Problem
Suppose that Hi-Fi Electronics is considering setting up a store in Kalgoorlie. They have two options: set up a 'Mega' Store, in which they will earn a rate of return of 30%, or set up a smaller, 'boutique' store with lower costs, and earn a rate of return of 50%. John Electronics, a competitor to Hi-Fi Electronics, is also considering setting up a store in Kalgoorlie. If John decide to also open a store in Kalgoorlie, they will split the market with Hi-Fi Electronics and both earn a rate of return of (i) 15% if Hi-FI set up a 'Mega Store', or (ii) 25% if Hi-Fi opt for the smaller store. Both firms will need a rate of return of at least 20% to justify setting up their store, and Hi-Fi Electronics will be ready to build well before John is ready.
1. Draw a decision tree of this situation;
2. What will be the sub-game perfect Nash equilibrium in this game? Clearly justify your reasoning.