Abstract
After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and offer an exact solution of our own. We also introduce a minor extension to the original game so that not only logical differences but also differences in action outcomes among those solutions become visible.
Highlights
The original version of social learning game is a problem with N learners in which each learner attempts to identify and act to the true status of a world, which is either in a state 1 with probability qext~0:5 or in another state {1 with probability 1{qext, from observing her own private signals and all previous learners’ actions (~aj{1~ða1a2 Á Á Á aj{1Þ) but without explicitly knowing the previous learners’ private signals (~sj{1~ðs1s2 Á Á Á sj{1Þ)
There is no solid mathematical foundation here to claim that this blind action-counting approach is the best or the exact solution, this approach is commonly used in analysis of the social learning games [2, 3, 6,7,8]
While we will provide a reason of the same action outcomes from the three solutions, we propose a minor extension of the social learning game, to which all the solutions, if proper to the original game, should be applicable as well
Summary
Data Availability: The authors confirm that all data underlying the findings are fully available without restriction. All relevant data are within the paper. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. After the social learning models were proposed, finding solutions to the games becomes a well-defined mathematical question. Almost all papers on the games and their applications are based on solutions built either upon an ad-hoc argument or a twisted Bayesian analysis of the games. We introduce a minor extension to the original game so that logical differences and differences in action outcomes among those solutions become visible
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