Coordination and equilibrium selection in games: the role of local effects

Criminal organizations exhibit hysteresis, resilience, and robustness by balancing security and efficiency

The interplay between (criminal) organizations and (law enforcement) disruption strategies is critical in criminology and social network analysis. Like legitimate businesses, criminal enterprises thrive by fulfilling specific demands and navigating their unique challenges, including balancing operational visibility and security. This study aims at comprehending criminal networks' internal dynamics, resilience to law enforcement interventions, and robustness to changes in external conditions. Using a model based on evolutionary game theory, we analyze these networks as collaborative assemblies of roles, considering expected costs, potential benefits, and the certainty of expected outcomes. Here, we show that criminal organizations exhibit strong hysteresis effects, with increased resilience and robustness once established, challenging the effectiveness of traditional law enforcement strategies focused on deterrence through increased punishment. The hysteresis effect defines optimal thresholds for the formation or dissolution of criminal organisation. Our findings indicate that interventions of similar magnitude can lead to vastly different outcomes depending on the existing state of criminality. This result suggests that the relationship between stricter punishment and its deterrent effect on organized crime is complex and sometimes non-linear. Furthermore, we demonstrate that network structure, specifically interconnectedness (link density) and assortativity of specialized skills, significantly influences the formation and stability of criminal organizations, underscoring the importance of considering social connections and the accessibility of roles in combating organized crime. These insights contribute to a deeper understanding of the systemic nature of criminal behavior from an evolutionary perspective and highlight the need for adaptive, strategic approaches in policy-making and law enforcement to disrupt criminal networks effectively.

Evolutionary games on multilayer networks: coordination and equilibrium selection

We study mechanisms of synchronisation, coordination, and equilibrium selection in two-player coordination games on multilayer networks. We investigate three possible update rules: the replicator dynamics (RD), the best response (BR), and the unconditional imitation (UI). Players interact on a two-layer random regular network. The population on each layer plays a different game, with layer I preferring the opposite strategy to layer II. We measure the difference between the two games played on the layers by a difference in payoffs, and the inter-connectedness by a node overlap parameter. We discover a critical value of the overlap below which layers do not synchronise, i.e. they display different levels of coordination. Above this threshold both layers typically coordinate on the same strategy. Surprisingly, there is a symmetry breaking in the selection of equilibrium-for RD and UI there is a phase where only the payoff-dominant equilibrium is selected. It is not observed, however, for BR update rule. Our work is an example of previously observed differences between the update rules. Nonetheless, we took a novel approach with the game being played on two inter-connected layers. As we show, the multilayer structure enhances the abundance of the Pareto-optimal equilibrium in coordination games with imitative update rules.

Deterministic and stochastic cooperation transitions in evolutionary games on networks

Although the cooperative dynamics emerging from a network of interacting players has been exhaustively investigated, it is not yet fully understood when and how network reciprocity drives cooperation transitions. In this work, we investigate the critical behavior of evolutionary social dilemmas on structured populations by using the framework of master equations and Monte Carlo simulations. The developed theory describes the existence of absorbing, quasiabsorbing, and mixed strategy states and the transition nature, continuous or discontinuous, between the states as the parameters of the system change. In particular, when the decision-making process is deterministic, in the limit of zero effective temperature of the Fermi function, we find that the copying probabilities are discontinuous functions of the system's parameters and of the network degrees sequence. This may induce abrupt changes in the final state for any system size, in excellent agreement with the Monte Carlo simulation results. Our analysis also reveals the existence of continuous and discontinuous phase transitions for large systems as the temperature increases, which is explained in the mean-field approximation. Interestingly, for some game parameters, we find optimal "social temperatures" maximizing or minimizing the cooperation frequency or density.

Network coevolution drives segregation and enhances Pareto optimal equilibrium selection in coordination games

In this work we assess the role played by the dynamical adaptation of the interactions network, among agents playing Coordination Games, in reaching global coordination and in the equilibrium selection. Specifically, we analyze a coevolution model that couples the changes in agents' actions with the network dynamics, so that while agents play the game, they are able to sever some of their current connections and connect with others. We focus on two action update rules: Replicator Dynamics (RD) and Unconditional Imitation (UI), and we define a coevolution rule in which, apart from action updates, with a certain rewiring probability p, agents unsatisfied with their current connections are able to eliminate a link and connect with a randomly chosen neighbor. We call this probability to rewire links the 'network plasticity'. We investigate a Pure Coordination Game (PCG), in which choices are equivalent, and on a General Coordination Game (GCG), for which there is a risk-dominant action and a payoff-dominant one. Changing the plasticity parameter, there is a transition from a regime in which the system fully coordinates on a single connected component to a regime in which the system fragments in two connected components, each one coordinated on a different action (either if both actions are equivalent or not). The nature of this fragmentation transition is different for different update rules. Second, we find that both for RD and UI in a GCG, there is a regime of intermediate values of plasticity, before the fragmentation transition, for which the system is able to fully coordinate on a single component network on the payoff-dominant action, i.e., coevolution enhances payoff-dominant equilibrium selection for both update rules.

Game modelling and stability strategy research on distributed leadership pattern: A tripartite evolutionary game perspective

Distributed leadership pattern has been a topic of growing interest in recent years, recognizing that much remains to be known about this phenomenon. The research on distributed leadership acknowledges that responsibility and power are not exclusively limited to one formal leader, but are distributed between formal and informal leaders. The decision-making behavior of team members plays a vital role in optimizing cooperation and team performance. Nevertheless, little attention is paid to investigating the underlying mechanisms about how people in a team cooperate to initiate effective interactions and enhance team performance. Game theory offers a comprehensive analysis of rational behavior under the circumstances of strategic interdependence. By organizing the formal leader, the informal leader, and the ordinary employee in a team, this study constructs a tripartite evolutionary game model and analyzes the internal mechanism of distributed leadership patterns. The study finds that the equilibrium of the three parties is affected by multiple factors. The simulation results reveal that the empowerment of the formal leader to the informal leader is indispensable to promoting optimal cooperation and team performance in distributed leadership patterns. These findings have theoretical implications for the distributed leadership literature and managerial implications for practitioners.