The authors study a model of the dynamic provision of funds to projects that generate public profits. It is described in the form of a discrete-time $n$-person game with the following structure: Each player $i$ chooses an amount $z_i(t)$ as his contribution of private good to a public project in each period $t = 0, 1, \ldots$. Contributions are nonrefundable, and they cannot be made after a fixed contributing horizon $T\leq \infty$. For $t\leq T$ any $z_i(t)$ is feasible, and only $z_i = 0$ is feasible in period $t>T$. At any period $t$, the knowledge of a player $i$ is $(z_i(\tau)$, $Z(\tau))_{\tau=0}^{t-1}$, where $Z(\tau)=\sum_{j=1}^n z_j(\tau)$. The payoff (total benefit) function of a player $i$ depends on the entire sequence contribution of all players, $z = \{z_i(t): 1 \leq i \leq n, t=0,1,\ldots \}$, by the formula: $U_i(z) = f_i(X(T)) - x_i(T)$, where $x_i(T)=\sum_{t\leq T}z_i(t)$, $X(T)=\sum_{i=1}^n x_i(T)$ and each $f_i(X)$ is considered to be a linear function for $X<X^*$ and constant for $X\geq X^*$ with a fixed point $X^*$. For such a game, Nash equilibria, Markov perfect equilibria and perfect Bayesian equilibria are widely discussed in terms of their existence and structure.