<p>No-regret learning has been widely used to compute a Nash equilibrium in two-person zero-sum games. However, there is still a lack of regret analysis for network stochastic zero-sum games, where players competing in two subnetworks only have access to some local information, and the cost functions are subject to stochastic uncertainty. Such a game model can be found in network interdiction problems, when a group of inspectors work together to detect a group of evaders. In this paper, the authors propose a distributed stochastic mirror descent (D-SMD) method, and establish the regret bounds <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O({\sqrt T})\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>O</mi> <mo stretchy="false">(</mo> <mrow> <msqrt> <mi>T</mi> </msqrt> </mrow> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> and <i>O</i>(log <i>T</i>) in the expected sense for convex-concave and strongly convex-strongly concave costs, respectively. The proposed bounds match those of the best known first-order online optimization algorithms. The authors then prove the convergence of the time-averaged iterates of D-SMD to the set of Nash equilibria. Finally, the authors show that the actual iterates of D-SMD almost surely converge to the Nash equilibrium in the strictly convex-strictly concave setting.</p>