I thought I had a pretty good grasp of Nash Equilibrium but I wanted others insight … In regards to the question below
[question removed by moderator]
The Answer is 1, but I’m curious why it wouldnt be that they both close at 9. They both produce a larger output that way… Is the key that they are attempting to move to the 24 hour format already and if one of them does it they will greatly out produce the other and therefore they both must?
Please refer to the following improvised pic for the solution of the Nash equilibrium in the proposed game:
Note that regardless of what Chain 2 does, remaining open is the dominant strategy of Chain 1 as they will get 540 vs 180 in case Chain 2 closes at 9 or 108 vs 55 if Chain 2 also remains open (indicated by the vertical red arrows). In a similar fashion Chain 2’s dominant strategy is also to remain open regardless of what Chain 1 does (as indicated by the horizontal red arrows). Nash equilibrium occurs in the cell where both arrows point to, as it is in that cell that both players apply their dominant strategies.
If both shops Close at 9, you will have the Most efficient equilibrium. Unfortunately, it is not stable. If shop 2 closes at 9:00, shop 1 would maximize its profit if it opens 24/7. The same would bei true if shop 1 decides to close at 9:00.
A possible solution would be collusion: both parties agree to close at 9:00. This would maximize the joint profit. Then again, both shops would face an incentive to break the agreement in oder to maximize its individual profit given the closing time of the other shop.
Since both shops expect the other shop to cheat on such agreement, they choose the best outcome given this behavior, which ist to open 24 hours and therefore represents a stable (though not most efficient) equilibrium.
Thanks guys! That is where my mind was leading to, but I was jumping to it. Now I completely understand. Appreciate your help!