Suppose the government announces a prize for a solution to its need. Both firm 1

Question

Suppose the government announces a prize for a solution to its need. Both firm 1 and firm 2 have an idea for a technology to satisfy the government’s need. Firm 1’s idea is (1, 1) = (8,10) and firm 2’s idea is (2, 2) = (7, 2), where is the per-period consumer surplus of the technology if competitively supplied, and is the cost of developing the idea into a technology. Interest rate is 10%. The government wants to hold a Vickery auction to pick the best idea.

If you are the CEO of firm 1 and someone you trust tells you that firm 2 will report a social value of $85. What is your profit if you win the bid? If you lose the bid?

Explanation / Answer

In what we call a normal-form representation of a game, each player in our game choses

a strategy simultaneously, and the combination of strategies determines what payo each

player receives.

We can illustrate the normal-form representation with the famous example of a game: the

Prisoner's Dilemma.

Example. Two suspects are arrested and charged with a crime. The police lack sucient

evidence to convict the suspects, unless at least one confesses. The police hold the suspects

in separate cells, and explain the consequences that will follow from the actions they could

take. If neither confesses, then both will be convicted of a minor oense and sentenced to one

month in jail. If both confess, both will be sentenced to jail for six months. If one confesses

and the other doesn't, then the confessor will be released immediately and the other will be

sentenced to nine months in jail. We can represent this dilemma with the following bi-matrix:

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