Nash game in which firms decide if they will allow debts to be rolled forward in time. In such a setting, if we include a delay for payment due to, e.g., bankruptcy court so that defaulting firms do not pay any obligations until after the terminal time $T$, then the optimal strategy for all firms (up until the terminal time $T$) would be to always allow other firms to roll all debts forward so as to maximize payments.

\[ass:initial\] Before the time of interest, all firms are solvent and liquid. That is, $V_i(-1) \geq 0$ for all firms $i \in {\mathcal{N}}_0$.

We can now construct the total liabilities and relative liabilities at time $t \in {\mathbb{T}}$ as $$\begin{aligned}
\bar p_i(t,V_{t-1}) &:= \sum_{j \in {\mathcal{N}}_0} L_{ij}(t) + V_i(t-1)^-\\
\pi_{ij}(t,V_{t-1}) &:= \begin{cases} \frac{L_{ij}(t) + \pi_{ij}(t-1,V_{t-2})V_i(t-1)^-}{\bar p_i(t,V_{t-1})} &\text{if } \bar p_i(t,V_{t-1}) > 0 \\ \frac{1}{n} &\text{if } \bar p_i(t,V_{t-1}) = 0, \; j \neq i\\ 0 &\text{if } \bar p_i(t,V_{t-1}) = 0, \; j = i \end{cases} \quad \forall i,j \in {\mathcal{N}}_0.\end{aligned}$$ In this way, coupled with the accumulation of positive equity over time, the clearing wealths must satisfy the following fixed point problem in time $t$ wealths: $$\label{eq:EN-discrete}
V(t) = V(t-1)^+ + 