Markovian α-Double Auctions

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 $R\equiv\{\alpha_1, \alpha_2, \cdots, \alpha_r\}$, $0\le \alpha_1<\alpha_2<\cdots<\alpha_r\le 1$. The convergence results in Xu et al. (2014) hold, with $\alpha$ replaced with the average $\alpha^*=\frac{1}{r}\sum_{\theta=1}^r \alpha_\theta$. We also identify the conditions under which the price process generated by such a Markovian $\alpha-$double auction converges to a Walrasian equilibrium of the underlying exchange economy. The assignment problem and an exchange economy with indivisible goods (Bikhchandani and Mamer 1997) typified by the noted job matching model in Kelso and Crawford (1982) are two examples covered by our convergence results. A number of simulations are conducted and these simulations show that the excess volatility in equity market may in part come from the use of double auction mechanisms