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.

We consider a transportation station, where customers arrive according to a Poisson process, observe the delay information and the fee imposed by the administrator and decide whether to use the facility or not. A transportation facility visits the station according to a renewal process and serves all present customers at each visit. We assume that every customer maximizes her individual expected utility and the administrator is a profit maximizer. We model this situation as a two‐stage game among the customers and the administrator, where customer strategies depend on the level of delay information provided by the administrator. We consider three cases distinguished by the level of delay information: observable (the exact waiting time is announced), unobservable (no information is provided) and partially observable (the number of waiting customers is announced). In each case, we explore how the customer reward for service, the unit waiting cost, and the intervisit time distribution parameters affect the customer behavior and the fee imposed by the administrator. We then compare the three cases and show that the customers almost always prefer to know their exact waiting times whereas the administrator prefers to provide either no information or the exact waiting time depending on system parameters.

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