We study a continuous-time problem of public good contribution under uncertainty for an economy with a finite number of agents. Each agent aims to maximize his expected utility allocating his initial wealth over a given time period between private consumption and repeated but irreversible...

We study a continuous-time problem of optimal public good contribution under uncertainty for an economy with a finite number of agents. Each agent can allocate his wealth between private consumption and repeated but irreversible contributions to increase the stock of some public good. We study...

We study a continuous-time problem of optimal public good contribution under uncertainty for an economy with a finite number of agents. Each agent can allocate his wealth between private consumption and repeated but irreversible contributions to increase the stock of some public good. We study...

In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous—time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a...

In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous- time analogue of the same mapping has been studied even earlier by Brown and von Neumann. This differential equation has recently been suggested as a plausible...

Brown and von Neumann introduced a dynamical system that converges to saddle points of zero sum games with finitely many strategies. Nash used the mapping underlying these dynamics to prove existence of equilibria in general games. The resulting Brown--von Neumann--Nash dynamics are a benchmark...

Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the...

We introduce a notion of subgames for stochastic timing games and the related notion of subgame-perfect equilibrium in possibly mixed strategies. While a good notion of subgame-perfect equilibrium for continuous-time games is not available in general, we argue that our model is the appropriate...

Knightian uncertainty leads naturally to nonlinear expectations. We introduce a corresponding equilibrium concept with sublinear prices and establish their existence. In general, such equilibria lead to Pareto inefficiency and coincide with Arrow-Debreu equilibria only if the values of net...

This paper develops a general theory of irreversible investment of a single firm that chooses a dynamic capacity expansion plan in an uncertain environment. The model is set up free of any distributional or any parametric assumptions and hence encompasses all the existing models. As the first...