Firm A/Firm B Invest A Abstain Invest 1/1 4/0 0/4 Abstain 0/0 Firm A/Firm B Invest Abstain В Invest 1/1 4 /-6 -6 4 -6/-6 Abstain Firm A/Firm B Invest Invest Abstain 7/7 10/0 0/10 0/0 Abstain D None of the above
Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions.
The “research and development” game is best analyzed as a simultaneous move game, because the parties lack information about each other’s investment decisions.
Which game (in the attached image)describes the “research and development game” properly? Remember that investment costs $6, and that this should be reflected, whenever appropriate, in the correct game matrix.
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