Week 5 – additional questions
Donna – the boss – is the principal of a start‐up firm. As the entrepreneur and the start‐up’s financier, Donna’s payoff is a fixed (positive) share of the total surplus generated by her two programmer agents, Jonny and Simon (that is, Donna’s objective is to maximise the joint payoff between her two workers, as this maximises her payoff (profit) from the firm).
Consider a model of the workplace with the following timing. Donna first chooses the office structure, either “Standalone” offices or “Open Plan”.
If Donna chooses Standalone, the two agents play the following simultaneous game. Jonny and Simon can each either choose Share or Guard. The payoffs to the players are as follows. If both choose Share, each agent gets a payoff of 5. If both Jonny and Simon choose Guard each of the agents gets 3. Finally, if one agent chooses Share and the other Guard, the agent choosing Share gets 1 and the agent who opted for Guard gets 6.
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On the other hand, if Donna chooses Open Plan, the agents again simultaneously choose either Share or Guard, but the payoffs are different. Specifically, if both agents choose Share, Simon and Jonny gets 2 each. If both choose Guard, the payoff is 4 to each agent. Finally, if one agent chooses Guard and the other Share, each agent gets a payoff of 0.
(a) Consider the game played by the agents following a choice of “Standalone”. What are the Nash equilibria? Briefly explain your answer.
(b) Consider the game played by the agents following a choice of “Open Plan” by Donna. What are the Nash equilibria? Briefly explain your answer.
(c) Given your answers in parts (a) and (b), what office structure will Donna choose? Explain your answer.
(d) In the context of a firm’s organisational architecture, what else can Donna do (other than choosing the office structure) to try to get the outcome (equilibrium) she wants?
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