Irreversible investment in oligopoly
研究了寡头垄断市场中企业采用开放环策略进行资本积累的博弈，发现均衡时只有当前规模最小的企业进行投资，结果适用于任意初始资本和一般随机冲击过程。
We take a general perspective on capital accumulation games with open loop strategies, as they have been formalized by Back and Paulsen (Rev. Financ. Stud. 22, 4531-4552, 2009). With such strategies, the optimization problems of the individual players are of the monotone follower type. Consequently, one can adapt available methods, in particular the approach of Bank (SIAM J. Control Optim. 44, 1529-1541, 2005). We obtain consistency in equilibrium by proving that with common assumptions from the oligopoly literature on instantaneous revenue, equilibrium determination is equivalent to solving a single monotone follower problem. In the unique open loop equilibrium, only the currently smallest firms invest. This result is valid for arbitrary initial capital levels and general stochastic shock processes, which may be non-Markovian and include jumps. We explicitly solve an example, the specification of Grenadier (Rev. Financ. Stud. 15, 691-721, 2002) with a L,vy process.