Question

Clear Vision is a start up company who has discovered a new technology for video conferencing. Clear Vision lacks the capability of marketing and selling the nal product and it has therefore decided to sell the technology. There are three tech giants interested in acquiring the technology: Booble, Microtough and Umaton. These companies value the technology dierently. This is not because they have information dierences, but rather for their dif- ferent abilities to use the technology. This is what is common knowledge in the market place. The technology is worth $1b to Booble. Umaton and Microtough know their own valuations of the technology, but their valuations are unknown to everybody else involved in the interaction. It is believed that: (i) the valuations of Umaton and Microtough are independent random variables; (ii) Umatons valuation is either $300m or $500m with equal probability; (ii) Microtoughs valuation is either $350m or $450m with equal probability. Clear Visions payo is equal to the (expected) revenues of the sale. The payos of the three potential buyers are equal to their valuations minus the payment for acquiring the technology if they get the technology, and zero oth- erwise. The game is as follows. First, Booble makes a take it or leave it oer. Clear Vision can either accept or reject the oer. If it accepts it the game is over. If Clear Vision rejects the oer, it runs a second price sealed bid auction with Microtough and Umaton as bidders (participants). Clear Vision then collects the revenues of the auction and the game is over. a) Suppose that Clear Vision rejects Boobles oer and runs a second price closed-sealed auction with the two other companies as bidders. What are the Nash equilibrium bidding strategies of Microtough and Umaton? What are their expected payos? What are the expected revenues for Clear Vision? b) Consider now the whole game. What is the credible Nash equilibrium? Describe the playersstrategies. What is the outcome of the game? For an additional investment of $50m, the engineers of Clear Vision can design one of two dierent technologies. The rst technology design increases the valuation of Booble by $400m, but leaves unchanged the valuations of the other two potential buyers. The second design decreases the valuation of Booble by $200m, but increases the valuations of the other two companies by $100m. Everything else is unchanged. c) Find the credible Nash equilibrium. Will Clear Vision make the additional investment? If it does, what technology design will it choose? The rst design or the second design?