Evolutionary stable strategies in networked games: the influence of topology

Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a population. If a strategy is weak evolutionarily stable, the competing strategy may manage to survive within the network. Understanding the network-related factors that affect the evolutionary stability of a strategy would be critical in making accurate predictions about the behaviour of a strategy in a real-world strategic decision making environment. In this work, we evaluate the effect of network topology on the evolutionary stability of a strategy. We focus on two well-known strategies known as the Zero-determinant strategy and the Pavlov strategy. Zero-determinant strategies have been shown to be evolutionarily unstable in a well-mixed population of players. We identify that the Zero-determinant strategy may survive, and may even dominate in a population of players connected through a non-homogeneous network. We introduce the concept of `topological stability' to denote this phenomenon. We argue that not only the network topology, but also the evolutionary process applied and the initial distribution of strategies are critical in determining the evolutionary stability of strategies. Further, we observe that topological stability could affect other well-known strategies as well, such as the general cooperator strategy and the cooperator strategy. Our observations suggest that the variation of evolutionary stability due to topological stability of strategies may be more prevalent in the social context of strategic evolution, in comparison to the biological context

Social Network Reciprocity as a Phase Transition in Evolutionary Cooperation

In Evolutionary Dynamics the understanding of cooperative phenomena in natural and social systems has been the subject of intense research during decades. We focus attention here on the so-called "Lattice Reciprocity" mechanisms that enhance evolutionary survival of the cooperative phenotype in the Prisoner's Dilemma game when the population of darwinian replicators interact through a fixed network of social contacts. Exact results on a "Dipole Model" are presented, along with a mean-field analysis as well as results from extensive numerical Monte Carlo simulations. The theoretical framework used is that of standard Statistical Mechanics of macroscopic systems, but with no energy considerations. We illustrate the power of this perspective on social modeling, by consistently interpreting the onset of lattice reciprocity as a thermodynamical phase transition that, moreover, cannot be captured by a purely mean-field approach.Comment: 10 pages. APS styl

Advances towards a General-Purpose Societal-Scale Human-Collective Problem-Solving Engine

Human collective intelligence has proved itself as an important factor in a society's ability to accomplish large-scale behavioral feats. As societies have grown in population-size, individuals have seen a decrease in their ability to activeily participate in the problem-solving processes of the group. Representative decision-making structures have been used as a modern solution to society's inadequate information-processing infrastructure. With computer and network technologies being further embedded within the fabric of society, the implementation of a general-purpose societal-scale human-collective problem-solving engine is envisioned as a means of furthering the collective-intelligence potential of society. This paper provides both a novel framework for creating collective intelligence systems and a method for implementing a representative and expertise system based on social-network theory.Comment: Collective Problem Solving Theory and Social-Network algorith

Beyond pairwise strategy updating in the prisoner's dilemma game

In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.Comment: 9 two-column pages, 5 figures; accepted for publication in Scientific Report

Network effects in a human capital based economic growth model

We revisit a recently introduced agent model[ACS {\bf 11}, 99 (2008)], where economic growth is a consequence of education (human capital formation) and innovation, and investigate the influence of the agents' social network, both on an agent's decision to pursue education and on the output of new ideas. Regular and random networks are considered. The results are compared with the predictions of a mean field (representative agent) model.Comment: to appear in Physica

Threshold games and cooperation on multiplayer graphs

Objective: The study investigates the effect on cooperation in multiplayer games, when the population from which all individuals are drawn is structured - i.e. when a given individual is only competing with a small subset of the entire population. Method: To optimize the focus on multiplayer effects, a class of games were chosen for which the payoff depends nonlinearly on the number of cooperators - this ensures that the game cannot be represented as a sum of pair-wise interactions, and increases the likelihood of observing behaviour different from that seen in two-player games. The chosen class of games are named "threshold games", and are defined by a threshold, $M > 0$, which describes the minimal number of cooperators in a given match required for all the participants to receive a benefit. The model was studied primarily through numerical simulations of large populations of individuals, each with interaction neighbourhoods described by various classes of networks. Results: When comparing the level of cooperation in a structured population to the mean-field model, we find that most types of structure lead to a decrease in cooperation. This is both interesting and novel, simply due to the generality and breadth of relevance of the model - it is likely that any model with similar payoff structure exhibits related behaviour. More importantly, we find that the details of the behaviour depends to a large extent on the size of the immediate neighbourhoods of the individuals, as dictated by the network structure. In effect, the players behave as if they are part of a much smaller, fully mixed, population, which we suggest an expression for.Comment: in PLOS ONE, 4th Feb 201