A Stochastic Competitive R&D Race Where “Winner Takes All”

Abstract

The paper considers a race among multiple firms that compete over the development of a product. The first firm to complete the development gains a reward, whereas the other firms gain nothing. Each firm decides how much to invest in developing the product, and the time it completes the development is a random variable that depends on the investment level. The paper provides a method for explicitly computing a unique Nash equilibrium, parametrically in the interest rate; for a given interest rate, the Nash equilibrium is determined in time that is linear in the number of firms. The structure of the solution yields insights about the behavior of the participants. Furthermore, an explicit expression for a unique globally optimal solution is obtained and compared to the unique Nash equilibrium.

NPD project portfolio selection using reinvestment strategy in competitive environment

“…ain focus of analysis Key Tools (Gerchak & Parlar, 1999) The competitive situation between two firms for resource allocation on limited R&D projects Game theory (Souza, 2004) The competition between two firms for introducing new products to market Game theory (Chao & Kavadias, 2008) Balance between incremental and radical innovations for developing right new products in portfolio Strategic Bucket (Golany & Rothblum, 2008) Investments in development projects within competitive environments under uncertainty Linear Programming (Solak et al, 2010) (Wei & Chang, 2011) Uncertainty and impact of several criteria on decision making for selecting new products Fuzzy Linear Programming (Canbolat et al, 2012) A race among multiple firms that compete over the development of a product Game theory (Belenky, 2012) Reinvesting during time horizon in project portfolio selection Boolean Programming (Wang & Yang, 2012) Managerial flexibility in an innovative R&D project Real Options (Lin & Zhou, 2013) The Cross-market effect on R&D project portfolio Game theory (Hassanzadeh et al, 2014) Imprecise information in objective of R&D project selection Robust Optimization (Jafarzadeh et al, 2015) Flexible time horizon considering reinvestment in project selection Integer Programming (Kettunen et al, 2015) Managerial flexibility for developing new product in competitive environment Dynamic Programming (Wang & Song, 2016) Time-dependent budget on reinvestment strategy Integer Programming…”

“…This approach holds unnecessary details about the problem and makes it more complex. In other studies, game theory is a major helpful tool (Canbolat et al, 2012;Etro, 2007;Imai & Watanabe, 2006). Due to the changeable conditions of the environment and for avoiding the complexity of the problem, we applied the expected value concept to actualize the competitive environment.…”

Constant risk aversion in stochastic contests with exponential completion times

“…A primary application arena for this model is the competition in R&D markets involving technology‐intensive products and processes. As suggested in , companies operating in such markets make decisions whether to invest or not to invest in a project that will require a substantial payment and take an uncertain amount of time. Furthermore, some projects will be attractive to several companies in the market, so any company that chooses to invest in them will face a competitive situation where often the first one to develop the product or the process will have the advantage in the market.…”

“…For example, Bilgiç and Güllü prove the existence of a Nash equilibrium for their model of an innovation race (where the winner does not necessarily take all) between two risk‐neutral players when completion times are generally distributed; however, they assume exponentially distributed completion times to investigate the properties of this equilibrium. Gerchak and Kilgour argue that assuming an exponential distribution is reasonable in situations “where success is rare, where promising ideas or designs often turn out to be ‘infeasible,’ and where higher levels of success are increasingly unlikely.” The application of the model described in this article to R&D races and its relation to the existing literature is discussed further in . The purpose of this article is to introduce risk aversion into a model where involved parties have conflicting interests and large sums of money are at stake.…”

New product development flexibility in a competitive environment

“…What is not yet fully known, however, is how the value of flexibility in NPD is influenced by the competitive environment in which a firm operates. Some of the previous works (Canbolat et al 2012, Chronopoulos et al 2014 have employed game theoretical approaches to account for the competitive market environment when valuing NPD flexibilities. Whilst game theoretical approaches can be effective in dealing with duopoly markets with homogenous players, they may not be easily extendable for markets with several firms that are heterogeneous in their development capabilities, assets, and strategic development goals.…”