[1] Customer loyalty and multi-stop shopping -with Jong Jae Lee 
      (Accepted in  Journal of Economic Theory and Econometrics) 

[ABSTRACT] This paper studies how customer loyalty impinges on the existence of a multi-stop shopping equilibrium. A particular focus lies on the pricing decisions of firms in two distinct modes of retail, the department store and the shopping mall. We show that a multi-stop shopping equilibrium exists, but the required level of customer loyalty exceeds the total traveling costs. This seemingly unnatural gap arises only to discourage the individual retailer of the shopping mall from raising the price independently, knowing that the loyal customers would not leave him easily.