Quiz 3
Dominant Strategy vs. Nash Equilibrium
- Dominant: "Im doing the best I can no mapper what you do. You're doing the best you can no matter what I do." -Nash: "Im doing the best I can given what you're doing. You're doing the best you can given what I am doing."
Finding equilibrium prices in Bertrand
- In nash equilibrium, P1 = P2 = 1 - Profits = 0 - With only two firms, same outcome as PC - however, collusion means that if firm 1 knows that firm 2 will charge P=16, the best thing it can do is to charge a price P1 just below 16 and dominate the entire market - a firm will never set price below its own MC
The Bertrand Paradox
- Price Competition - Oligopoly model in which firms produce a homogeneous good, each firm treats the price of its competitors as fixed, and all firms decide simultaneously what price to charge - If one price is lower, it gets the whole market. If prices are the same, they split the market - Total demand is Q = D(p), where p is the low price - the only reliable floor on price is MC - if p2>c and p2<pm, i want to set my price a penny below my competitor - if p2 > pm, i may as well set the monopoly price - if p2<c, i know that if i set a price above c, i get no customers and if i set a price below c, i can only loose money when making a sale.
Cournot Equilibrium
- in cournot equilibrium, each firm correctly assumes how much its competitors will produce and thereby maximizes its own profits - find the best response curve and figure out where they cross - each firm's reaction curve tells it how much to produce given the output of its competitor - equilibrium in the cornet model is when each firm correctly assumes how much its competitor will produce and sets its own production level accordingly -example of nash equilibrium - Whichever firm has the lower MC will produce more and have a higher profit. -If both firms collude and cooperate, the best they can do is to produce the monopolist output (in total, but individually they both produce half)
Infinitely Repeated Game
- my competitor and I repeatedly set prices month after month, forever
Matrix form (normal form)
-A way to represent a game -Best suited for games with simultaneous decisions (making decisions at the same time) -Start by looking at dominant, dominated strategies -If that fails, equilibrium is given by intersection of best response mappings
Ways out of the Bertrand trap?
-Be the cost leader -implicit or explicit agreement on price (this is illegal) -Limit capacity ( this is less illegal) -Product differentiation and branding
Nash Equilibrium
-Combination of moves in which no player would want to change her strategy unilaterally. Each chooses its best strategy given what the others are doing (best response). -Each player is doing the best given what the other player is doing
Oligopoly - Equilibrium
-Firms are doing the best they can and have no incentive to change their output or price -all firms assume competitors are taking rival decisions into account
First Mover Advantage: Stakelberg Model
-Going first gives Firm 1 the advantage -Firm 1'output is twice as large as Firm 2's -Firm 1's profit is twice as large as Firm 2's - Going first allows firm 1 to produce a large quantity. Firm 2 must take this into account and produce less unless it wants to reduce profits for everyone.
Cournot Equilibrium and Collusion
-If both firms collude they will increase profits - When two firms collude, the total output they produce is at the monopoly quantity and they split it. - Dow firms want to follow this agreement? No. - If one firm deviates, it will earn more profits while the other would earn less than if it did not collude at all. If they both deviate, they will both earn less.
How do we know if collusion if possible?
-If the PV of cooperating is higher than the PV of deviating -since firms care about future profits, the repeated interaction and the possibility of punishment (that is, the low profit from the cornet equilibrium) reduces the incentives to deviate from the agreement. -when interest rates are higher, firms care less about future profits, increasing the incentives to deviate from the agreement -the firms will follow the proposed agreement when they sufficiently value future profits aka when the interest rate is sufficiently low. the same is true for the Bertrand game
The Cornet Model
-Oligopoly model in which firms produce a homogenous good, each firm treats the output of its competitors as fixed, and all firms decide simultaneously how much to produce. -Quantity Competition
Mixed Strategy
-Player makes a random choice among two or more possible actions, based on a set of chosen probabilities. -Equilibrium requires mixed strategies. -With a mixed strategy, random choice leads to nash equilibrium.
Extensive Form of a Game
-Representation of possible moves in a game in the form of a decision tree -Move from the bottom to the top
The Reaction Curve
-The relationship between a firm's profit maximizing output and the amount it thinks its competitor will produce -A firm's profit-maximizing output is a decreasing schedule of the expected output of Firm 2 - Firm 1's reaction curve shows how much it will produce as a function of how much it thinks Firm 2 will produce -Firm 2's reaction curve shows how much it will produce as a function of how much it thinks Firm 1 will produce -"Best response function"
Game-tree form (extensive form)
-Way to represent a game -Best for games with sequential moves -Solve game backwards, starting from endnodes -Strategies: set of contingent decisions at each node
Finite Number of Repetitions
-game is repeated a finite number of times (N months)
Stackelberg model
-oligopoly modeling which one firm sets its output before other firms do. -The first mover advantage -When solving: 1) Fist consider Firm 2 profit max (MR=MC) 2) Then consider Firm 1. (A)When choosing its output, the leader (firm 1) understands how the follower (firm 2) will choose Q2 as a function of Q1, and takes this into account. (B) Find rev, but before finding MR, plug in Q2 into the REV1 equation.
Equilibrium in dominant strategies
-outcome of a game in which each firm is doing the best it can regardless of what its competitors are doing -optimal strategy is determined without worrying about the actions of other players -however, not every game has a dominant strategy for each player -the optimal decision of a player without a dominant strategy will depend on what the other player does
Dominant strategy
-pay off is greater than any other strategy regardless of rival's choice -rule 1: if there is one, choose it
Dominated strategy
-payoff is lower than some other strategy regardless of rival's choice -rule 2: do not choose dominated strategies
The "Bertrand trap"
-prices are driven down to the competitive price (MC). Economic profits are zero, accounting profits could be negative if there are sunk costs -neither higher demand nor lower costs increase profits -ex. airlines -avoid this game!
Oligopoly - Long Summary
-products may or may not be differentiated -only a few firms account for most or all of production - some or all firms earn substantial profits over the long run because barriers to entry make it hard for new firms to enter - ex. automobiles, steel, aluminum, petrochemicals, computers, electrical equipment.
Empty Threat
-when firms know the payoff of each other's actions, firms cannot make threats the other firm knows they will not follow
How can producers provide high-quality goods when asymmetric information will drive out high-quality goods through adverse selection?
1) Reputation 2) Standardization 3) Signaling
How to make a credible threat?
1. Demonstrate commitment 2. Firm 1 must do more than announce they will produce sweet cereal - (Invest in expansive advertising campaign; Buy large order of sugar and send invoice to Firm 2) 3. Commitment must be enough to induce Firm 2 to make the decision Firm 1 wants it to make
Two key characteristics of Monopolistic Competition
1. Firms compete by selling differentiated products that are highly substitutable for one another but not perfect substitutes -(Note: (a) firm is only producer of its brand, so downward facing demand curve; (b) P>MR=MC; (c) outcome is inefficient in the short and long run - DWL) 2. There is free entry and exit: it is easy for few firms to enter the market with their own brands and for existing firms to leave if their products become unprofitable. -(Note: (a) if profits are positive in the short run, profits attract new firms with competing brands; (b) the firm's market share falls, and its demand curve shifts downward; (c) in the long run, the firm earns zero profit even though it has monopoly power, P=AC)
Equilibrium in Oligopoly
Each firm will want to do the best it can given what its competitors are doing, and these competitors will do the best they can given what that firm is doing (nash equilibrium)
Adverse selection
Form of market failure resulting when products of different qualities are sold at a single price because of asymmetric information, so that too much of the low-quality product and too little of the high-quality product are sold.
Sequential Game
Game in which players move in turn, responding to each other's actions and reactions.
Agent
Individual employed by a principal to achieve the principal's objective
Principal
Individual who employs one or more agents to achieve an objective=
Monopolistic competition
Market in which firms can enter freely, each producing its own brand or version of a differentiated product
Oligopoly - Short Summary
Market in which only a few firms compete with one another, and entry by new firms is impeded. -Cournot Model (Quantity competition) -Stackelberg Model (Quantity Leadership) -Bertrand Model (Price Competition)
Cartel
Market in which some or all firms explicitly collude, coordinating prices and output levels to maximize joint profits
Duopoly
Market in which two firms compete with each other
Pure Strategy
Player makes a specific choice or takes a specific acton
Market Signaling
Process by which sellers send signals to buyers conveying information about product quality
Strategy
Rule or plan of action for playing a game
Asymmetric Information
Situation in which a buyer and a seller possess different information about a transaction. -Low quality goods drive high quality goods out of the market - the lemons problem -The market has failed to produce mutually beneficial trade -Too many low and too few high quality cars are on the market -Adverse selection occurs; the only cars on the market will be low quality cars
Game
Situation in which players make strategic decisions that take into account each other's actions and responses
Optimal strategy
Strategy that maximizes a player's expected payoff
Entry Deterrence
To deter entry, the incumbent firm must convince any potential competitor that entry will be unprofitable
Payoff
Value associated with a possible outcome
Moral Hazard
When a party whose actions are unobserved can affect the probability or magnitude of a payment associated with an event. About how the contact changes the attitudes of the players
Grim-Trigger
each firm agrees to collude as long as the other firm does not deviate from the agreement. If at some period t one firm deviates from the agreement, starting at period t+1 both firms produce the Cornet equilibrium quantity forever.
Repeated game
game in which actions are taken and payoffs received over and over again
Principal-agent problems
problem arising when agents (e.g., a firm's managers) pursue their own goals rather than the goals of the principals (e.g., the firm's owners)
Tit-for-Tat Strategy
repeated-game strategy in which a player responds in kind to an opponent's previous play, cooperating with opponents and retaliating against uncooperative ones.
Commitment
the limitation of your choices (as in, you're committed to a particular course of action)
The lemons problem
with asymmetric information, low quality goods can drive high-quality goods out of the market
