Analysis and Control of Strategic Interactions in Finite Heterogeneous Populations under Best-Response Update Rule

For a finite, well-mixed population of heterogeneous agents playing evolutionary games choosing to cooperate or defect in each round of the game, we investigate, when agents update their strategies in each round using the myopic best-response rule, how the number of cooperating agents changes over time and demonstrate how to control that number by changing the agents’ payoff matrices. The agents are heterogeneous in that their payoff matrices may differ from one another; we focus on the specific case when the payoff matrices, fixed throughout the evolution, correspond to prisoner’s dilemma or snowdrift games. To carry out stability analysis, we identify the system’s absorbing states when taking the number of cooperating agents as a random variable of interest. It is proven that when all the agents update frequently enough, the reachable final states are completely determined by the available types of payoff matrices. As a further step, we show how to control the final state by changing at the beginning of the evolution, the types of the payoff matrices of a group of agents

Homophily, heterophily and the diversity of messages among decision-making individuals

To better understand the intriguing mechanisms behind cooperation among decision-making individuals, we study the simple yet appealing use of preplay communication or cheap talk in evolutionary games, when players are able to choose strategies based on whether an opponent sends the same message as they do. So when playing games, in addition to pure cooperation and defection, players have two new strategies in this setting: homophilic (respectively, heterophilic) cooperation which is to cooperate (respectively, defect) only with those who send the same message as they do. We reveal the intrinsic qualities of individuals playing the two strategies and show that under the replicator dynamics, homophilic cooperators engage in a battle of messages and will become dominated by whichever message is the most prevalent at the start, while populations of heterophilic cooperators exhibit a more harmonious behaviour, converging to a state of maximal diversity. Then we take Prisoner's Dilemma (PD) as the base of the cheap-talk game and show that the hostility of heterophilics to individuals with similar messages leaves no possibility for pure cooperators to survive in a population of the two, whereas the one-message dominance of homophilics allows for pure cooperators with the same tag as the dominant homophilics to coexist in the population, demonstrating that homophilics are more cooperative than heterophilics. Finally, we generalize an existing convergence result on population shares associated with weakly dominated strategies to a broadly applicable theorem and complete previous research on PD games with preplay communication by proving that the frequencies of all types of cooperators, i.e. pure, homophilic and heterophilic, converge to zero in the face of defectors. This implies homophily and heterophily cannot facilitate the long-term survival of cooperation in this setting, which urges studying cheap-talk games under other reproduction dynamics

Evolutionary dynamics of homophily and heterophily

Most social interactions do not take place at random. In many situations, individuals choose their interaction partners on the basis of phenotypic cues. When this happens, individuals are often homophilic, that is, they tend to interact with individuals that are similar to them. Here we investigate the joint evolution of phenotypic cues and cue-dependent interaction strategies. By a combination of individual-based simulations and analytical arguments, we show that homophily evolves less easily than earlier studies suggest. The evolutionary interplay of cues and cue-based behaviour is intricate and has many interesting facets. For example, an interaction strategy like heterophily may stably persist in the population even if it is selected against in association with any particular cue. Homophily persisted for extensive periods of time just in those simulations where homophilic interactions provide a lower (rather than a higher) payoff than heterophilic interactions. Our results indicate that even the simplest cue-based social interactions can have rich dynamics and a surprising diversity of evolutionary outcomes

Asynchronous Decision-Making Dynamics Under Best-Response Update Rule in Finite Heterogeneous Populations

To study how sustainable cooperation might emerge among self-interested interacting individuals, we investigate the long-run behavior of the decision-making dynamics in a finite, well-mixed population of individuals, who play collectively over time a population game. Repeatedly each individual is activated asynchronously to update her decision to either cooperate or defect according to the myopic best-response rule. The game's payoff matrices, chosen to be those of either prisoner's dilemma or snowdrift games to underscore cooperation-centered social dilemmas, are fixed, but can be distinct for different individuals. So, the overall population is heterogeneous. We first classify such heterogeneous individuals into different types according to their cooperating tendencies stipulated by their payoff matrices. Then, we show that no matter what initial strategies the individuals decide to use, surprisingly one can always identify one type of individuals as a benchmark such that after a sufficiently long but finite time, individuals more cooperative compared to the benchmark always cooperate, while those less cooperative compared to the benchmark defect. When such fixation takes place, the total number of cooperators in the population either becomes fixed or fluctuates at most by one. Such insight provides theoretical explanation for some complex behavior recently reported in simulation studies that highlight the puzzling effect of individuals' heterogeneity on collective decision-making dynamics

How feeling betrayed affects cooperation

For a population of interacting self-interested agents, we study how the average cooperation level is affected by some individuals' feelings of being betrayed and guilt. We quantify these feelings as adjusted payoffs in asymmetric games, where for different emotions, the payoff matrix takes the structure of that of either a prisoner's dilemma or a snowdrift game. Then we analyze the evolution of cooperation in a well-mixed population of agents, each of whom is associated with such a payoff matrix. At each time-step, an agent is randomly chosen from the population to update her strategy based on the myopic best-response update rule. According to the simulations, decreasing the feeling of being betrayed in a portion of agents does not necessarily increase the level of cooperation in the population. However, this resistance of the population against low-betrayal-level agents is effective only up to some extend that is explicitly determined by the payoff matrices and the number of agents associated with these matrices. Two other models are also considered where the betrayal factor of an agent fluctuates as a function of the number of cooperators and defectors that she encounters. Unstable behaviors are observed for the level of cooperation in these cases; however, we show that one can tune the parameters in the function to make the whole population become cooperative or defective

A survey on the analysis and control of evolutionary matrix games

In support of the growing interest in how to efficiently influence complex systems of interacting self interested agents, we present this review of fundamental concepts, emerging research, and open problems related to the analysis and control of evolutionary matrix games, with particular emphasis on applications in social, economic, and biological networks. (C) 2018 Elsevier Ltd. All rights reserved