Econ 207 test 2
Adverse Selection
A high-risk person benefits more from insurance, so is more likely to purchase it.
What is a second movers advantage?
A second-mover advantage can permit a firm to earn a higher payoff by freeriding on the investments made by the first mover and produce at lower costs. Can also learn from first mover's mistake
How do you measure risk
An option is riskier if it has a larger variance.
Assumption about cheating in game with infinite periods
Assumes that you only cheat in the first period.
Optimal strategy for English auction in an independent auction
Assuming risk neutral. Stay active until the price exceeds your own valuation of the object - once the price exceeds valuation, exit the auction. If 𝒗1 > 𝒗2 -> 𝒃1 = 𝒗2 + 𝟎. 𝟎𝟏
Where does the residual demand start? Where does it lie in regards to ATC(Limit pricing)
At P^L. Because at this point D^M - Q^L = 0. The residual demand curve lies below the average cost curve, so entry is not profitable.
Why is the optimal strategy for Dutch and first price auction in independent auctions optimal?
Because if b=V, then U=0
Shade Bids
Bid below your valuation. b < v
Optimal strategy for second price auction in independent auction (Assuming risk neutral):
Bid truthfully
Why truth telling is the dominant strategy for second-price auction in an independent Auction if v1 < b2
Bidder 1's U = 0 (losing). Bidding below b2 will not help him win (no gain from lying). • Bidding above b2 will win the auction, but will have to pay b2 (no gain from lying).
Market failure because of Asymmetric information:
Buyers don't know the quality of a car We assume that the car is equally likely to be a good quality and bad quality. Sellers will sell good car for 2000, and a bad car for 1000 Buyers are willing to buy a good car for 2400 and 1200 for a bad car. It is 50% prob that a car is good or bad Then the buyer is willing to pay the expected value of the car: 𝐸𝑃 =0.5*2400 + 0.5*1200 = £1800 1800 is then the reservation price of the buyer This means that only bad quality cars will be sold in this market Had there been perfect information in the market, car sellers would sell both types of car, but because of the asymmetric information, only low quality cars will be sold because of the buyer's reservation price.
Grim trigger strategy
Cooperate until opponent defect, then defect forever. Removes incentive to cheat
What will be the change in p and Q for the incubent firm? (Limit pricing)
Decrease in p (p^L) and increase in Q (Q^L)
Optimal production q and p (with uncertain Demand):
E(MR) = MC Which is the same as E(p) = MC
What is Perfect information item? Example?
Everyone knows exactly what the item is worth. For example money
Value of information. Search for a lower price if:
Expected benefits > expected cost of additional search.
What is a Common-value auction? Example?
Extreme case of affiliated. 1. Correlated value estimates. 2. True underlying value of the item is the same for all bidders. 3. Individual tastes play no role in shaping bidders' value estimates. 4. Uncertainty: different bidders use different information to form their estimates of common value of the item. For example Oil field
Optimal strategy for all auctions in a common-value (Assuming risk neutral):
For english auction, information will be made available throughout the auction, so bidders can re-evaluate their valuation. The item for sale has the same value to every potential buyer. • Potential buyers differ in their own estimates of this common value. • Bidder 𝑖'𝑠 estimate is 𝒗i = 𝒗 + ei 𝑣: common value ei: is bidder 𝑖′𝑠 estimation error.
E(V) cheating (other firm plays grim trigger strategy if they cheat):
How much more you will earn in period that you cheat, than after punished + what you will earn after having cheated * (1+r)/r
Optimal strategy for all auctions in Correlated auction (Assuming risk neutral):
Optimal bidding requires that the players should use the information available during the auction process to update their value estimates.
E(V) not cheating (other firm plays grim trigger strategy if they cheat)
Payoff w/ collaboration * (1+r)/r
Why second price auction generates second most revenue for auctioneer in affiliated values auctions
Players learn nothing about the value estimates of other bidders. - Winner does not have to pay his own bid, but the bid of second highest. - The second-highest bid is linked to information another bidder has about the item's valuation . - This mitigates winner's curse to some extent. - Thus players shrink their bids by more than English auction, but less than they would in first-price auction.
Why revenue equivalence theorem does not hold in affiliated value auction
Players shrink their bids below what they would have bid based purely on their private value estimates in order to avoid winner's curse.
What will the entrant's P and Q be be? What will profits be? (Limit pricing)
Produce Q where residual demand = ATC. So, P=ATC. Profits will be 0. Which means that if entry has a cost, the entrant will face a negative profit
How do you calculate profit from becoming a duopoly?
Profit from being a monopoly + (profit after entry / i)
What is limit pricing?
Reducing the price of a good to just above average cost to deter the entry of new firms into the market. Prices are set at levels which are likely to make it unprofitable for potential entrants who might consider coming into the market
What type of consumer does this graph belong to? How is U calculated?
Risk averse. U=square root of v
What type of consumer does this graph belong to? How is U calculated?
Risk loving consumer. U=v^2
Why English auctions generates max rev for auctioneer if item is Affiliated value:
Risk neutral bidders will not bid their own private estimates to mitigate winner's curse. Thus, there will be an additional incentive for bidders to shade their bids below their estimated valuations. The English auction format provides bidders the most information (therefore allowing them to pool information to some extent), mitigating this problem. For this reason, the English auction would generate the highest expected revenues in this case.
What type of consumer does this graph belong to? How is U calculated?
Risk neutral. U=v
Finite number of turns. Opponent will play grim trigger strategy. What will be the solution?
The firms know that the game will be repeated exactly 10 times. Since there is no 11th period, the firms cannot punish their rivals for actions taken in the 10th period. If managers of Firm 1 and Firm 2 meet and decide to choose Low Advertising strategy, and then if Firm 1 cheats, Firm 2 cannot punish Firm 1, because there is no interaction after the 10th period. Let us look for the best responses of the firms in period 10. In the 10th (last) period, both firms will do 'Aggressive Advertising'. Using this logic for all the periods, the firms will always do 'Aggressive Advertising' in each period. Ends up at (A,A)
Explanation of revenue equivalence theorem
The price paid by the winner in the English auction is the second highest valuation plus a penny. In second-price auction you pay the value of second highest bid anyways. In a first-price and dutch auction, each bidder has an incentive to shade his bid, so they estimate how far below his valuation next highest bid is, and then shrinks his bid by that amount. On average, price paid to auctioneer is equal to second-highest bid.
What is predatory pricing?
The pricing of a product below cost with the intent to drive competitors out of the market.
Winner's Curse. Which auction item most apparent? Which auction most apparent?
The winners estimate of the item's value exceeds the estimates of all other bidders by a lot. In common value, the winner is the person with the highest estimate of valuation. Will be biggest in first price auctions as no information is given.
Exception for Grim trigger strategy
There are different periods, with a finite number of turns.
Nash Equilibrium
There is no incentive to deviate from initial strategy
Why truth telling is the dominant strategy for second-price auction in an independent Auction if v1 > b2
U = v1 - b2 > 0. Bidding just slightly above b2 will not change anything (price paid is b2 anyways). • Bidding less than b2 will make him lose the auction. (no gain from lying).
dominant strategy
a strategy that is best for a player in a game regardless of the strategies chosen by the other players
Optimal bidding strategy for risk neutral players (general)
a strategy that maximizes a bidder's expected profit
Signalling
an attempt to mitigate the adverse selection by an informed party to send an observable indicator of his or her hidden characteristics or hidden action to an uninformed party. Labour market: job applicants' resume, advanced degree such as PhD or MBA, etc
Screening
an attempt to mitigate the adverse selection by an uninformed party to sort individuals according to their characteristics. Self-selection mechanism F.eks. There are two workers. One is a good salesman. one is a good administrator. The owner does not know their characteristics. So he offers a contract: "Administrators earn a fixed salary £20,000; sales-person receives a 10% sales commission."
Optimal strategy for dutch and first price auction in independent (Assuming risk neutral):
b = v - (v-L)/n L: Lowest possible valuation H: Highest possible valuation
Best response analysis:
fixing the opponent on a particular strategy, and selecting the best possible response
Raising fixed cost example
lobbies for a regulation requiring any firm operating in the market to obtain a license from the government at a costs
A risk-averse consumer preferences
prefers a sure amount of £𝑀 to a risky prospect with an expected value of £𝑀.
How do you calculate profit from maintaining a monopoly?
profit from being a monopoly * (1+i)/i
What needs to happen for Limit pricing to be effective?
the pre-entry price must be linked to the post-entry profits of potential entrants. Needs a commitment mechanism and reputation effects.
How can a firm raise a rivals costs?
• Strategies involving marginal cost. • Strategies involving fixed cost.
Limit pricing is profitable if (written formula):
(Profit after limit pricing - profit in duopoly) / i > profit from being a monopoly - Profit of limit pricing
How to check if predatory pricing is profitable:
(Profit after predatory pricing / i) - cost of predatory pricing > Profit from maintaining duopoly * (1+i)/i
Limit pricing is profitable if (denotation formula):
(p^L - p^D)/i > p^M - p^L
First-price sealed-bid auction rules:
- Each bidder writes his bid in a sealed envelope. - Bidders do not see the bids of the other bidders. - Winner: bidder with the highest bid. - Payment: winner pays his bid. No information made available throughout auction.
Rules for second price auction. Information?:
- Each bidder writes his bid in a sealed envelope. - Bidders do not see the bids of the other bidders. - Winner: bidder with the highest bid. - Payment: winner pays the 2nd highest bid.
Dutch Auction rules. Information?
- Price p is announced each time. - At the beginning, p = maximum price. - Seller lowers the price by £1 at each period. - First buyer to bid, wins the item. No information is made available before the item gets sold.
Rules for an English auction. Information?
- Price p is announced each time. - At the beginning, p=0. Information is gained throughout the acution
For signaling to be effective it must be:
- observable by the uninformed party, - a reliable indicator of the unobservable characteristic(s), - difficult for parties with other characteristics to easily mimic
Why first price and dutch auction generates least revenue for auctioneer in affiliated values auctions
- players learn nothing about the value estimates of other bidders. - Winner pays his own bid. - Higher possibility of winner's curse. - Shrink the bids the most.
What is Affiliated (correlated) value estimates item? Example?
1. Bidders do not know their own valuation of the item or the valuations of the others. 2. Each bidder uses his or her own information to estimate their valuation, and these value estimates are affiliated. 3. The higher a bidder's value estimate, the more likely it is that other bidders also have high-value estimates. For example Art with uncertain authenticity
What is an Independent private values item? Example?
1. Each bidder knows his own valuation of the item but does not know other bidders' valuations. 2. Each bidder's valuation is independent. For example a comic book with some emotional value
Counter tactics to predatory pricing:
1. Stop production entirely and cause the predator to lose more money each period. 2. Purchase the product from the predator and stockpile it to sell when predatory pricing ceases.
How to calculate variance
1. Subtract each score from the mean 2. Square the result 3. Add them all up 4. Divide by how many there is
Moral Hazard
1. When one party has an incentive to behave differently once an agreement is made between parties 2. After transaction occurs 3. One way of mitigating the moral hazard problem is an incentive contract (Bonuses etc.) F.eks. Communism because people does not have an incentive to work hard
Firm A earns 20 in the period it cheats. In all future periods Firm A will earn 5. What is the formula for E(V) of cheating?
15 + 5 (i+r)/r
Firm A earns 70 in the period it cheats. So, in all future periods, Firm A gets a payoff of 30 What is the formula for E(V) of cheating?
40 + 30 (1+r)/r
Infinitely repeated game with interest rate. When to cheat or not.
If E(V) cheating > E(V) not cheating, then cheat.
What is a reputation effect?
If a firm establishes a reputation of being tough on entrants, then entrants will deter from entering the market in the future So, charging a low price today (to punish an entrant) discourages entry by other firms, which increases profits in long term.
How is the residual demand calculated? (Limit pricing)
If the entrant believes that the incumbent is going to produce 𝑸𝑳 at a price 𝑃𝐿, then assuming the total market demand is 𝑫𝑴 , the residual demand will be : 𝑫𝑴 − 𝑸𝑳 .
What is a commitment mechanism?
If the incumbent can somehow 'tie its own hands' and credibly commit to maintain a post-entry output at 𝑸𝑳. Incumbent may make such a commitment by building a plant that is incapable of producing less than 𝑄𝐿. (Can't go back) Entrant knows that at least 𝑄𝐿 is going to be produced and thus the entrant faces the residual demand curve - which lies below the average costs (Entry not profitable.)
When can you experience a first mover advantage?
In a sequential game
What are requirements for the firm that does the predatory pricing?
Involves a trade-off between current and future profits, so it is profitable only when the present value of the higher future profits offsets the losses required to drive rivals out of the market. • Must have greater financial resources than the prey in order to outlast it
What kind of a problem is this?
Mixed problem
What is asymmetric information? What to pay in this situation
One person has more/better information than others. Pay expected (p)