Consider two start-up companies (players 1 and 2) who are working on a joint project and a VC, Venture

Capitalist, (player 3) who is a potential investor in the project. First, the entrepreneur firms simultaneously decide whether to devote high or low effort to research on the project. Then they make a pitch deck presentation to the VC. If both firms choose high effort in their preliminary research, then the presentation goes well, and otherwise it goes poorly. The VC only observes the outcome of the presentation and not the firms' effort levels. After thepresentation, the VC decides whether to invest in the project. Each start-up company receives a payoff of 5 if the VC invests and zero otherwise. In addition, choosing high effort costs each firm 1, while choosing low effort is free of charge. From the VCs' point of view, investing in a new project is risky and costly. In this case for our VC it costs 2 but it also generates a return of 3 from each firm who chose high effort (i.e., a return of 6 if both chose high effort, 3 if only one did, and 0 if neither did). If the VC does not invest, his payoff is zero. All players are risk neutral.

A. Draw an extensive form representation of this game. Show all the actions and payoffs. How do you analyze the best decision by the players and Nash equilibrium? Note: The extensive form here has two key features. First, player 2 does not observe the choice of player 1 and therefore there is an information set connecting the two possible decision nodes of player 2 which means player 2 cannot evaluate the effort level of player 1. Second, player 3 only observes the choices of the two players if they both choose H, therefore there is an information set connecting the three nodes associated with choices HL, LH and LL.

Now let's assume that you and your team member represent firms 1 and 2 in the question, while I am firm 3. You must work on your project and present it together as one joint paper. Here, high effort means that you work hard and communicate with the other player eagerly. By contrast, low effort means a lack of teamwork stamina, poor communication, bringing no idea or solution to the table, etc. I can only observe your output i.e. the submitted paper and not how you have worked together. This means my judgment about the quality of your paper is merely based on the submitted file and not on how you have gone through the teamwork (you decided not to present a preliminary report, and only on a few occasions did you contact me to discuss your project).

B. Similar to the question above and without knowing the payoff values, discuss how is the best way of evaluating each team member's effort and marking their paper to minimize the free-riding problem? How do you improve this game? Note: A free rider, most broadly speaking, is someone who receives a benefit without contributing towards the cost of its production.