comm 295 econ final

final study notes (RECHECK ALL GRAPHS IN NOTEBOOK.)

What is an Oligopoly? (a market where a small… / has to have 4 characteristics)

An oligopoly is a market where a small # of firms have enough market power that each firm must consider rival reactions when making a decision.

There HAS to have the following characteristics:

1. There are only a few sellers. Oligopoly firms have some market power, but they are constrained by rival firms! They cannot act like a pure monopoly unless they collude.

2. Entry is limited, perhaps by patents or economies of scale. A patent will give the firm legal protection over an invention, so this can prevent competitors from copying the product for a period of time. Economies of Scale matter because this means Average Cost decreases as output increases, so larger firms can produce at a lower cost than small entrants, which may deter entry.

3. Products may be identical or differentiated.

4. Firms are aware of strategic interdependence with each other. “My best decision depends on what I think my competitors will do”.

Ex. of Oligopoly: Airlines, Telecom, Game Consoles, etc.

What are the different models of oligopoly behaviour? (4, Ca/Co/Be/St)

1. Cartel Model: Firms decide to collude and act like a monopoly. This happens when firms cooperate instead of compete. They jointly decide to restrict output and raise price. The goal is to maximize joint profit, not each firm’s individual profit.

   1. Since it acts like one big monopolist, the cartel chooses output where MR = MC, then charges the price on the demand curve. After it selects the price and quantity, the cartel has to DIVIDE production amongst its members.

2. Cournot Model: Firms compete on quantities, aka how much to produce. Each firm decides how much to produce, and the market price is then determined by total output. Q = q1 + q2. This creates a Best Response Function, where it tells us one firm’s optimal quantity for every possible quantity chosen by the rival.

3. Bertrand Model: Firms compete on prices, aka what prices to charge. This model is important when products are similar and customers can easily compare prices. If 2 firms sell identical products and one charges a slightly lower price, consumers will buy from the cheaper firm, so firms have a strong incentive to keep undercutting each other until P=MC. So, in a simple Bertrand Model with identical products and CONSTANT MC, P=MC. This is surprising because even with 2 firms, the outcome can look like perfect competition!

4. Stackleberg Model: Firms make decisions sequentially, aka leader & follower. Usually, Stackleberg is presented as quantity competition. The leader can have a first-mover advantage, so the leader chooses output while anticipating how the follower will respond. This model is also more advanced than Cournot because Cournot is simultaneous, while Stackleberg is sequential.

What is a Cartel and how does it work? (collude in setting prices/quantities to…)

Oligopolistic firms will sometimes form cartels where they collude in setting prices/quantities to increase their profits. Because competition pushes price down, if firms compete independently, each firm may produce more to capture more sales. BUT when all firms produce more, total market output increases, which pushes market price down. This will create something like PC if they keep pushing.

Therefore, in a cartel, each firm member agrees to reduce its output from the level it would produce if it acted independently. As a result, total market output is smaller, market price rises, and firms earn higher profits!

If firms reduce market output to the monopoly level, they achieve the highest possible collective profit at MR=MC. Output still needs to be divided amongst cartel members afterward.

Why do cartels usually fail? (external reasons illegal/no ctrl./may attract vs. internal reasons cheat)

External Reasons:
-Cartels are generally illegal in developed countries; Fines and possible jail terms may prevent collusion.

-Some cartels fail because they do not control enough of the market to significantly raise the price. (Ex. If a cartel controls only 30% of the market, then when they reduce output to try to lower prices, the other 70% of producers outside of the cartel will simply increase their own output. Then, the market price will not rise by much.)
-A successful cartel may attract entry by new firms. New entrants can come in and sell at slightly lower prices, increasing total market output and weakening the cartel price… Successful cartels can destroy themselves.

Internal Reasons: EVERY MEMBER HAS AN INCENTIVE TO CHEAT!

-Joining the cartel raises the price for everyone, but once the cartel price is high, each individual firm wants to quietly produce more than its assigned quantity because it can earn extra profits by producing more!

-HOWEVER, this is conditional on the other firms in the cartel not retaliating! If one firm secretly increases output and others do nothing, the cheating firm gains. But if everyone responds by increasing output too, then the total market output rises a lot, which causes the price to fall and the cartel profits to collapse.

What are the formula considerations involved with a Cartel? (__ = __, P*() < _)

When firms form a cartel, they collectively act as a monopoly:

Therefore, MR = MC, MR < P.

P(1 + 1/E) < P

MR = P + (dP/dQ)Q, where P = revenue gained from selling one more unit, and (dP/dQ)Q = the revenue lost because selling more units lowers the price on existing units. Since demand slopes downward, dP/dQ < 0, therefore MR < P.

The (1 + 1/E) comes from the inverse of E = (dQ/dP) * (P/Q), but inverted and putting Q and dP/dQ on the same side and swapping out with MR.
Since for normal downwards sloping demand, E < 0 (is always negative because price and quantity move in different directions), that means 1/E < 0, so P(1 + 1/E) < P.

**MR is the derivative of total revenue with respect to quantity. TR = pq, but for a monopoly/cartel, the price is not fixed. It depends on the quantity, which is P = P(Q)!

>TR = pq

>TR = p(q) * q

>MR = p(q)*(dq/dq) + (dp/dq)*q

>MR = P(Q) + (dP/dQ) (Q) ⭐️

What is the idea behind why in a cartel, individual firms might want to produce at the P=MC level?

We know that the group profit maximizing rule chooses an output where MR = MC, and this is because if MR > MC, producing one more unit can increase total profit, and vice versa. The best collective output is where MR = MC.

HOWEVER, when the firm only considers themselves, the market price is set by the cartel. Then, the individual firm thinks MC = P, because it treats the cartel price as the market price. It behaves like a price taker.

In this case, the firm thinks, “The cartel already created a high market price. If I produce one extra unit, I can sell it at price P”. They think MR = P, so the individual firm will want to produce until P = MC. If P > MC, then producing one more unit is profitable.

Q = total market output

q = one firm’s individual output

So, nq = Q!

What conditions are best for a cartel to remain stable? (id.c, monitoring…)

A cartel is most likely to remain stable when firms have identical costs and monitoring rivals is easy. When firms have the same cost structures, it is much easier to agree on a single, mutually beneficial price and output level. If firms can easily monitor their rivals, cheating can be detected instantly and punished, which deters firms from breaking the agreement in the first place.

*Also, cartels NEED higher barriers to entry to survive.

**If firms face highly elastic market demand, it means that if one firm cheats and lowers their prices even slightly, it will capture the whole market, which creates instability.

What is Game Theory? (the study for strategic int…)

What is a Nash Equilibrium? (the situation where every player is choosing their best response to… 4 conditions)

What is a Best Response? (the best strat. a player can choose for a gv..)

Game theory is the study of strategic interaction, where each player’s best decision depends on what the other player does.

Nash Equilibrium is a situation where every player is choosing their best response to the other player’s strategy.

1. There are 2 players, each with a fixed # of strategies.

2. The rule determines the payoff of each player based on both of their strategies.

3. For each of the players, they can derive their best response to a given strategy of the other player.

4. The Equilibrium is where no one will regret their decision. Their strategies are simultaneously the best responses to their rivals’ strategies.

A Best Response is the best strategy one player can choose for a given strategy of the other player. “If firm A produces 20 units, what quantity should I produce to maximize my profit?”
→ It is CONDITIONAL on the other’s choice.

This creates a Best Response (BR) Function.

How does a Cournot Model compete?

Cournot is a model of oligopoly where firms compete by choosing QUANTITY, not price. Total market quantity is Q = q1 + q2, and market price depends on the total quantity, P = P(Q).

So, firm 1’s profit depends on BOTH q1 and q2. Even though each firm controls only its own quantity, the market price depends on the TOTAL QUANTITY produced by both firms.

In Cournot, the NE happens when both firms’ BR functions intersect. Also, if rivals produce more, “I” will produce less because the total market quantity is already high, meaning P will be lower. So, BR Function slopes downward.

*Students make the mistake of thinking NE means best total outcome… It does NOT. It only means that no one wants to change their decision alone.

How does the quantity/price produced in Cournot compare to monopoly and PC?

Quantity Ranking:
Qmonopoly < Qcournot < Qpc

This is because a monopoly restricts quantity the most to keep prices high, while a Cournot is in between because firms still compete, but not as aggressively as PC!

Price Ranking:
Pmonopoly > Pcournot > Ppc

What are the 4 basic assumptions of a Cournot model? (few, id.pr, id.c, indep+sim)

1. There are only a few firms, and there is no entry (Oligopoly assumption).

2. Firms produce identical products (Homogeneous).

3. Firms have identical COST.

4. Firms decide independently and simultaneously how much to produce.

*We need identical products because if the products were differentiated, firms would have more pricing power.

**If firms have identical MC, it usually leads to a symmetric equilibrium, where q1 = q2 at equilibrium, so both firms produce the same quantity.

Keep in mind that because decisions are simultaneous, neither firm observes the other firm’s actual choice before deciding.

How does the Cournot differ from PC and Monopoly? (pc firm is so small, monopoly onedc.

-Because the firms set quantities, prices will adjust in the market. This is different from PC, because in PC, firms choose quantity, but each firm is so small that its output does not affect the market price. However, in Cournot, each firm is large enough to affect the total market quantity, so the total quantity affects price.

-Cournot is similar to Monopoly because quantity determines price. The only difference is that a monopoly has one decision maker, while Cournot has multiple firms. Each firm’s profit is affected by every other firm’s quantity!

How do we achieve Nash Cournot Equilibrium? What do we consider? (no change…)

What is a duopoly?

The Equilibrium arises when each firm is choosing the best output it can, GIVEN the output of the other firms (Best Response). In Cournot, the strategy variable is QUANTITY.

Definition: A set of strategies chosen by oligopolistic firms is a Nash Equilibrium if, holding the strategies of other firms constant, no firm can obtain a higher profit by choosing a different strategy. "

-”Can I personally increase profit by changing my own output while everyone else stays the same? If no, then Nash Equilibrium”.

**In Cournot, each firm does NOT fully internalize the damage its extra output causes to other firms. It ignores the negative effect on rivals, which is why its total output is > Monopoly output.

Also, Cournot Equilibrium usually does NOT maximize total industry profit; the Monopoly/Cartel would give higher combined profit. But here, each firm has an incentive to produce more than the cartel amount because extra output can increase its own profit while reducing rival’s profits.

Duopoly: A market with exactly 2 firms.

Consider the Airline example for Cournot, with Q = 339 - P and constant MC = 147. Describe how you would reach the BR functions for this example.

Terms: Residual Demand, Get BR Curve by setting MR = MC, Shortcut:
> if P = x - qa - qu, MRa = x - 2qa - qu . (The firm’s own quantity gets doubled).

Another Shortcut: if 2 firms are identical with constant MC “c”, and demand is P = a - Q, then each firm’s Cournot Quantity is: q = (a-c)/3.

1. Q = qa + qu

2. So, finding inverse demand to be P = 339 - Q, P = 339 - (qa - qu)

3. Now, we can find the residual demand functions for each firm.

American: qa = Q - qu // qa = (339 - P) - qu

United: qu = Q - qa // qu = (339 - P) - qa

→ We can expand the revenue functions to be:
(American ex) : TRa = P * qa // TRa = (339 - qu -qa)(qa) // TRa = 339qa - quqa - qa²

We treat qu as constant because American is choosing its own quantity:

Therefore, MRa = 339 - qu - 2qa.

>Set MC = MR for maximum profit,

147 = 339 - qu - 2qa // qa = 96 - 0.5qu (BR CURVE)

“For every additional output United produces, American decreases its output by 0.5 units”.

Following the same logic, qu = 96 - 0.5qa (BR CURVE).

We can find the Nash Equilibrium by plugging in:

qa = 96 - 0.5(96 - 0.5qa) // qa = 48 + 0.25qa // qa = 64. So, qu = 64.

Total market Q = 64 + 64 = 128, so P = 339 - 128 = 211.

Each firm’s profit: profit = (P-MC)(q) = (211-147)(64) = $4096

What can we say about the direction of a Cournot firm’s BR curve? (downward sloping…, as a function of..)

Both BR curves in a duopoly market are downward sloping, which means if your rival produces more, your best response is to produce less. If market price is lowered because total market output increases, it becomes less profitable for you to produce as much.

However! The firm does not reduce output 1-to-1. This is because the firm still has an incentive to produce some output and earn margin as long as price is above MC.

*In a Cournot duopoly, a firm’s BR curve shows the firm’s best output as a function of the other firm’s output. It also depends on MC, because the firm chooses output by setting MR = MC.

How can we interpret a Cournot Equilibrium Graph of the BR Functions? Where does NE lie? What does a point on the BR curve mean?

• Every point on the BR curve shows one firms profit maximizing output, given the other firm’s output.

• Both curves slope downward because in Cournot, if the rival produces more, your best response is to produce less. Rival output increases market output Q, and higher total output lowers price (ex. P = 339 - Q)

• If a point only lies on the American BR curve, it means only American is optimizing. Equilibrium MUST be on both curves, which means it is the intersecting point in the graph.

We know the Cournot Model is a theory of how firms behave. What can we use it for? (predict # (pc), assess the extent, predict the e of change in c, predict prod diff)

1. Predict the effect of changing the # of firms through mergers or by entry.

   1. Mergers: 2 firms combine, and the market becomes less competitive.

   2. In Cournot, more firms → Higher total output → Lower price. More Cournot firms push the market closer to Perfect Competition! (P=MC)

2. Assess the extent of market failure (DWL) from the oligopoly of this type.

   1. In Cournot Oligopoly, P > MC. This creates DWL because some mutually beneficial trades do not happen.

3. Predict the effect of changes in costs or taxes on price and output.

   1. If MC increases, then each firm’s BR curve shifts inward, so q dec, Q dec, P inc.

4. Predict the effect of product differentiation on profit, prices, and output.

   1. More differentiation means less direct competition, so higher prices/profits!

What is a game? What are elements of Game Theory? (a game is any situation where 2 or more p… // pl,str,payo,rules)

Definition: A game is any situation in which 2 or more players make strategic decisions that affect returns or payoffs to the players.

A game needs:
-Players: Use strategies to interact with each other, and receive PAYOFFS. Examples include individuals, firms, governments, etc.

-Strategies: A possible action/plan chosen by a player that specifies the actions/moves they will make. (Ex. in Cournot, the strategy is to change quantity).

-Payoffs: The benefits received by the players from the game’s outcome. It depends on ALL players’ strategies! We assume that players seek to maximize their payoffs :)

-Rules of the Game: Include who the players are, timing of the players’ moves, various actions available to the players, how payoffs are determined, etc.

What is Common Knowledge vs Complete information? (piece of info that is known by… // everyone’s strategies+payoffs are c…)

Common Knowledge: A piece of information that is known by ALL players. Everyone knows the information, and everyone knows that everyone knows it, and everyone knows that everyone knows that everyone knows, etc…

(Strategic Reasoning depends on what players believe others know).

Complete Information: The assumption that all players have complete information, which means everyone’s strategies and payoffs are common knowledge to all players.

**Complete information DOES NOT EQUAL Perfect information!! Complete information is when everyone knows the structure of the game, while perfect information is when you observe previous moves before making the decision.

What does “Solving the Game” entail? Describe Dominant Strategy vs. Best Response Strategy, as well as how Nash Equilibrium plays a role in this.

To solve a game means to find the stable outcome where players are making optimal choices given what the other players are doing. This is basically Nash Equilibrium!
- NE: A set of strategies such that each player is doing the best it can, given the strategies of the other players. Ex. s* = (s1*, s2*).

**No player has a positive gain from deviating at the Equilibrium, and this is a self-enforcing agreement with no outside enforcement…

***A NE does NOT mean the outcome is best for everyone as a group! It only means no individual player has a profitable unilateral deviation.

Dominant Strategy: A strategy that produces the highest payoff to a player, no matter what the rival strategies are. It is stronger than a BR strategy, and the rival’s strategy does not matter.

Best Response Strategy: A strategy that maximizes a player’s payoff given its beliefs about its rivals’ strategies. BR can change depending on the rival’s strategy, and BR is a function to the rival's strategies.

**A Dominant strategy is the best response to every possible rival strategy, but a BR strategy does not equal a dominant strategy!

What is a dominant strategy equilibrium?

Definition: This happens when every player chooses a dominant strategy.
“I am doing the best I can no matter what you do; you are doing the best you can no matter what I do.” → This is stronger than a NE!

A Dominant strategy is a special case of NE 🙂 Every dominant strategy equilibrium is a NE. Also, the NE may not necessarily be unique (ex. there can be multiple NE.)

What is Prisoner’s Dilemma? (2 key properties, domstr and worse for both)

A Prisoner’s Dilemma has 2 key properties:

1. Each player has a dominant strategy, and therefore a dominant strategy solution.

2. The dominant strategy equilibrium is worse for both players than another possible outcome.

The players will always choose the respective dominant strategies, but it leads to a worse overall outcome. This is because firms do not automatically choose the best joint outcome, as it requires trust/coordination. This outcome is fragile because each firm has an incentive to cheat.

→ Individually rational behaviour leads to a collectively worse outcome…

In terms of surplus and profit, what does a Monopoly maximize vs. Perfect Competition?

A Monopoly/Cartel outcome maximizes Producer Profit/Total Firm Profit at MR=MC, while PC equilibrium at P=MC maximizes Efficency/Total Surplus.

**The PC outcome does NOT maximize firm profit because competition pushes Long Run Economic Profit to 0.

What are the calculations we should know regarding multiple Cournot firms? (“n” symmetric firms with MC “m”)

Suppose we have n symmetric firms with MC m. Therefore,

Q = qi +q-i, where q-i is the total quantity produced by all other firms.

P = a - bQ // P = a - b(qi + q-i)

Residual Demand: qi = (a - P - bq-i)/b

Inverse Residual Demand: P = a - bqi - bq-i

Profit Maximization: MRi = a - 2bqi - bq-i // MC = a - bqi - bq-i →

→ Best Response Function: qi = [(a-m)/2b] - [(q-i)/2]

Because all firms are symmetric, that means each firm produces the same quantity, so qi = q. And since there are n total firms, q-i = (n-1)q.

Now, if we substitute into the BR Function, we get:

qi = [(a-m)/2b] - [((n+1)q)/2] // q = (a - m)/(n+1)b ← Main Formula!

And since Q = nq, Q = n(a - m)/(n+1)b.

For Market Price when P = a - bQ, we can plug in to:

P = a - b(n(a - m)/(n+1)b) // P = (a + nm)/(n+1) ← Market Price Formula!

IMPORTANT: As n gets very large, n → infinity, so firm output q → 0, so each individual firm becomes tiny.

> Looking at Q = n(a - m)/(n+1)b, which can be seperated into Q = (n/n+1)*(a-m/b),

(n/n+1) approaches 1 as n → infinity, so Q = (a-m)/b.

BUT! This is just the PC quantity because PC is: MC = a - bQ (from P=MC) // Q = (a-m)/b!

To conclude, this shows that as the # of Cournot firms grows large, the market approaches Perfect Competition.

**This is also seen in P = (a + nm)/(n+1), where nm dominates if n → infinity, so P → MC as n gets large.

What can we conclude about the # of Cournot firms getting larger and larger? What is the effect on Q, P, and profit?

As # of firms increase, Q inc, P dec, Profit dec. More firms “n” also means individual firm output decreases, so as Q inc, q dec.

**(For Q = nq, we can get q = Q/n, so as n increases, the total market is split amongst more firms, and each individual firm produces less.)

-Price moves closer to MC as # of firms increases.

-Cournot Oligopoly bridges Monopoly and PC. With one firm, it is a Monopoly. As the # of firms becomes very large, the outcome approaches Perfect Competition where P = MC.

What are the 4 Key Elements of a Bertrand Oligopoly? (prices, simu, maxi, NE)

1. Firms treat prices as the strategic variables.

2. Prices for all firms are set at the same time, aka simultaneously.

3. Each firm chooses its price to maximize profit, taking the expected price of the other firm as given.

4. We use NE in prices.

*We will consider only the 2-firm case (duopoly).

How do we determine Equilibrium for a Bertrand Model with Homogenous Products?

Since the good is homogeneous, consumers will buy from the lowest price seller. If prices are different between firms, consumers will buy from just 1 firm, but if prices are the same, then consumers are indifferent.

We know that P > MC cannot be a stable Bertrand Equilibrium. Why? →

• If P > MC, suppose both firms are charging a price above MC. They will both get some market share, but if one firm can slightly undercut, with their BR Function being P = 10 - e where e is a tiny amount like 1 cent, then the undercutting firm becomes the cheaper seller, captures the whole market, and still earns profit because P - e > MC. So, if P > MC, the firm will want to undercut.

• If P < MC, then selling each unit loses money. The firm does not want to sell, so it would rather raise the price slightly, lose customers, and avoid making losses.

Now! If all firms charge P = MC, then no firm wants to change. If one lowers the price, it gets all customers but loses money on each unit. If one raises the price, the rival becomes cheaper and gets all the customers, so the firm that raised the price sells nothing.

TO CONCLUDE: The Bertrand NE with homogenous products occurs where each firm prices at MC (P = MC). The outcome is just like PC.

*This assumption heavily depends on products being identical! If products are differentiated, each firm can have pricing power.

What are the differences between Cournot + Bertrand Models? (q vs p, timing, dmd elasticity)

The main difference is the strategy employed by firms: Quantity vs Price.

-Cournot: “How much should I produce?”
-Bertrand: “What price should I charge?”

The strategic variable depends on the nature of production, which is how the industry actually produces and sells its product.

⭐️ For a Cournot Model:
- The amount of output has to be decided in advance. Firms compete by choosing q1, q2,… and the market price adjusts based on total quantity.

• Prices are the same for all firms, so there is no price competition.

• In basic Cournot, firms sell a homogeneous product at one market-clearing price! A firm does not directly choose its own price.

-Demand Elasticity matters because total output determines price, and price affects MR.

> If demand is very elastic, increasing output causes a big revenue problem because price falls sharply (ex. drops from $20 to $12, so firms might not even be making a profit at all.

> If demand is less elastic, firms can restrict output and maintain higher prices more easily.

**Cournot pricing power depends on how strongly the price responds to total output!

⭐️ For a Bertrand Model:

• Firms can set prices and then let output adjust to clear the market.

  • Firms choose price, then consumer demand determines how much they sell. This fits markets where firms can easily adjust output after setting price (e.g., online retailers selling identical products).

  • If a firm sets the lowest price, consumers go to that firm, and the firm supplies the demanded quantity.

• Demand is “perfectly elastic”.

  • For a homogenous product, if your price is higher than your rival’s, demand for your product drops to 0, and vice versa. If prices are equal, consumers split between firms.

  • However, only individual firm demand is guaranteed to be highly elastic because of price competition. The whole market demand is not necessarily perfectly elastic!

**Bertrand gives a lower price than Cournot because in Cournot, if one firm increases output, price falls for everyone, so the firm only partially steals business from rivals. In Bertrand, it can steal the whole market if lowered by even 1 cent!!

How does a Bertrand model with differentiated products differ from a Bertrand model with identical products? What becomes the profit-maximizing price?

In a basic Bertrand model with homogenous products, firms undercut each other until P = MC, so firms earn 0 economic profit. If products are identical, Bertrand competition becomes extremely intense and drives P down to MC.

SO! Firms seek to produce differentiated products! This is when consumers do not see the 2 firm’s products as perfect substitutes.

• In differentiated Bertrand, raising price above rival loses some consumers, but not all. This is because of brand loyalty, taste differences, location, quality, etc.

• So, this allows P > MC to be charged by firms!

Also, the BR functions slope upward. This means when [Coke] increases price, Pepsi also increases price. This is because the 2 are substitutes! If coke raises price, some consumers switch towards Pepsi. Pepsi now has more demand and can profitably raise its own price too.

> BRc (Pp), if Pp increases, the BRc(Pp) increases.

> Upward sloping BR means prices are strategic complements. If one firm raises its price, the other firm’s BR is also to raise its price.

That is how we know that Bertrand firms have a stronger incentive to produce differentiated products compared to Cournot firms. Bertrand firms want to escape the brutal P=MC competiton…

What are some IRL examples of when Cournot models should be used, vs. Bertrand models? (choosing output like airline vs price like gas)

Cournot is better when competing by choosing output, like airline seat capacity, mining, etc.

> Airlines decide how many flights/seats to offer on a route. Once total seats are available, ticket prices adjust based on demand and capacity.

> Firms decide how much copper, iron ore, lithium, etc. to extract. More total output pushes the market price down.

Bertrand is better when competing by choosing price, such as gas stations, grocery stores, etc.

> Nearby gas stations often sell similar products, so they compete heavily by posting prices.

> For grocery stores, stores choose prices for similar products, and consumers compare prices.

What is Monopolistic Competition? What are its 4 characteristics? (sits betw, many f, free e+e LR, usually dif, may be sym or dif)

Characteristics:

• Many firms.

• Free entry + exit in the long run. If making above normal profit, new firms will enter.

  • R = TC, P = AC. (Firms make 0 economic profit in the long run, so Revenue = Total Cost).

• Products are usually differentiated.

• Firms may be symmetric, or they may differ.

Ex. Restaurants.

In SR, firms may make above-normal profits. The diagram looks like the standard monopoly diagram 🙂. This is because each firm has some market power because products are differentiated, but free entry + exit prevents firms from earning positive economic profit in the Long Run.

How does a Monopolistic Competition behave in the Short Run and Long Run? What is its profit-maximizing formula?

In the short run, a monopolistic competition behaves somewhat like a Monopoly. Each individual firm faces a downward-sloping demand curve and chooses output where MR = MC.

The marginal firm in the LR makes 0 profits. In Long Run Monopolistic Competition, the demand curve is TANGENT to the AC Curve at the output.

> P = AC, Pq = AC*q => TR = TC

How does a Monopolistic Competitive Firm compare to a Perfectly Competitive firm? ( p, mc, ac..)

For PC - Long Run:
> P = MC = minimum AC

For MonoComp - Long Run:

> P = AC, so economic profit = 0, BUT,

> P > MC.

The reason why there is still market power despite profits being 0 is that some consumers may still specifically like one shop for other reasons, so it can charge above MC.

**For MonoComp firms, it does not operate at minimum AC because it has some excess capacity. The demand curve is tangent to AC, but this tangency usually happens before min. AC.

** Zero Economic Profit means P = AC, not P = MC! Free entry removes LR economic profit, but it does not remove product differentiation. So firms can still have P > MC.

What is a marginal firm? (the firm that is barely..)

Definition: The firm that is barely willing to stay in the market. It earns zero economic profit, meaning P = AC.

Why is demand tangent to the AC curve for a Monopolistic Competitive market in the Long Run?

In the Short Run, demand is tangent to AC because if P > AC, leading to a positive economic profit, new firms will enter. When new firms enter, each existing firm loses some demand. So, the firm-specific demand curve shifts left. This continues until demand is just touching the AC curve.

>If demand were above AC, the firm would earn a profit and more firms would enter.

>If demand were below AC, the firm would make losses, and some firms would exit.

So, the stable long-run point is where the demand curve just touches the AC curve.

What is different about LR profits in a MonoComp market with identical products vs. differentiated products?

> If firms are identical, then there is zero economic profit.

> However, if firms differ because of product differentiation or different production costs, then low-cost firms or firms with superior products may earn positive economic profits.

*Free entry drives the marginal firm to zero profit, but stronger firms (ex. more famous) may still earn positive profits at P > AC.

What is Multiple Equilibria? When does it happen?

A game has multiple equilibria when there is more than one Nash Equilibrium.
- NE is when no player wants to change alone, so multiple NE means there are several stable outcomes, and the theory alone may not tell us which one will happen.

Multiple Equilibria usually happen in Coordination Games, where players want to avoid conflict/mismatch, but there may be more than one way to coordinate.

What is the issue we face with Coordination Games, in comparison to Prisoner’s Dilemma?

Unlike Prisoner’s Dilemma, where each player has an incentive to defect from the cooperative outcome, the problem in a Coordination Game is which outcome they coordinate on.

• In PD, there is a better joint outcome, but it is not stable. Players have incentives to cheat.

• In Coop. Games, there are multiple stable outcomes, and the issue is selecting which one we choose. Once players coordinate on one Equilibrium, no one wants to deviate.

What is Cheap Talk in Game Theory? (preplay comms…)

What is a pareto criterion?

Cheap Talk is pre-play communication made before the game that doesn’t impact payoff directly, since it is not a contract. The purpose of Cheap Talk is to help players coordinate, and it is credible when the speaker has an incentive to actually do what they said (Ex, Coordination Games), but it is NOT credible when the speaker has an incentive to lie/break the promise (Ex, Prisoner’s Dilemma).

A Pareto criterion is when you select a solution which is best for all parties. If there are multiple NE with different payout outcomes, we should choose the better one.

• An outcome can be Pareto but not Nash, like the Coop. Option in Prisoner’s Dilemma.

What is a Pure Strategy? (a complete and deterministic plan for…)

What is a Mixed Strategy? (the player randomizes…)

A pure strategy is a complete and deterministic plan for how a player will act in every possible situation in a game. The player chooses one action with certainty, and the notation is: BR(s-i) = s* → (given what the other player does, my best response is one specific strategy).

• S1, S2, Sn is all pure strategy.

A mixed strategy is when the player randomizes among pure strategies according to specific probabilities. The notation is: σi = (σ1(s1), σ2(s2)…. σn(sn))

**The sum of Pure Strategy probabilities adds up to 1.

Mixed strategy matters because some games do not have a pure strategy stable outcome.

What is Mixed Strategy Equilibrium? When does it happen? What conditions are needed for it? (if each player is choosing the best prob weights given…)

What do we need to have in every game with a finite # of players and strategies?

Mixed Strategy Equilibrium: If each player is choosing the best probability weights GIVEN the other player’s probability weights, then we have a NE in mixed strategy.

• Mixed Strategy Equilibrium ALWAYS exists in finite games. Pure Strategy is just a special case of mixed strategy (with probabilities 1 and 0), and the condition for Mixed NE is that given your rival’s Mixed Strategy, you are indifferent between your pure strategies. A player only mixes if they are indifferent between pure strategies.

• Also, the expected payoff of a mixed strategy is an average over possible outcomes. Ex. In actual play, payoff = 20 or -2, but before knowing the random outcome, the Expected Payoff = 9.
  
  ⭐️ Every game, with a finite # of players and strategies, should have at least one PURE or MIXED strategy equilibrium.

• Games with both pure and mixed equilibria happen in coordinate-type games, or games with multiple pure equilibria.

• A mixed strategy equilibrium usually works by making the other player indifferent between their pure strategies. The randomization makes your opponent equally happy choosing another action.

• In a mixed strategy, the player is indifferent because the rival’s probabilities make the expected payoffs equal!

What should you look for if you are given a game with no pure strategy equilibrium?

We should look at mixed strategies, either with given probabilities or by assuming 50-50.

You calculate the expected value of a Mixed Strategy by computing:
> E(x) = p*(a) + (1-p)*(b)

What are the 3 criteria for Full Information? (our own, the rival’s, payoffs)

In a game, we normally assume Full Information:

1. We know our own possible strategies.

2. We know the rival’s possible strategies.

3. We know the payoffs of each player for every possible outcome.

What is the Rationality Assumption? What is Bounded Rationality?

The Rationality Assumption states that we normally assume rationality, which means players consistently choose in the best of their interests and exhaust/use all available information.

• This is also the profit-maximizing assumption, as a rational firm would choose the action that gives the highest expected profit, given what it believes rivals will do. Rationality is assumed to be common knowledge! (everyone knows, and everyone knows that…”

Bounded Rationality: This is when individuals’ rationalities are limited. We might have limited ability in calculations, logical inference, processing information, etc, which is why even if a strategy is mathematically optimal, a real person may not choose it because the game is too complicated.

**Private/incomplete information can prevent the efficient equilibrium.

What is the Maxmin Strategy? When do we use it? What is a Maxmin Solution?

The Maxmin Strategy is used when a player isn’t confident about the rival’s actions. In this circumstance, we use Maxmin, which is a Risk-Averse Strategy.

• This strategy maximizes the Minimum possible payoff. The player asks, “What is the minimum payoff I could get if I use this strategy?” Then, then player woould choose the strategy with the highest minimum payoff.

Maxmin Solution: This occurs when both firms play a Maxmin Strategy.

**Maxmin Solution does not equal Nash Equilibrium! (Maxmin is about protecting yourself from the worst outcome, while NE is about mutual best responses).

What is a Repeated Game? How does it differ from a Static Game?

Repeated Game: When a static game is repeated. It can be a finite repeated game, or an infinite repeated game. Repetition can change game results!!

- In one static game like Prisoner’s Dilemma, each player has an incentive to cheat because cheating gives the higher immediate payoff. Strategies and actions are the same.

> BUT, in a repeated game, a strategy is a sequence of actions that a player takes throughout the game. It is a full contingent plan… A strategy tells you what to do in every period depending on what happened before.

What is the Discount Factor B in an infinitely repeated game?

B(beta) measures how much you care about future payoffs.
So, → 0 < B < 1

What is the Trigger Strategy in an infinitely repeated game?

A Trigger Strategy is a punishment strategy. There are 3 stages:

1. Start by being good. (Cooperative!!)

2. Continue being good if the other player is good.

3. If the other player is ever bad, punish forever by being bad forever.
   

This can make cooperation stable if future punishment is painful enough.

> If you deviate today, profits = 10 (from being bad solo) + 0 + 0 + 0…. = 10 total.

BUT, if you behave good forever, you know you will get 5 each period, but you also have to consider that future payoffs are discounted by B, so the present value is:

profit = 5 + 5b + 5b² + 5b³….. = 5/(1-B) ← General Formula!! Remember.

Cooperation will work if the payoff from cooperating forever is at least as good as deviating once: 5/(1-B) >= 10 // so, B >= 0.5.

> So, when B >= 0.5, it means I care about my future and don’t want to deviate.

**One needs to COMMIT to the trigger for this strategy to work! No mercy and no forgivement. Players need to believe that cheating results in future punishment.

What is the T4T Strategy in an infinitely repeated game?

In a TitforTat Strategy, we start by cooperating, then copy what the other player did last period.
- This method is more forgiving than Trigger Strategy, because punishment can be one period if the other returns to being good.

If everyone is good forever, we get the formula of 5 + 5b + 5b² +…. = 5/(1-B), so its the same as the Trigger Strategy path!

However, if we cooperate until time t, “I” would get 10, then -1, then repeat…

> The formula then becomes 10 + (-1)b + 5b²…

> Cooperation is only better if 5 + 5b >= 10 - b // So, B has to be >= 5/6

**Compared with the Trigger Strategy, this method requires a higher care for the future for the strategy to work because the punishment is weaker.

And, if we kept repeating G-B-G-B pattern, we would get 10 - 1 + 10 - 1… which comes out to 9 every 2 periods.

Therefore, T4T can be part of a NE by making both sides cooperate in fear of potential punishment.

How does a finitely