We construct Cournot games with limited demand, resulting into capped sales volumes according to the respective production shares of the players. We show that such games admit three distinct equilibrium regimes, including an intermediate regime that allows for a range of possible equilibria. When information on demand is modeled by a delayed diffusion process, we also show that this intermediate regime collapses to a single equilibrium while the other regimes approximate the deterministic setting as the delay tends to zero. Moreover, as the delay approaches zero, the unique equilibrium achieved in the stochastic case provides a way to select a natural equilibrium within the range observed in the no lag setting. Numerical illustrations are presented when demand is modeled by an Ornstein–Uhlenbeck process and price is an affine function of output.

中文翻译：

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需求有限的古诺游戏：从多重均衡到随机均衡

我们构建需求有限的古诺（Cournot）游戏，从而根据玩家各自的生产份额限制了销量。我们证明，此类博弈接受三种不同的均衡机制，其中包括允许一系列可能均衡的中间机制。当通过延迟扩散过程对需求信息进行建模时，我们还表明，当延迟趋于零时，该中间状态崩溃到单个平衡，而其他状态近似确定性设置。此外，当延迟接近零时，在随机情况下获得的唯一平衡提供了一种在无滞后设置下观察到的范围内选择自然平衡的方法。当需求通过Ornstein–Uhlenbeck过程建模且价格是产出的仿射函数时，将提供数字插图。