301 Ch 13-18

game of chicken

-Coordination is REALLY important in this game. -first mover advantage stops the other firm from taking your advantage

to price discriminate:

-Identify different groups with different price elasticities or different values. -Find a way to prevent arbitrage

Examples of How Risk Aversion Influences Decisions

-Product quality (Informative advertising, Free samples, Guarantees) -Chain stores -Insurance

Optimal Bidding Strategy in a Second-Price Sealed-Bid Auction

-The optimal strategy is to bid your own valuation of the item. -This is a dominant strategy. -You don't pay your own bid, so bidding less than your value only increases the chance that you don't win. -If you bid more than your valuation, you risk buying the item for more than it is worth to you.

uncertainty

-uncertainty about the distribution of the random variables. -E.g., which probabilities should be assigned to the various values the random variables can take?

Bundle the goods

With enough bargaining power, the entire consumer surplus can be capture, if not, then bargain over how to split it.

Optimal Bidding Strategy in an English Auction

With independent private valuations, the optimal strategy is to remain active until the price exceeds your own valuation of the object.

rules of thumb for PD

be nice be easily provoked be forgiving dont be envious be clear

"trigger strategy"

-"Don't advertise, provided the rival has not advertised in the past. If the rival ever advertises, "punish" it by engaging in a high level of advertising forever after." -each firm agrees to "cooperate" so long as the rival hasn't "cheated" in the past. "Cheating" triggers punishment in all future periods.

Dutch Auction

-A descending price auction. -The auctioneer begins with a high asking price. -The bid decreases until one bidder is willing to pay the quoted price. -Strategically equivalent to a first-price auction.

Nash Equilibria

-A set of strategies, one for each player, such that no player has incentive to unilaterally change her action -Players are in an equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy.

how to get out of the prisoners dilemma

-Change the payoff structure of game so your profits are not dependent on others' actions -Differentiate the product so that it can't be easily imitated. -Find a way to lower cost

Entry "game"

-If an entrant decides to enter the industry, the incumbent has two paths of action: Accommodate the entry or Fight the entry. -By modeling the situation using game theory, we find that accommodating an entrant leads to profits while fighting an entrant leads to losses.

Natural experiments

-To gather information about the benefits and costs of a decision

Volume discounts

-Volume of purchase can also be used to discriminate between buyers -If a seller sets a single price, she will sell all units where MR > MC -To increase profitability the seller must find a way to sell the additional units at a lower price without lowering the price of the earlier units sold

risk

-how we characterize uncertainty about values that are variable. -Risk is modeled using random variables.

pure strategies

-players randomly choose actions, called "mixing" -Idea is to keep your opponent guessing -shirking/monitoring game -

Indirect Price Discrimination

Cannot identify members of groups; OR cannot prevent arbitrage Instead, discriminate by offering two products, a higher-priced, higher-quality good and a lower-priced, lower-quality good.

How do you respond to an invitation from a friend to invest in a real estate venture that depends on uncertain future demand and interest rates?

-Calculate the potential gains and loses based on different combinations of high and low interest rates and high and low demand -Whoever proposed the venture probably presented the best case scenario (low interest rates and high demand) - and that is the only combination (of four possible outcomes) under which you will do well. -Either don't invest or find a way that aligns your friend's incentives with your own, i.e., he gets a payoff only if the venture does well.

winner's curse

-If you win, you learn that you were the one who had the highest and most optimistic estimate of the unknown value of the item -worse when there are More bidders and Other bidders have better information

Bargaining: a sequential-move game

-In sequential-move bargaining the first "player" makes an offer that the second "player" can accept or refuse -look ahead and reason back to determine the how her rival will react to each possible move. Then the first-mover can determine the consequences of each possible move. -In this case, the sequential-move games present a "first-mover advantage"

avoiding collusion

-Keep cartels in the dark, so it is difficult for them to organize and to punish cheaters. -do not hold small and frequent auctions; -do not disclose information to bidders—do not announce who the other bidders are, who the winners are, or what the winning bids are.

modeling uncertainty

-Learn to make better decisions -Identify the source(s) of risk in a decisions -Compute the value of collecting more information. -use random variables to compute the expected costs and benefits of a decision

Optimal Bidding Strategy in a First-Price, Sealed-Bid Auction

-Optimal bids are less than bidders' private values. -If there are n bidders who all perceive valuations to be evenly (or uniformly) distributed between a lowest possible valuation of L and a highest possible valuation of H, then the optimal bid for a risk-neutral player whose own valuation is v is: b = v - [(v-L)/N]

Price discrimination in software

-Software manufacturers discriminate between high- and low-value consumers by offering different versions of software designed, and priced, to appeal to different groups.

Reacting to bid-rigging

-The government is frequently the victim of bid-rigging schemes. tips: -Do not rely on purchasing agents (those running the auction) who have little interest in buying at a low price. Instead, reward agents for making good (high-quality and low-price) purchases. -Do not use the procurement process to further a social agenda (small business set-asides, public lands, national defense, etc.) that is irrelevant to the goal of purchasing goods at low prices.

Third-Degree Price Discrimination

-The practice of charging different groups of consumers different prices for the same product. Group must have observable characteristics for third-degree price discrimination to work. Examples include student discounts, senior citizen's discounts, regional & international pricing.

How Nash's view differs from strategic

-The strategic view of bargaining places a greater emphasis on timing and commitment in determining the outcome of the game. -With the labor/management example, the union's commitment to strike, or management making the first move, changes the equilibrium of the game. -But neither action changes the gains of the agreement so neither would affect the Nash bargaining outcome. -The Nash bargaining outcome incorporates the idea that if you decrease your own gain to agreement you become a better bargainer. -This is similar to the idea of "opportunity cost."

Bargaining: a simultaneous game

-Two possible strategies are available to each player: "bargain hard" or "accommodate." -If both bargain hard, no deal is reached. Neither side gains. -If both accommodate, they split the gains from trade. -If one player bargains hard and the other accommodates, then the player who bargains hard takes 75% of the "pie"

Uncertainty in Pricing

-Uncertainty in pricing arises when the demand for a product is unknown. -To model this uncertainty, classify the number and type of potential customers

Dealing with uncertainty

-Uncertainty is unavoidable. -gather more or better information to cope

Nash's axiomatic approach

-[ S1(z) - D1 ] x [ (S2(z) - D2 ] -z is the agreement -S1(z) is the value of the agreement to player 1 (sub 2 for player two) -D1 is "disagreement value," or pay-off if no agreement is reached, for player 1 (sub 2 for player two) -So player 1's gain from agreement is (S1(z) - D1)

non strategic view

-acknowledges that real life negotiations don't have fixed rules as formal games do. -agrees that alternatives to agreement determine the terms of agreement, regardless of the rules of the negotiating game. -If you can increase your opponent's relative gain, or decrease your own, you can gain a bigger share of the pie.

price discrimination

-allows sellers to avoid the tradeoff -higher prices for some, lower prices for the others -the practice of charging different prices that are not cost-justified to different people

strategic view

-analyzes bargaining using the tools of game theory -Bargaining can be viewed as either a simultaneous-move game with two equilibria or a sequential-move game, where one player gains an advantage by committing to a position.

"Folk Theorem"

-any price at or above marginal cost and at or below monopoly price can be sustained if the discount rate is sufficiently small. -Small discount rate makes the present value of the annuity from cooperative pricing larger and favors a cooperative outcome.

avoiding winners curse

-bid less aggressively as the number of bidders increases -Bidders should reduce their value estimates to protect against this. -If you are the auctioneer release info to mitigate winners' curse.

collusion

-can be sustained as a Nash equilibrium when there is no certain "end" to a game. Doing so requires: -Ability to monitor actions of rivals. -Ability (and reputation for) punishing defectors. -Low interest rate. -High probability of future interaction.

trinomial random variable, X

-can have three values, x1,x2, or x3, with probabilities p1, p2, and 1-p1-p2. -The mean for a trinomial random variable is: E[X]= p1*x1+ p2*x2+(1- p1-p2) x3

binomial random variable, X

-can have two values, x1 or x2, with probabilities, p and 1-p -the expected value (mean) for a binomial random variable is: E[X]=p*x1+(1-p)x2

Bid Rigging or Collusion

-criminal violation of antitrust laws in the US and many other countries. -In one type of bid-rigging, cartel members re-auction the items won in a second-auction to cartel members in a second or "knockout" auction. -Bidders can increase their profit by agreeing not to bid against one another. -Such collusion or bid rigging is more likely to occur in open auctions and in small, frequent auctions.

Threats/credible commitments

-difficult to make because they require players to commit to a course of action against their self-interest. -the best threat is one you never have to use.

Discount coupons

-grocery stores allow more price sensitive consumers (shoppers with a lower income) to use coupons to receive lower prices, high-income/value shoppers are less price sensitive and less likely to clip coupons -This pricing scheme can be dangerous, though. High-value customers have the option of clipping coupons, and if too many do the scheme will become unprofitable.

Minimizing expected error costs

-helpful when one alternative would work well only under certain conditions, and you are uncertain about whether the conditions hold. -The optimal decision is the one with the smaller expected error costs, i.e. Tax if (1-p)*Cost(Type I) < p*Cost(Type II) -This type of analysis is especially useful for balancing the risks associated with pricing errors (over- v. under-), e.g., for airlines, hotels, cruise ships; as well as production errors (over v. under)

diff in risk and uncertainty

-is critical in financial markets - Risk can be quantified, priced and traded - people are comfortable with risk. Dealing with uncertainty is much more difficult. -Mistaking risk for uncertainty can be a costly mistake.

To represent values that are uncertain

-list the possible values the variable could take, -assign a probability to each value, and -compute the expected values (average outcomes) by calculating a weighted average using the probabilities as the weights.

english auction

-or oral -bidders submit increasing bids until only one bidder remains. -The item is awarded to this last remaining bidder. -second-highest bidders' value determines the price

Second-Price Sealed-bid Auctions

-or vickrey -a sealed-bid auction in which the item is awarded to the highest bidder, but the winner pays only the second-highest bid. -encourage bidders to bid more aggressively. -bidders are willing to bid up to their values, so the outcome is the same as an oral auction -easier to run than English auctions because the bidders can bid in remotely, and asynchronously (at different places and times) -equivalent to oral auctions and are well suited for use on the Internet. -ex. ebay

simultaneous-move

-player plans a move without knowing the other player's move in advance -we use a matrix or "normal-form" of the game. -likely outcomes are Nash equlibria, where no player has an incentive to change (each player is doing the best they can) -each player's payoffs can be modeled in a table/matrix by assigning player One to choose row strategies and player Two to choose column strategies -Compute Nash Equilibrium by finding pairs of strategies where both players are choosing the best possible response to their competitor's strategy

sequential-move games

-players take turns -Each competitor is given the opportunity to evaluate their rival's move before selecting how to proceed -extensive--form -Equilibrium is when each player chooses a best available move, anticipating how the other will react

dating game

-rotation increases payoffs but only possible if the game is repeated -firms can also analyze the tension between different divisions of a corporation (saturn and cadillac under GM)

prisoners dilemma (PD)

-self-interest leads to outcomes that reduce both players' payoffs -conflict and cooperation are in tension

Bonuses for agreement

-similar to incentive compensation schemes -When salespeople are offered bonuses it increases their eagerness to reach agreement and this induces them to accept "weaker" agreements.

auctions

-simply another form of competition, like price competition or bargaining. -set a price and identify the high-value buyer or low-cost seller. -often used in combination with bargaining, e.g., first an auction is used to identify the high-value buyers and then there is a negotiation over the final price. -identify the high-value bidder ("efficiency") and set a price for an item, with no negotiating necessary. For these reasons, economists love auctions.

Non-strategic View (axiomatic)

-the gains from bargaining relative to the alternatives to bargaining, determine the terms of any bargain -teaches that to increase your bargaining power, you can increase your opponent's gain from reaching agreement or decrease your own OR if your rival has more to gain by agreeing, he becomes more eager to reach agreement, and accepts a smaller share of the surplus.

First Price Sealed-Bid Auctions

-the highest bidder gets the item at a price equal to the highest bid. -A higher bid reduces the profit if you win, but also raises probability of winning (difficult tradeoff for bidders) -Bidders balance these two effects by bidding below their values ("shading"). -Experience and knowing the competing bidders are the keys to these auctions, but in general, bid more aggressively - shade less - if the competition is strong.

Common-Value Auctions

-the value is the same for each bidder, but no one knows what it is. Each bidder has only an estimate of the value. -possibility of winners curse -rivals learn something about the item's value by observing your bid, which creates an incentive to hide your bid. -By submitting bids at the last minute, bidders can effectively hide their bids and turn what resembles an oral auction into a sealed-bid auction. -oral auctions return higher prices than sealed-bid auctions in this setting because oral bids reveal information But oral auctions are more vulnerable to collusion.

Deterring Entry

-threaten (in such a manner as to be truly believable) to "commit" to fight the entry and price low -By committing to fight entry, the incumbent can benefit, even though the incumbent would be worse off if entry did occur, and the incumbent had to fight (the best threat is one you do not have to use)

bid-rotation scheme

-type of collusion -This scheme uses quid pro quo bidding -Bidders in these cartels submit weak bids or refrain from bidding against each other until it is their turn to "win." -each cartel member must wait for his turn to win - a weakness that leaves these schemes vulnerable to cheating.

two-part pricing

-fixed price plus a per-unit price -pricing consists of a fixed fee and a per unit charge (costco membership) -Charge a per-unit price low enough to consummate all wealth-creating transactions -When it isn't feasible to charge different prices for different units sold, but demand information is known, two-part pricing may permit you to extract all surplus from consumers. 1. Set price at marginal cost. 2. Compute consumer surplus. 3. Charge a fixed-fee equal to consumer surplus.

A player can gain bigger share of the "pie" by:

1) changing a simultaneous-move game into a sequential- move game with a first-mover advantage; or by 2) committing to a position.

major types of auctions

English First-price, sealed-bid Second-price, sealed-bid Dutch

Direct Price Discrimination

Identify members of the low-value group Charge low-value costumers a lower price Prevent resale (arbitrage) to higher-value consumers.

motivation of price discrimination

allows a firm to sell items to low-value customers who otherwise would not purchase because the price is too high (the firm consummates a wealth-creating transaction!)

successful price discrimination

attracts competition

difference-in-difference estimator

good way to gather information about the benefits and costs of a decision. -The first difference is before versus after the decision or event. -The second difference is the difference between a control and an experimental group. -controls for unobserved factors that can influence changes

Alternatives to agreement

incorporates the effect of alternatives to agreement on the agreement itself. This creates some sound bargaining advice: To improve your own bargaining position, increase your opponent's gain from reaching agreement, S2(z) - D2, or reduce your own gain from reaching agreement, S1(z) - D1. When you increase your opponent's gain in agreement, you make him more willing to agree. Reducing your own gain makes you less willing to compromise and helps to improve your position

random variable

is simply a way of representing numerical outcomes that occur with different probabilities.

extensive--form of a game

look ahead and reason back

'tying' the sales of one product to another

may violate antitrust laws

Type I error

not pregnant when you're are

Immediate Benefit - PV of Future Cost > 0

pays to cheats

individual demand curve.

price represents the value the consumer places on each unit consumed

damaged goods strategy

purposely making sure one model is the preferred product, by making the other model less desirable

uncertain about the costs or benefits of a decision?

replace numbers with random variables and compute expected costs and benefits.

two complementary way to look at bargaining

strategic view non strategic view

3 elements of a game

players, options/moves available and the payoffs resulting from each combination of moves.

Type II error

pregnant when you're not

types of games

simultaneous move sequential moves

Offer volume discounts

ex. buy one for $7, but the second for $6

diff levels of price elasticity with price discrimination

(P1-MC1)/P1=1/|elasticity1| (P2-MC2)/P2=1/|elasticity2| -The bigger the difference between group elasticities, the more profit there is in designing a price discrimination scheme.

If Immediate Benefit - PV of Future Cost 0

doesn't pay to cheat

Metering schemes

used to identify high-value consumers and allow for indirect price discrimination.

risk neutral

An individual who is indifferent between a risky prospect where E[x] = $M and a sure amount of $M.

Risk loving

An individual who prefers a risky prospect with an expected value, E[x], of $M to a sure amount of $M.

risk averse

An individual who prefers a sure amount of $M to a risky prospect with an expected value, E[x], of $M.

uses of auctions

Art Treasury bills Spectrum rights Consumer goods (eBay and other Internet auction sites) Oil leases