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Information, economics, and game theory

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Bundling Bundling is also a nice way to deal with heterogeneous consumer preferences. Example: two items: i 1 and i 2, two consumers c 1 and c 2 c 1 values i 1 at $5 and i 2 at $3 c 2 values i 2 at $5 and i 1 at $3 Assigning separate prices to each item, the best a seller can do is charge $3 and make $12 total. If a seller can bundle the two items together, he can charge $8 and make $16 total. –(there are similar examples in which consumers do better with bundling)

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Value-added bundling Bundling can be used to add value to an existing product. A seller filters, bundles and organizes existing information goods. –RedHat –AP news wire –Brokerages –Cable packages Helps consumers deal with the glut of information Takes advantage of complementarity (two things are more valuable together than separately)

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Price Schedules Bundling is just one of a number of price schedules that are possible when marginal cost is very low. This makes a number of new schemes possible for the sale of information goods. Gives producers more flexibility to distinguish themselves from each other. –Specialists (searchers) often prefer single items –Generalists (browsers) want larger quantities

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Price Schedules Per-article pricing (linear pricing): Every item costs $p. –Example: mp3 sales, back-dated NYT articles Bundling: Consumers pay a fixed price $b for access to all goods. –Example: cable packages, Salon, Netflix (sort of) Two-part tariff (subscription + fee) – Consumers pay an entry fee $f, plus a per-item price $p. –Buying clubs, rebates (fee is negative), amusement parks, shared computer resources

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Price Schedules Mixed Bundling: Consumers are offered a choice between a linear price and a bundle. –Microsoft Office vs Word, Excel Block pricing (discount pricing): Consumers pay a price $p1 for the first n items, and $p2 for each additional item. –Grain, electricity, bandwidth

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Price Schedules Nonlinear pricing –Consumer pays a different price for each item. –Logical extension of block pricing. –Power consumption, water usage Each of these schedules implements a form of price discrimination.

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Price Schedules More complex schedules are able to fit consumer demand more exactly.

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Price Discrimination Goal: Charge different prices to different consumers. –Extract more surplus (consumer $$) –Make it possible for more consumers to buy. First-degree price discrimination: explicitly charge different prices to different consumers. –Hard to do, potentially illegal

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Price Discrimination Second-degree price discrimination –Different prices are charged for different quantities. Third-degree price discrimination –Consumers are grouped into different classes, which are charged different rates. Different versions of software Airlines Senior discounts

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Issues with Schedule Complexity In theory, a more complex schedule is better for the producer –Allows him to match consumer demand more precisely. Problems –Complex schedules are difficult and confsing for people Agents may help with this –If producers must learn what prices to offer, a tradeoff develops Extra profit from a more complex schedule vs the cost of learning more parameters.

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Fixed Price Schedules Simpler schedules can be learned more easily, but extract lower long-run profit

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Summary Information goods have a number of characteristics that differentiate them from physical goods –Nonrivalry, nontransparency, nonexcludability, zero marginal cost Sellers of information goods need to account for the fact that traditional market rules may not apply.

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Summary Information goods can be easily packaged and bundled. More complex pricing schedules are also available –Trade off the ability to precisely meet consumer demand against number of parameters needed.

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Negotiation Once agents have discovered each other and agreed that they are interested in buying/selling, they must negotiate the terms of the deal. Might be simple (take it or leave it) or complex (iterated bargaining) Might involve only price, or many other dimensions (quality, service contract, warranty, delivery, payment terms, etc.)

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Mechanism Design By setting up the rules that agents use to negotiate, we can ensure that particular sorts of behavior or solutions occur. –Truth-telling –Maximize profit –Maximize social welfare –Maximize participation –Reach solutions quickly –Etc. Choosing rules that lead to a particular outcome is known as mechanism design

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Supply and Demand Supply and demand are the two parameters that govern a market’s behavior Supply: quantity of product available Demand: amount of product wanted at a particular price.

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Demand We can visualize demand as a downward- sloping curve Price Quantity demanded

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Supply Similarly, supply can be visualized as an upward-sloping curve. Price Quantity demanded Quantity supplied

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Equilibrium The point at which supply and demand intersect is called the competitive equilibrium Price Quantity demanded Quantity supplied In a perfect world, prices will drive supply and demand to the equilibrium

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Equilibrium One of the central tenets of market economies is the invisible hand If there is too much supply, prices will fall due to competition – this increases demand. If there is too much demand, prices will increase – this encourages supply. In equilibrium, the quantity supplied will equal the quantity demanded.

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Breaking an Equilibrium There are many things that can keep a market from equilibrium –Lack of sellers (monopoly/oligopoly) –“Lock-in” among buyers –Incomplete or slow-moving information –Collusion among (usually) sellers or buyers –External price controls –Etc.

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Properties of an Equilibrium Equilibria have some nice properties: –Everyone who wants to buy/sell at this price can. –This sort of solution is called “efficient” –Given this price, no one wants to change. –The system is stable; given that you are at an equilibrium you will stay there.

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Rationality Rationality is the assumption that an agent (human or software) will act so as to maximize its happiness or advantage. We often try to measure this advantage numerically using utility Money can sometimes serve as a substitute for utility

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Markets and Games Markets are useful for understanding interactions among a large group of agents –No need to speculate about individual actions In many e-commerce settings, negotiation takes place in a one-on-one format In this case, game theory is a more useful analytical tool. –Also very useful for designing agents that operate in open environments.

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Game Theory Developed to explain the optimal strategy in two-person interactions. Initially, von Neumann and Morganstern –Zero-sum games John Nash –Nonzero-sum games Harsanyi, Selten –Incomplete information

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An example: Big Monkey and Little Monkey Monkeys usually eat ground-level fruit Occasionally climb a tree to get a coconut (1 per tree) A Coconut yields 10 Calories Big Monkey expends 2 Calories climbing the tree. Little Monkey expends 0 Calories climbing the tree.

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If BM climbs the tree –BM gets 6 C, LM gets 4 C –LM eats some before BM gets down If LM climbs the tree –BM gets 9 C, LM gets 1 C –BM eats almost all before LM gets down If both climb the tree –BM gets 7 C, LM gets 3 C –BM hogs coconut How should the monkeys each act so as to maximize their own calorie gain? An example: Big Monkey and Little Monkey

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Assume BM decides first –Two choices: wait or climb LM has four choices: –Always wait, always climb, same as BM, opposite of BM. These choices are called actions –A sequence of actions is called a strategy An example: Big Monkey and Little Monkey

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Big monkey w w w c c c 0,0 Little monkey 9,16-2,47-2,3 What should Big Monkey do? If BM waits, LM will climb – BM gets 9 If BM climbs, LM will wait – BM gets 4 BM should wait. What about LM? Opposite of BM (even though we’ll never get to the right side of the tree)

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These strategies (w and cw) are called best responses. –Given what the other guy is doing, this is the best thing to do. A solution where everyone is playing a best response is called a Nash equilibrium. –No one can unilaterally change and improve things. This representation of a game is called extensive form. An example: Big Monkey and Little Monkey

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What if the monkeys have to decide simultaneously? An example: Big Monkey and Little Monkey Big monkey w w w c c c 0,0 Little monkey 9,16-2,47-2,3 Now Little Monkey has to choose before he sees Big Monkey move Two Nash equilibria (c,w), (w,c) Also a third Nash equilibrium: Big Monkey chooses between c & w with probability 0.5 (mixed strategy)

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It can often be easier to analyze a game through a different representation, called normal form An example: Big Monkey and Little Monkey c cv v 5,3 4,4 0,09,1 Little Monkey Big Monkey

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Choosing Strategies In the simultaneous game, it’s harder to see what each monkey should do –Mixed strategy is optimal. Trick: How can a monkey maximize its payoff, given that it knows the other monkeys will play a Nash strategy? Oftentimes, other techniques can be used to prune the number of possible actions.

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Eliminating Dominated Strategies The first step is to eliminate actions that are worse than another action, no matter what. Big monkey w w w c c c 0,0 Little monkey 9,16-2,47-2,3 Little Monkey will Never choose this path. Or this one w c 9,14,4 We can see that Big Monkey will always choose w. So the tree reduces to: 9,1

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Eliminating Dominated Strategies We can also use this technique in normal- form games: a ab b 5,3 4,4 0,0 9,1 Row Column

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Eliminating Dominated Strategies We can also use this technique in normal- form games: a ab b 5,3 4,4 0,0 9,1 For any column action, row will prefer a.

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Eliminating Dominated Strategies We can also use this technique in normal- form games: a ab b 5,3 4,4 0,0 9,1 Given that row will pick a, column will pick b. (a,b) is the unique Nash equilibrium.

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Prisoner’s Dilemma Each player can cooperate or defect cooperatedefect 0,-10 -10,0 -8,-8 -1,-1 Row Column cooperate

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Prisoner’s Dilemma Each player can cooperate or defect cooperatedefect 0,-10 -10,0 -8,-8 -1,-1 Row Column cooperate Defecting is a dominant strategy for row

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Prisoner’s Dilemma Each player can cooperate or defect cooperatedefect 0,-10 -10,0 -8,-8 -1,-1 Row Column cooperate Defecting is a dominant strategy for row, And also for column

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Prisoner’s Dilemma Each player can cooperate or defect cooperatedefect 0,-10 -10,0 -8,-8 -1,-1 Row Column cooperate Frustration: even though mutual cooperation is a better strategy for everyone, defection is the Nash equilibrium!

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Prisoner’s Dilemma Relevant to: –Arms negotiations –Online Payment –Product descriptions –Workplace relations How do players escape this dilemma?

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Game Theory Developed to explain the optimal strategy in two-person interactions. Initially, von Neumann and Morganstern –Zero-sum games John Nash –Nonzero-sum games Harsanyi, Selten –Incomplete information

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An example: Big Monkey and Little Monkey Monkeys usually eat ground-level fruit Occasionally climb a tree to get a coconut (1 per tree) A Coconut yields 10 Calories Big Monkey expends 2 Calories climbing the tree. Little Monkey expends 0 Calories climbing the tree.

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If BM climbs the tree –BM gets 6 C, LM gets 4 C –LM eats some before BM gets down If LM climbs the tree –BM gets 9 C, LM gets 1 C –BM eats almost all before LM gets down If both climb the tree –BM gets 7 C, LM gets 3 C –BM hogs coconut How should the monkeys each act so as to maximize their own calorie gain? An example: Big Monkey and Little Monkey

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Assume BM decides first –Two choices: wait or climb LM has four choices: –Always wait, always climb, same as BM, opposite of BM. These choices are called actions –A sequence of actions is called a strategy An example: Big Monkey and Little Monkey

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Big monkey w w w c c c 0,0 Little monkey 9,16-2,47-2,3 What should Big Monkey do? If BM waits, LM will climb – BM gets 9 If BM climbs, LM will wait – BM gets 4 BM should wait. What about LM? Opposite of BM (even though we’ll never get to the right side of the tree)

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These strategies (w and cw) are called best responses. –Given what the other guy is doing, this is the best thing to do. A solution where everyone is playing a best response is called a Nash equilibrium. –No one can unilaterally change and improve things. This representation of a game is called extensive form. An example: Big Monkey and Little Monkey

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What if the monkeys have to decide simultaneously? An example: Big Monkey and Little Monkey Big monkey w w w c c c 0,0 Little monkey 9,16-2,47-2,3 Now Little Monkey has to choose before he sees Big Monkey move Two Nash equilibria (c,w), (w,c) Also a third Nash equilibrium: Big Monkey chooses between c & w with probability 0.5 (mixed strategy)

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It can often be easier to analyze a game through a different representation, called normal form An example: Big Monkey and Little Monkey c cv v 5,3 4,4 0,09,1 Little Monkey Big Monkey

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Choosing Strategies In the simultaneous game, it’s harder to see what each monkey should do –Mixed strategy is optimal. Trick: How can a monkey maximize its payoff, given that it knows the other monkeys will play a Nash strategy? Oftentimes, other techniques can be used to prune the number of possible actions.

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Eliminating Dominated Strategies The first step is to eliminate actions that are worse than another action, no matter what. Big monkey w w w c c c 0,0 Little monkey 9,16-2,47-2,3 Little Monkey will Never choose this path. Or this one w c 9,14,4 We can see that Big Monkey will always choose w. So the tree reduces to: 9,1

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Eliminating Dominated Strategies We can also use this technique in normal- form games: a ab b 5,3 4,4 0,0 9,1 Row Column

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Eliminating Dominated Strategies We can also use this technique in normal- form games: a ab b 5,3 4,4 0,0 9,1 For any column action, row will prefer a.

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Eliminating Dominated Strategies We can also use this technique in normal- form games: a ab b 5,3 4,4 0,0 9,1 Given that row will pick a, column will pick b. (a,b) is the unique Nash equilibrium.

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Prisoner’s Dilemma Each player can cooperate or defect cooperatedefect 0,-10 -10,0 -8,-8 -1,-1 Row Column cooperate

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Prisoner’s Dilemma Each player can cooperate or defect cooperatedefect 0,-10 -10,0 -8,-8 -1,-1 Row Column cooperate Defecting is a dominant strategy for row

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Prisoner’s Dilemma Relevant to: –Arms negotiations –Online Payment –Product descriptions –Workplace relations How do players escape this dilemma?

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Prisoner’s Dilemma Each player can cooperate or defect cooperatedefect 0,-10 -10,0 -8,-8 -1,-1 Row Column cooperate

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Prisoner’s Dilemma Each player can cooperate or defect cooperatedefect 0,-10 -10,0 -8,-8 -1,-1 Row Column cooperate

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