A Class of Evolutionary Models for Participation Games with Negative Feedback |
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Authors: | Pietro Dindo Jan Tuinstra |
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Affiliation: | 1.LEM, Scuola Superiore Sant’Anna,Pisa,Italy;2.Department of Quantitative Economics and CeNDEF, Faculty of Economics and Business,University of Amsterdam,Amsterdam,The Netherlands |
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Abstract: | We introduce a framework to analyze the interaction of boundedly rational heterogeneous agents repeatedly playing a participation
game with negative feedback. We assume that agents use different behavioral rules prescribing how to play the game conditionally
on the outcome of previous rounds. We update the fraction of the population using each rule by means of a general class of
evolutionary dynamics based on imitation, which contains both replicator and logit dynamics. Our model is analyzed by a combination
of formal analysis and numerical simulations and is able to replicate results from the experimental and computational literature
on these types of games. In particular, irrespective of the specific evolutionary dynamics and of the exact behavioral rules
used, the dynamics of the aggregate participation rate is consistent with the symmetric mixed strategy Nash equilibrium, whereas
individual behavior clearly departs from it. Moreover, as the number of players or speed of adjustment increase the evolutionary
dynamics typically becomes unstable and leads to endogenous fluctuations around the steady state. These fluctuations are robust
with respect to behavioral rules that try to exploit them. |
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