Question

Question 2

Three residents of a peaceful building face a major crisis. Their building is about to undergo an undesired renovation process. However, the renovation will not happen if at least one of the residents will show up to the discussion on this issue at the city hall and object. The residents decide simultaneously and privately (they don't coordinate) whether to go to this discussion or not while considering the following:

• Showing up to the discussion means they need to take a day off, which is equivalent to a loss of $50.
• If no one shows up, they would have to move out for a long period of time, and each one of them will suffer a cost of $1,000.

1. What are the strategies each resident faces?
2. Find the equilibria in this game - how many of the residents would choose to go to the discussion in an equilibrium? how many equilibria are there then?

Note: Do not try build a payoffs table, try think about all the combinations of strategies, and if any or some of those combinations can be an equilibrium.   

Bonus Question (10 points)

In the bicycle market there are two companies A and B. Each company can sell either electric bicycles or regular bicycles.

If they both sell electric bicycles, they will get $2m each.

If one store sells electric bicycles and the other store sells regular bicycles:

• The store that sells electric bicycles will get $5m
• The store that sells regular bicycles will get $2.5m

If they both sell regular bicycles, they will get $1m each.

1. Describe the situation as a simultaneous game.
2. Do any of the stores have a dominant strategy?
3. Is there a dominant strategy equilibrium?
4. Are there Nash equilibria? If so, which one of them is better?

Answer 1

Question 2

The each resident facing two strategy first go to discussion and second don't go to discussion.

The equilibria of this game is when one choose to go discussion and other two chosses don't go to discussion.if the guys who chooses not to go ,changes their decision to go ,so their net payoff will decrease.if guy who chooses yo go, change its decision and decide not to go will also decreases his payoff.so it is equilibrium.

One resident choose to go in discussion in the equilibrium

There are three equilibria in this game.each equilibrium with each resident's move to go to discussion and others two don't go to discussion.

Bonus question

A).company A and B facing a simultaneous game where they are facing two strategy ,one is to produce electric bicycles and second produce regular bicycles.

B) no none have a dominant strategy as in each given strategy of rival ,there is a different best move for player,so there is no dominant strategy.

C) there is no dominant strategy for any players ,so there is no dominant strategy equilibrium

D) yes ,the nash equilibria is when one choose to produces electric bicycles and other chooses to produce regular bicycles. In each equilibrium, the company who produces electric bicycles ,is better .so each equilibrium who produces electric bicycles ,that equilibrium is better for them .