Abstract: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 stu… Show more
“…These results hold for any symmetric game in which the pay-offs for mutual cooperation are greater than those for mutual defection. This battle and harmony of messages has been reported in the simulation work [ 34 ], but in a death–birth process and different game set-up. Figure 2.…”
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.
“…These results hold for any symmetric game in which the pay-offs for mutual cooperation are greater than those for mutual defection. This battle and harmony of messages has been reported in the simulation work [ 34 ], but in a death–birth process and different game set-up. Figure 2.…”
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.
“…P. Ramazi is with Statistical and Mathematical Sciences Department, University of Alberta, Canada and M. Cao is with ENTEG, Faculty of Science and Engineering, University of Groningen, The Netherlands, p.ramazi@gmail.com, m.cao@rug.nl attention since it is a powerful tool in understanding the evolution of cooperation among selfish individuals as reported by biologists, sociologists, economists, etc [21]- [26]. Researchers have found that network topology [27], phenotypic interactions [28], [29], punishment [30], population heterogeneity [31], as well as other components in game setups can all affect the success of cooperators in face of defectors. One stimulating mechanism for the evolution of cooperation that is generally believed to promote cooperation, especially in human societies [32], is direct reciprocity [33].…”
To understand the emergence and sustainment of cooperative behavior in interacting collectives, we perform global convergence analysis for replicator dynamics of a large, wellmixed population of individuals playing a repeated snowdrift game with four typical strategies, which are always cooperate (ALLC), tit-for-tat (TFT), suspicious tit-for-tat (STFT) and always defect (ALLD). The dynamical model is a three-dimensional ODE system that is parameterized by the payoffs of the base game. Instead of routine searches for evolutionarily stable strategies and sets, we expand our analysis to determining the asymptotic behavior of solution trajectories starting from any initial state, and in particular show that for the full range of payoffs, every trajectory of the system converges to an equilibrium point. What enables us to achieve such comprehensive results is studying the dynamics of two ratios of the state variables, each of which either monotonically increases or decreases in the half-spaces separated by their corresponding planes. The convergence results highlight three findings that are of particular importance for understanding the cooperation mechanisms among self-interested agents playing repeated snowdrift games. First, the inclusion of TFT-and STFT-players, the two types of conditional strategy players in the game, increases the share of cooperators of the overall population compared to the situation when the population consists of only ALLC-and ALLD-players. This confirms findings in biology and sociology that reciprocity may promote cooperation in social collective actions, such as reducing traffic jams and division of labors, where each individual may gain more to play the opposite of what her opponent chooses. Second, surprisingly enough, regardless of the payoffs, there always exists a set of initial conditions under which ALLC players do not vanish in the long run, which does not hold for all the other three types of players. So an ALLC-player, although perceived as the one that can be easily taken advantage of in snowdrift games, has certain endurance in the long run. Third, the parametric framework makes it possible to actually control the final population shares, a challenging topic in population dynamics, by tuning the payoffs of the base game.
“…The primary innovation of evolutionary game theory is that rather than assuming high levels of rationality in individual choices, perhaps a questionable assumption even for humans, strategies and behaviors propagate through populations via dynamic processes. In the biological world, this propagation is manifested through survival of the fittest and reproductive processes, which are widely modeled using population dynamics [1,7,8]. Systems of first-order differential equations such as replicator dynamics (RD) provide an elegant and powerful means to investigate collective behaviors, assuming infinite and well-mixed populations.…”
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