3. Equilibrium model for iron ore market 

In this section, a multi-sector mixed complementarity-based equilibrium model is built, we consider three major iron ore trade stakeholders, which are exporter, importer and carrier. To start, an overview of these stakeholders is conducted, followed by the definition of notations and finally we descript the model by modules.  

3.1 Overview of international iron ore trade stakeholders

In general, three major stakeholders can be recognized in international iron ore market, who are importers, exporters and carriers.
   It should be noticed that, port operator is also one of the stakeholders. It provides the cargo handling service for the importers/exporters, and ship berthing service for the carriers. Unlike above three stakeholders who are the independent decision makers in this model, we implicitly model the port in the cost function of importers, exporters and carriers.

3.2 Notations 

In this part, we discuss the sets of subscripts referring to variables in the model. Importer is denoted by \(c\in C,\) with \(C\) being the set of importers. Exporter is indexed by \(m\in M,\) with \(M\) being the set of exporters. In addition, destination port is denoted by \(d\in D(c)\) with \(D(c)\) being the set of destination port of importer \(c\in C.\) The origin port is indicated by \(o\in O(m)\) with \(O(m)\) being the set of origin ports of exporter \(m\in M.\) As each ship is an independent carrier in the shipping market, we can classify the carriers in term of ship sizes. For a certain carrier type (carriers with same ship size), we indicate it by \(k\in K\) with \(K\) being the set of carriers.
   Table 1-3 shows the relevant variables of the importer & exporter, the carrier, and the destination/origin port respectively. Table 4 gives the parameters. In this study, we clarify that a bar on a variable \(x\) (\(\overline{x}\)) indicates that the variable is exogenous.