone Marsan, Nicola Bellomo & Andrea Tosin
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

3.2 Cooperative and Competitive Stochastic Games

As we have seen in Chap.​ 2, the derivation of mathematical models according to the KTAP approach requires a detailed characterization of the microscopic interaction dynamics, which can be assimilated to nonlinearly additive stochastic games. The game rules depend, in general, on the specific system under consideration; however, some broad guidelines can be extracted from, for example, references [88, 95, 123].

The approach we propose in this chapter is based on game dynamics that can be classified as either cooperative or competitive. In particular, active particles are assumed to play a game at each interaction by choosing one of these two game regimes according to the strategy (viz., activity) they individually express.

It is worth anticipating that, in the socio-economic application of wealth redistribution we are concerned with, the activity of the particles coincides with their wealth status. As usual, the payoff of the game is a new wealth status (the test one), that a candidate particle gains, with a certain probability, after an interaction with a field particle depending on the kind of game they played. Bearing this in mind, let us describe in more detail what cooperation and competition rules consist of. Cooperation:The candidate particle either increases its wealth status, by benefiting from a field particle with higher status, or decreases it, by supporting a field particle with lower status. After the interaction, the states of the particles become closer together than before the interaction (see Fig. 3.1a).

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