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Information, economics, and game theory

Information, economics, and game theory. 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

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Information, economics, and game theory

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  1. Information, economics, and game theory

  2. Bundling • Bundling is also a nice way to deal with heterogeneous consumer preferences. • Example: two items: i1 and i2, two consumers c1 and c2 • c1 values i1 at $5 and i2 at $3 • c2 values i2 at $5 and i1 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)

  3. 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)

  4. 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

  5. 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

  6. 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

  7. 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.

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

  9. 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

  10. 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

  11. 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.

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

  13. 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.

  14. 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.

  15. 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.)

  16. 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

  17. 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.

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

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

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

  21. 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.

  22. 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.

  23. 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.

  24. 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

  25. 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.

  26. 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

  27. 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.

  28. An example:Big Monkey and Little Monkey • 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?

  29. An example:Big Monkey and Little Monkey • 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

  30. An example:Big Monkey and Little Monkey c w Big monkey c w c Little monkey w 0,0 9,1 6-2,4 7-2,3 • 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)

  31. An example:Big Monkey and Little Monkey • 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.

  32. An example:Big Monkey and Little Monkey • What if the monkeys have to decide simultaneously? c w Big monkey c w c Little monkey w 0,0 9,1 6-2,4 7-2,3 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)

  33. An example:Big Monkey and Little Monkey • It can often be easier to analyze a game through a different representation, called normal form Little Monkey c v Big Monkey 5,3 4,4 c v 9,1 0,0

  34. 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.

  35. Eliminating Dominated Strategies • The first step is to eliminate actions that are worse than another action, no matter what. c w Big monkey c w c w c 9,1 4,4 w Little monkey We can see that Big Monkey will always choose w. So the tree reduces to: 9,1 0,0 9,1 6-2,4 7-2,3 Little Monkey will Never choose this path. Or this one

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

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

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

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

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

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

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

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

  44. 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

  45. 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.

  46. An example:Big Monkey and Little Monkey • 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?

  47. An example:Big Monkey and Little Monkey • 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

  48. An example:Big Monkey and Little Monkey c w Big monkey c w c Little monkey w 0,0 9,1 6-2,4 7-2,3 • 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)

  49. An example:Big Monkey and Little Monkey • 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.

  50. An example:Big Monkey and Little Monkey • What if the monkeys have to decide simultaneously? c w Big monkey c w c Little monkey w 0,0 9,1 6-2,4 7-2,3 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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