Abstract
This paper studies the $\alpha-$double auction in Xu et al. (2014) and extends their results to the case where $\alpha$ is time-varying in a manner governed by a time non-homogeneous Markov chain specified in Ram et al. (2009) over a set of states defined by $R\equiv\{\alpha_1, \alpha_2, \cdots, \alpha_r\}$, $0\le \alpha_1
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