Imperfect Imitation Can Enhance Cooperation

The promotion of cooperation on spatial lattices is an important issue in evolutionary game theory. This effect clearly depends on the update rule: it diminishes with stochastic imitative rules whereas it increases with unconditional imitation. To study the transition between both regimes, we propose a new evolutionary rule, which stochastically combines unconditional imitation with another imitative rule. We find that, surprinsingly, in many social dilemmas this rule yields higher cooperative levels than any of the two original ones. This nontrivial effect occurs because the basic rules induce a separation of timescales in the microscopic processes at cluster interfaces. The result is robust in the space of 2x2 symmetric games, on regular lattices and on scale-free networks.Comment: 4 pages, 4 figure

Evolutionary Dynamics of Populations with Conflicting Interactions: Classification and Analytical Treatment Considering Asymmetry and Power

Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination or cooperation of interacting entities will occur, be it spins, particles, bacteria, animals, or humans. Here, we analyze the case, where the entities are heterogeneous, particularly the case of two populations with conflicting interactions and two possible states. For such systems, explicit mathematical formulas will be determined for the stationary solutions and the associated eigenvalues, which determine their stability. In this way, four different types of system dynamics can be classified, and the various kinds of phase transitions between them will be discussed. While these results are interesting from a physics point of view, they are also relevant for social, economic, and biological systems, as they allow one to understand conditions for (1) the breakdown of cooperation, (2) the coexistence of different behaviors ("subcultures"), (2) the evolution of commonly shared behaviors ("norms"), and (4) the occurrence of polarization or conflict. We point out that norms have a similar function in social systems that forces have in physics

Social and strategic imitation: the way to consensus

Humans do not always make rational choices, a fact that experimental economics is putting on solid grounds. The social context plays an important role in determining our actions, and often we imitate friends or acquaintances without any strategic consideration. We explore here the interplay between strategic and social imitative behaviors in a coordination problem on a social network. We observe that for interactions in 1D and 2D lattices any amount of social imitation prevents the freezing of the network in domains with different conventions, thus leading to global consensus. For interactions in complex networks, the interplay of social and strategic imitation also drives the system towards global consensus while neither dynamics alone does. We find an optimum value for the combination of imitative behaviors to reach consensus in a minimum time, and two different dynamical regimes to approach it: exponential when social imitation predominates, and power-law when strategic considerations dominate.Comment: 13 pages, 5 figures. Submitted to Scientific Report

Power struggles and gender discrimination in the workplace

This study explores the impact of power struggles on the emergence of gender discrimination within the organizational culture. Utilizing an agent-based model, we simulate power struggles as an asymmetric hawk and dove game where agents may categorize their opponents based on their observable traits to make effective decisions. Our model includes two categories: prestigious education and sex, with prestigious education having higher struggling power. We examine three categorization strategies: fine-grained, regular-grained, and coarse-grained categorization. Our results indicate that fine-grained categorizers gain an advantage when the cost of fighting is low. In contrast, coarse-grained categorizers become more peaceful, leading to an advantage when the cost of fighting is high. Our simulation reveals that although there is no meaningful difference between sexes, different behaviors emerge when fine-categorizing agents dominate

Evolutionary Matrix-Game Dynamics Under Imitation in Heterogeneous Populations

Decision-making individuals often imitate their highest-earning fellows rather than optimize their own utilities, due to bounded rationality and incomplete information. Perpetual fluctuations between decisions have been reported as the dominant asymptotic outcome of imitative behaviors, yet little attempt has been made to characterize them, particularly in heterogeneous populations. We study a finite well-mixed heterogeneous population of individuals choosing between the two strategies, cooperation, and defection, and earning based on their payoff matrices that can be unique to each individual. At each time step, an arbitrary individual becomes active to update her decision by imitating the highest earner in the population. We show that almost surely the dynamics reach either an equilibrium state or a minimal positively invariant set, a \emph{fluctuation set}, in the long run. In addition to finding all equilibria, for the first time, we characterize the fluctuation sets, provide necessary and sufficient conditions for their existence, and approximate their basins of attraction. We also find that exclusive populations of individuals playing coordination or prisoner's dilemma games always equilibrate, implying that cycles and non-convergence in imitative populations are due to individuals playing anticoordination games. Moreover, we show that except for the two extreme equilibria where all individuals play the same strategy, almost all other equilibria are unstable as long as the population is heterogeneous. Our results theoretically explain earlier reported simulation results and shed new light on the boundedly rational nature of imitation behaviors

On the Imitation Strategy for Games on Graphs

In evolutionary game theory, repeated two-player games are used to study strategy evolution in a population under natural selection. As the evolution greatly depends on the interaction structure, there has been growing interests in studying the games on graphs. In this setting, players occupy the vertices of a graph and play the game only with their immediate neighbours. Various evolutionary dynamics have been studied in this setting for different games. Due to the complexity of the analysis, however, most of the work in this area is experimental. This paper aims to contribute to a more complete understanding, by providing rigorous analysis. We study the imitation dynamics on two classes of graph: cycles and complete graphs. We focus on three well known social dilemmas, namely the Prisoner's Dilemma, the Stag Hunt and the Snowdrift Game. We also consider, for completeness, the so-called Harmony Game. Our analysis shows that, on the cycle, all four games converge fast, either to total cooperation or total defection. On the complete graph, all but the Snowdrift game converge fast, either to cooperation or defection. The Snowdrift game reaches a metastable state fast, where cooperators and defectors coexist. It will converge to cooperation or defection only after spending time in this state which is exponential in the size, n, of the graph. In exceptional cases, it will remain in this state indefinitely. Our theoretical results are supported by experimental investigations.Comment: 32 page

Emergence of cooperation in static networks - Evolutionary Dynamics of Coordination Games with Switching Costs

Brand loyalty is tightly connected with competition for market share between brands, as it describes consumers' willingness to maintain compatibility between subsequent purchases. Imposed by exogenous or endogenous factors, the reasons for brand loyalty can be summarized in the switching cost. However, consumers do not live in isolation, instead they influence and get influenced by peers. Especially if influence propagates via "word-of-mouth" and not direct marketing, peer pressure becomes invaluable as consumers reach for compatibility with other consumers. The evolution of market share competition can be described by coordination games played in networks over multiple periods. Consumers, acting as the players of the coordination game, contemplate the quality of the available choices while being susceptible at others' influence. By considering switching costs, inertia in their actions is also introduced. An important issue therefore arises - if the available choices are qualitatively similar, how do the switching costs in combination with network effects affect the competition outcome? In this thesis, we address this issue by introducing switching costs into the standard coordination game; the switching cost game thus describes potential losses inflicted on players by changing - switching - strategies. We particularly concentrate our efforts on the proportions of strategies at equilibrium. Compared to the cost-free game, the switching costs are responsible for the emergence of a coexistence region where all available strategies coexist in equilibrium. Numerical results on various network structures verified the coexistence outcome, along with the effect of cost values and their symmetry on the determination of the coexistence limits. Next, we investigate the monotonicity of the competition evolution. We exploit the monotonous behaviour of the switching cost game limiting cases over time to draw an analogy with bootstrap percolation and benefit from existing analytical methods to calculate their final outcome and create bounds of the general case. We also show how these bounds depend on the switching costs. Finally, we examine the effects of switching costs on the critical behaviour of the system by studying the properties of stable clusters.Open Acces