Studying Real Options with Genetic Algorithms

Mathematically oriented microeconomic research has contributed enormously to the understanding of economic behavior and the functioning of markets and institutions. However, theoretical as well as applied microeconomic studies may be driven too much by mathematical feasibility. An illustrative example is the real options approach which says that economic flexibility has a (monetary) value under conditions of uncertainty and irreversibility. According to the real options approach, irreversible investments require under certain conditions much higher returns (or trigger prices for the outputs) than traditional investment criteria suggest. Even though the idea of valuing options is quite intuitive and has a long tradition of practical use in finance and in stock markets, only a few decades ago microeconomists have begun to consider options as relevant for real investments, too. To some extent these shortcomings can be explained by the limited algebraic opportunities to use the real options approach. For instance, closed analytical solutions only exist if variables follow a geometric Brownian motion. All other processes require numerical approximations. Surely, this is the main reason why present research on real options is strongly focused on processes that consider geometric Brownian motion (cf. Dixit/Pindyk 1994). The purpose of this paper is to present and to discuss genetic algorithms (GA) as an alternative to analytical approaches for studying real options. GA are a heuristic optimization technique from artificial intelligence. GA utilize some well known mechanisms of natural evolution - such as selection, crossover, and mutation - which are repeatedly applied to a set (population) of solutions to the problem. A fundamental advantage of using GA for complex problems is the low prerequisites: Essentially, one just needs to specify the variables to be optimized, an environment for their evaluation, and the respective GA operators. We demonstrate the applicability for two types of problems with relevance to real options. Firstly, we apply GA to dynamic investment problems of a single firm, such as investments in hog production. Purpose is to demonstrate that a GA approach allows to solve many real options problems which are difficult to study analytically or by conventional real options techniques. For instance we show the applicability to various stochastic processes, interrelated investment options, etc. Secondly, we study competition of a number of agents (firms) having the opportunity to invest into a dynamic market. The agents use social-mimicry GA learning to determine Nash equilibrium strategies for their investments. We assume an isoelastic demand curve for a non-storable good. The demand curve is shifted randomly. Time is considered discrete and there is a time lag between any investment decision and the starting time of production (time to build). We find that competing firms invest at significantly lower trigger prices than in the monopolistic case. This result deviates from Dixit/Pindyk (1994) who argue for a continuous time model without time to build that competition has no impact on the trigger price. The explanation for the different results is that the production lag allows in some situations much higher output prices and makes it more attractive to enter production. Because real investments often need a significant period of time to establish production, we conclude that an agent-based GA approach allows in these cases a more realistic modeling of the firms' strategic interaction. In a further step we study the impacts of stabilization policies. We assume that the government ensures a minimum price for the producers, i.e. the periodical returns cannot fall below a certain share of the long-run production costs. We find that a stabilization policy may even lead to critical trigger prices that are below the production costs. Accordingly, stabilization policies may cause severe overproduction and thus inefficiency. REFERENCE DIXIT, A.; PINDYCK, R. (1994): Investment under Uncertainly. Princeton University Press, Princeton.