Answer to Question #138190 in Economics for Dhritabrata Paul

Question

Three firms are considering whether to participate for the invention of a spaceship. The firms differ in their ability in research: firm 1 has ability a1 = 3, firm 2 has ability a2 = 2, and firm 3 has ability a3 = 1. They need to make decisions simultaneously, and each of them makes a binary choice: participate or not participate. For a participating firm i, the probability that it succeeds first is a/(2+3ja), where j is an arbitrary participating firm. For example, if firms 1 and 2 participate, then firm 1 will succeed first with probability 3/(2+3+2) = 3/7, and firm 2 will succeed first with probability 2/(2+3+2) = 2/7, and no one will succeed with the remaining probability 2/7. Whoever succeeds first earns a reward of value 80.Find Nash Equilibrium of this game.

Answer 1

In this case, if only two firms participate, there will be no NASH equilibrium , since someone will be the first, and no one else will be able to achieve success with the remaining probability.

Therefore, it is necessary that three companies participate at once at the same time.

Therefore, it is necessary that three firms participate at once simultaneously, then the probabilities will be 3/8 , 2/8, 1/8, respectively. Each firm will be the first in 75%, 25% - no one will succeed