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Why You Should Charge Your Friends for Borrowing Your Stuff

Why You Should Charge Your Friends for Borrowing Your Stuff. Kijung Shin , Euiwoong Lee, Dhivya Eswaran , Ariel Procaccia Carnegie Mellon University. In Partial Fulfillment of the Speaking Requirement. Sharable Goods: Question. DVDs. IKEA toolkit. portable crib.

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Why You Should Charge Your Friends for Borrowing Your Stuff

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  1. Why You Should Charge Your Friends for Borrowing Your Stuff Kijung Shin, Euiwoong Lee, DhivyaEswaran, Ariel Procaccia Carnegie Mellon University In Partial Fulfillment of the Speaking Requirement

  2. Sharable Goods: Question DVDs IKEA toolkit portable crib “What do they have in common?” Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  3. Sharable Goods: Properties Used occasionally Lend to friends Do not lend to strangers Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  4. Social Network: Question Carol Alice Bob “How many people should buy an IKEA toolkit for everyone to useit?” • Consider a social network, which is a graph • Nodes: people • Edges: friendship Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  5. Social Optimal Decision Alice Bob “Does everyone want to stick to their current decisions?” The answer is at least people Socially optimal: with minimum purchases (or with minimum cost) everyone uses a toolkit Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  6. Individually Optimal Decision Alice Bob The answer is No Individually optimal: everyone best responses to others’ decisions Socially inefficient (suboptimal): 4 purchases happen when 2 are enough Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  7. Social Inefficiency Carol Dan “How can we prevent this social inefficiency?” Individually optimal outcome with 6 purchases Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  8. Moving toward Social Optimum Alice Bob “How can we make people to stick with this socially optimal outcome?” Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin) Recall the socially optimal outcome

  9. Imposing Access Costs Alice Bob “Does everyone want to stick to their current decisions?” Renters pay a cost for getting permanentaccess Access cost is half the price of a toolkit Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  10. Socially & Individually Optimal Alice Bob • The answer is Yes • Alice & Bob:arepaid more than the price • The others: renting is cheaper than buying • Individually optimal • Socially optimal with minimum (2) purchases Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  11. Goal and Approaches Sharable good game (SGG) Sharable good game with access cost (SGG-AC) • Goal: To examine incentives to buy sharable goods • Approaches: game-theoretic models with equilibrium analysis and simulations • Questions: • Q1. How sociallyinefficient are individually optimal outcomes? • Q2. Do access costs reduce the social inefficiency? • Q3. What is the proper access cost? Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  12. Road Map • Concepts in Game Theory • Game-theoretic Models • Sharable Good Game • Sharable Good Game with Access Cost • Simulation • Conclusion Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  13. Road Map • Concepts in Game Theory << • Game-theoretic Models • Sharable Good Game • Sharable Good Game with Access Cost • Simulation • Conclusion Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  14. Concept: Game • A normal-formgame consists of • Players: entities who make decisions • Strategy set: possible strategies that each player can take • Outcome: a vector of strategies where is the strategy of player • Utility of each player at each outcome • : utility of player • : utility of player at outcome Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  15. Example: Prisoner’s Dilemma • Players: two men who are charged with a crime • Strategy set: {cooperate, defect} • cooperate: stay silent • defect: talk to the police and admit their crime • Utility: • both cooperate: both will be jailed for 1year • both defect: both will be jailed for 6years • one defects and the other cooperates: one who defectswill be freed while the other will be jailed for 9 years Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  16. Example: Prisoner’s Dilemma Player 2’s strategy Utility of Player 1 Cooperate Defect -9,0 -1,-1 Cooperate Utility of Player 2 Player 1’s strategy -6,-6 0,-9 Defect Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  17. Concept: Nash Equilibrium other players’ current strategies (FIXED) current strategy of player possible strategy of player • Nash Equilibrium (NE): • is an outcome • where each player’s strategy is a best response • when fixing the other players’ strategies • Formally, in an NE , for each player , Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  18. Example: Nash Equilibrium Player 2’s Strategy Cooperate Defect -9, 0 -1, -1 Cooperate Utility of Player 1 Player 1’s Strategy -6, -6 0, -9 Defect Utility of Player 2 Claim: (Defect, Defect) is an NE in Prisoner’s Dilemma Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  19. Example: Nash Equilibrium Player 2’s Strategy Cooperate Defect -9,0 -1, -1 if Player 1 changes its strategy Cooperate Player 1’s Strategy -6,-6 0, -9 Defect Claim: (Defect, Defect) is an NE in Prisoner’s Dilemma Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  20. Example: Nash Equilibrium Player 2’s Strategy Cooperate Defect -9, 0 -1, -1 Cooperate Player 1’s Strategy -6,-6 0,-9 if Player2 changes its strategy Defect Claim: (Defect, Defect) is an NE in Prisoner’s Dilemma Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  21. Example: Nash Equilibrium Player 2’s Strategy Cooperate Defect -9, 0 -1, -1 Cooperate Player 1’s Strategy -6, -6 0, -9 Defect Claim: (Defect, Defect) is an NE in Prisoner’s Dilemma Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  22. Example: Nash Equilibrium Player 2’s Strategy Cooperate Defect -9, 0 -1, -1 Cooperate Player 1’s Strategy -6, -6 0, -9 Defect Claim: (Cooperate, Cooperate) is not an NE Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  23. Example: Nash Equilibrium Player 2’s Strategy Cooperate Defect -9,0 -9,0 -1,-1 if Player 2 changes its strategy Cooperate Player 1’s Strategy -6, -6 0, -9 Defect Claim: (Cooperate, Cooperate) is not an NE Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  24. Concept: Social Optimum social optimum Nash equilibrium • Social welfare in an outcome • sum of utilities of all players in the outcome • Social optimum: • an outcome where social welfare is maximized • Generally, Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  25. Example: Social Optimum Player 2’s Strategy Cooperate Defect -9 + 0 = -9 -1 + -1 = -2 Cooperate Player 1’s Strategy -6 -6 = -12 0 -9 = -9 Defect Claim: (Cooperate, Cooperate) is a social optimum Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  26. Example: Social Optimum Social optimum Player 2’s Strategy Cooperate Defect -9, 0 -1, -2 Nash equilibrium Cooperate Player 1’s Strategy -6, -6 0, -9 Defect Nash equilibrium social optimum Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  27. Game Theory Concepts: Summary Nash equilibrium: an outcome where each user best responds to others’ strategies Social welfare: sum of utilities of all players Social optimum: an outcome where the social welfare is maximized Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  28. Road Map • Concepts in Game Theory • Game-theoretic Models • Sharable Good Game << • Sharable Good Game with Access Cost • Simulation • Conclusion Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  29. Sharable Good Game (SGG) ) free rider (friends of the owner) underprivileged owner • Consider a good sharable with friends • Players: nodes in a social network • Strategy set: buy a good ( ) or not buy ( ) • Utility: • owner: (benefit) – (price) () • free rider: (benefit) • underprivileged: Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  30. Nash Equilibrium: Conditions Utility comparison: free rider > owner > underprivileged underprivileged owner owner free rider • no underprivilegednodes • underprivileged nodes become owners by changing their strategy to “buy” • owners have no owner friends • otherwise, owners become free riders by changing their strategy to “not buy” Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  31. Nash Equilibrium: Existence Theorem [Existence of NEs in SGG]: In any social network, there exists a Nash Equilibrium. “Do Nash equilibria exist in every social network?” • initialize the strategy of every node to “not buy” • repeat until there is no underprivileged node • choose an underprivileged node • change its strategy to “buy” Proof: The following algorithm always gives an NE Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  32. Detail Proof of Existence • initialize the strategy of every node to “not buy” • repeat until there is no underprivileged node • choose an underprivileged node • change its strategy to “buy” Underprivileged Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  33. Detail Proof of Existence (cont.) • initialize the strategy of every node to “not buy” • repeat until there is no underprivileged node • choose an underprivileged node • change its strategy to “buy” Underprivileged Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  34. Detail Proof of Existence (cont.) • initialize the strategy of every node to “not buy” • repeat until there is no underprivileged node • choose an underprivileged node • change its strategy to “buy” Underprivileged Underprivileged Free riders Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  35. Detail Proof of Existence (cont.) • initialize the strategy of every node to “not buy” • repeatuntil there is no underprivileged node • choose an underprivileged node • change its strategy to “buy” Underprivileged Underprivileged Underprivileged Free riders Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  36. Detail Proof of Existence (cont.) • initialize the strategy of every node to “not buy” • repeat until there is no underprivileged node • choose an underprivileged node • change its strategy to “buy” Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin) • The outcome is a Nash Equilibrium • no underprivilegednodes • this is the termination condition • owners have no owner friends • new owners are chosen among underprivileged nodes

  37. Nash Equilibrium: Non-uniqueness “Is there a unique Nash equilibrium in every social network?” Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  38. Nash Equilibrium: Non-uniqueness Theorem [Non-uniqueness of NEs in SGG]: There can be multiple Nash equilibria with different social welfare Social Optimum NE with social welfare NE with social welfare Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin) Example:

  39. Measuring Inefficiency Fixed Fixed benefit # nodes price # owners • In every NE and social optima • no underprivileged node • every node gets benefit from a good • Use # owners to measure inefficiency of NEs Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  40. Measuring Inefficiency (cont.) # owners in the NE inefficiency of an NE := # owners in a social optimum PoA (Price of Anarchy) maximum inefficiency over all NEs := PoS (Price of Stability) minimum inefficiency over all NEs := Given a social network, Given a social network, Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  41. Worst-case Analysis Theorem [Worst-case Analysis in SGG]: There exists a social network with nodes where both PoA and PoS are … Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin) Example : …

  42. Worst-case Analysis (cont.) Theorem [Worst-case Analysis in SGG]: There exists a social network with nodes where both PoA and PoS are … social optimum( owners) most efficient NE ( owners) least efficient NE ( owners) Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin) Example : … … … … …

  43. Reason of Inefficiency … “How can we incentivize nodes with many friends to buy a good?” social optimum( owners) most efficient NE ( owners) least efficient NE ( owners) • A Nash equilibrium is inefficient when • nodes with many friends free ride • nodes with few friends buy a good Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin) … … … … …

  44. Summary of SGG • Definition: • Players: nodes in a social network • Strategy set: “buy”, “not buy” • Utility: free rider > owner > underprivileged • Nash Equilibrium: • always exists but not unique • Efficiency of Nash Equilibria: • both best and worst NEs can be highly inefficient Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  45. Road Map • Concepts in Game Theory • Game-theoretic Models • Sharable Good Game • Sharable Good Game with Access Cost << • Simulation • Conclusion Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  46. SGG with Access Cost (SGG-AC) ) underprivileged renter renter owner • Consider a good sharable with friends • Players: nodes in a social network • Strategy set: • buy a good ( ) or not buy ( ) • renta good from a friend by paying an accesscost( ) to the friend Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  47. Utility in SGG-AC underprivileged renter renter owner Utility comparison: rich owner > renter > poor owner > underprivileged • Utility: • owner: (benefit) (price) (access cost) (# its renters) • renter: (benefit) (access cost) • underprivileged: (assumption: ) • Rich owner and poor owner: • rich owner: owner with at least renters • poor owner: owner with less than renter Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  48. Nash Equilibrium: Conditions Utility comparison: rich owner > renter > poor owner > underprivileged • no underprivilegednodes • underprivileged nodes become owners by changing their strategy to “buy” • poor owners have no owner friends • otherwise, poor owners become renters by changing their strategy to “rent” underprivileged poor owner renter poor owner Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

  49. Existence and Non-uniqueness Theorem [Existence of NEs in SGG-AC]: In any social network, there exists a Nash Equilibrium. Theorem [Non-uniqueness of NEs in SGG]: There can be multiple Nash equilibria with different social welfare NE with 5 owners NE with 1 owner Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin) Example :

  50. Measuring Inefficiency: Review # owners in the NE inefficiency of an NE := # owners in a social optimum PoA (Price of Anarchy) maximum inefficiency over all NEs := PoS (Price of Stability) minimum inefficiency over all NEs := Given a social network, Given a social network, Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)

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