We propose a mathematical model of the $N$-person prisoner’s dilemma game played by a continuous population of agents with a time-dependent aspiration level. The model—a system of differential equations—takes into account the evolution of the aspiration level and of the mean frequency of the cooperators in the population. The dependence of the asymptotic level of cooperation on the individual payoffs and on the transition rates determining the agent’s reaction to the received payoffs is studied. In general the existence and the magnitude of the asymptotic level of cooperation depends on $N$, the payoffs and the transition rates, and decreases with increasing $N$.

The article proposes the concept of modeling that uses multi-agent systems of mutual interactions between city residents as well as interactions between residents and spatial objects. Adopting this perspective means treating residents, as well as buildings or other spatial objects, as distinct agents that exchange multifaceted packages of information in a dynamic and non-linear way. The exchanged information may be reinforced or diminished during the process, which may result in changing the social activity of the residents. Utilizing Latour’s actor–network theory, the authors developed a model for studying the relationship between demographic and social factors, and the diversified spatial arrangement and the structure of a city. This concept was used to model the level of residents’ trust spatiotemporally and, indirectly, to study the level of social (geo)participation in a smart city. The devised system, whose test implementation as an agent-based system was done in the GAMA: agent-based, spatially explicit, modeling and simulation platform, was tested on both model and real data. The results obtained for the model city and the capital of Poland, Warsaw, indicate the significant and interdisciplinary analytical and scientific potential of the authorial methodology in the domain of geospatial science, geospatial data models with multi-agent systems, spatial planning, and applied social sciences.

We introduce the concept of evolutionary coalitional games played in a large population. The members of the population play a strategy chosen from a finite set and interact in randomly formed coalitions. The interactions are described by a multiplayer strategic game. Each coalition generates a total utility, identified with the value of the coalition, and equal to the sum of the payoffs of its all members from the multiplayer game. The total utility is distributed among the coalition members, proportionally to their Shapley values. Evolution of the whole population is governed by the replicator equations. Polymorphic stationary states of the population are studied for various types of the multiplayer social dilemma games. It is argued that application of coalitional game theory solution concepts to social dilemma models of evolutionary game theory can foster cooperation in the long run.

We propose an axiomatic derivation and a classification of multiperson social dilemma games. For the two-person symmetric games, the axiomatization leads to three types of the social dilemmas only: the Prisoner’s Dilemma (PD) game, the Chicken (Snowdrift) game and the Stag Hunt game. The popular multiperson games, such as for example the N-person PD, the Public Goods, the Tragedy of the Commons, the Volunteer’s Dilemma and the Assurance game, are included in the proposed frame. For general social dilemma games with arbitrary payoffs, their simple classification is proposed, based on the number of stable equilibria of the corresponding replicator dynamics.