How feeling betrayed affects cooperation.
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Then we analyze the evolution of cooperation in a well-mixed population of agents, each of whom is associated with such a payoff matrix.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.
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Affiliation: ENgineering and TEchnology institute Groningen (ENTEG), Faculty of Mathematics and Natural Sciences, University of Groningen, Groningen, The Netherlands.
ABSTRACT
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. No MeSH data available. Related in: MedlinePlus |
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Mentions: One of the simplest functions one can imagine for b is a linear function of nD:b(nC,nD)=a1-a2nDfor some real parameter a1 and a positive a2. In this case, the betrayal would be a strictly decreasing function, which means that the probability that the corresponding agent will cooperate after many encounters with defectors tends to zero. One problem with such a function is that the betrayal of the agent gets affected equally after meeting a defector for the first time or for several times. However, in ‘reality’ it is more probable that the first negative encounter really touches an agent’s feelings, but after a while, the agent numbs and gets used to being defected upon and will start to defect as well. So it would be more realistic to choose a negative exponential function for b:b(nC,nD)=a1e-a2nDwhere a1 and a2 are positive. Now the first encounters with a defector have a large negative effect; however, as nD increases further, that is to meet more defectors, the magnitude of b slowly tends to zero. The exponential curve of b for parameters a1 and a2 set to 1 is depicted in Fig 9. The main problem with such an exponential function is that no matter how many times an agent encounters a cooperator, her betrayal increases, and hence, her willingness to cooperate decreases by increments in meeting defectors. Based on the fact that someone’s willingness to cooperate can both grow and diminish over time, we modify the above function to capture the effect of meeting cooperators as in the followingb(nC,nD)=a1e-a2nDnC+nD+a3nCnC+nD.(20)As emotions fade over time and are put in perspective as an agent gains experience, we moderate the emotions by the total number of games that the agent has played, nC + nD. The effect of each of the encounters can be enlarged or diminished by the variables a2 and a3. |
View Article: PubMed Central - PubMed
Affiliation: ENgineering and TEchnology institute Groningen (ENTEG), Faculty of Mathematics and Natural Sciences, University of Groningen, Groningen, The Netherlands.
No MeSH data available.