Micro/macro viability analysis of individual‐based models: Investigation into the viability of a stylized agricultural cooperative

The mathematical viability theory proposes methods and tools to study at a global level how controlled dynamical systems can be confined in a desirable subset of the state space. Multilevel viability problems are rarely studied since they induce combinatorial explosion (the set of N agents each evolving in a p ‐dimensional state space, can evolve in a Np dimensional state space). In this article, we propose an original approach which consists in solving first local viability problems and then studying the real viability of the combination of the local strategies, by simulation where necessary. In this article, we consider as multilevel viability problem a stylized agricultural cooperative which has to keep a minimum of members. Members have an economical constraint and some members have a simple model of the functioning of the cooperative and make assumptions on other members' behavior, especially proviable agents which are concerned about their own viability. In this framework, the model assumptions allow us to solve the local viability problem at the agent level. At the cooperative level, considering mixture of agents, simulation results indicate if and when including proviable agents increases the viability of the whole cooperative. © 2014 Wiley Periodicals, Inc. Complexity 21: 276–296, 2015