An Analysis Of Investment Under Uncertainty With Game Theory

The most essential difference between real options and financial options is that in most cases real options are not exclusive. In the early research of real options, they always put firms into a perfectly competitive or monopoly market. The outcomes potentially assume that firms need not consider strategic interactions of competitors when they make project decisions. But it is not the case in real world. When a firm has a project option, it cannot exclude another firm also has the same option. It implies that firms must consider competitors' behaviors while assessing investment value. Furthermore, sometimes influences of strategic interactions on the values of options are so huge that the traditional NPV are of in effect again. Obviously, only merging game theory and real options can make up the latter to provide a more accurate assessment of projects for the firms. In analysis of option games, we find out that after consideration of strategic interactions, influences of uncertainty of future profits of project on value of projects are consistent. Given other conditions, waiting value of real options increases with uncertainty. Another two kinds of uncertainties are discussed in this article. One is technological uncertainty in patent races, whose influences can be analyzed with a hazard rate following a Poisson distribution. Another is information uncertainty in a imperfect information game. The information that firms receive can weaken the influences of these two uncertainties. However, the increase of them can also postpone the investment timing, just like profits uncertainty does. Influences of strategic interactions on value of real options are first mover advantages (FMA) and second mover advantages (SMA). FMA arise when monopoly profits outweigh options value. The motive that two game players eager to be the leader makes them have to advance the investment timing to the preemption threshold, and could not assimilate options values completely. Since the article endogenously assumes that competitors enter the market rationally, in the preemption game there not only exist sequential equilibria, but also maybe arise simultaneous equilibria. So strategy of this game is not pure strategy but mixed strategy. Moreover, the probability of arising simultaneous equilibria increases with FMA. What to be noticed is that simultaneous strategy is inferior strategy. In the model of this article, SMA are from information spillover effects. Comparing with leader, follower could always get more information involved project. In the new market model of taking into account future technological improvements, arriving of information about new technology influences directly investment strategy of firms. And there will arise two different kinds of equilibria——preemption equilibria and wars of attrition. In the imperfect information model, to what extent to know the market situation depends on quantity and quality of received information. According to received information, firms modify their beliefs by Bayesian Rule. The magnitudes of modified beliefs dominate firms' investment strategies. Analysis indicates that the balance of FMA and SMA can change firms' investment strategies. More FMA cause firm try to enter market earlier and preemption equilibria arise. Otherwise, firms would not preempt so that follower could receive more information and wars of attrition arise. It could be seen whether preemption and wars of attrition will come forth inferior strategies two firms would not want to see. Individual rational leads to collectivity irrational. In all models discussed in this article, the magnitudes of investment costs positively correlate with option value. Whether considering strategic interactions or not, more investment costs correspond to more option value. It is because investment costs are (fully or partly) irreversible. But in the asymmetric firms model the cases are not so simple. It is shown that the relationship between the firm's value and the cost asymmetry is non-monotonic and discontinuous. The level of asymmetry causes three different kinds of equilibira arise in the game. At same time, this article also analyzes the relationshipbetween the cost asymmetry and social welfare. Consequently, influences of government policies on the economy are discussed. In the concluding part we discuss the optimal investment rule. For consideration of strategic interactions, there does not exist a single optimal rule. Traditional NPV method or real options could not assess the project value accurately under any circumstances. Given all other conditions, if FMA are bigger, NPV may be more efficient; otherwise, real options will be preferable. Finally, we prospect the future directions of research on the option games. All along, the impacts of game theory on real options are very huge, and it is very helpful for project value assessment accurately. If real options are very important modifications of traditional NPV method,the introduce of game theory is a huge ideaistic reformation of real options.