Question

Google is a large and existing firm that is considering developing a video
chat platform. If Google goes forth with the development, there is a 50% chance
of success. There are also three UVA students thinking of developing a similar
platform. They as well have 50% chance of success. Both Google and the UVA
students are deciding simultaneously whether or not to invest in research and development. If both players
succeed in developing the video chat platform, they enter a price competition and
they will both receive 0 revenues. If only one of the players succeeds in developing
the platform, they receive revenue of $12. Development costs are $4, regardless of
whether or not the endeavor was successful.
(a) Write the payoff matrix
(b) Are there any pure strategy equilibria in this game?
(c) Are there are any mixed strategy equilibiria?

(d) Consider now that the government wants to increase investment in R&D in order
to induce growth and therefore wants to give firms who invest in developing new
technology a $2 subsidy. As the government can only observe R&D expenditure of
active listed firms, only Google would enjoy this subsidy. What would happen
to the probability of inventing a new technology as a result of the subsidy? If
the subsidy does not work, what can the government do in order to increase the
probability of innovation?

Answer 1

Answer)

The subsidy will increase the probability of inventing a new technology.

Suppose, if the probability of inventing is 0.5 , it will increase to 0.8.

Subsidies have a positive impact on the probability of inventing a new technology since it minimize the cost of inventing and therefore, the losses if the technology doesn't work.

If subsidy do not work, then government can reduce the cost of inventing, or the government should maximize the revenues generated from inventing a technology.

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