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 ID: 669119
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Slide1
Why You Should Charge Your Friends for Borrowing Your Stuff
Kijung Shin, Euiwoong Lee, Dhivya Eswaran, Ariel ProcacciaCarnegie Mellon University
In Partial Fulfillment of the Speaking RequirementSlide2
Sharable Goods: QuestionWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)2/73
“What do they have in common?”
portable crib
IKEA toolkit
DVDsSlide3
Sharable Goods: PropertiesUsed occasionallyLend to friendsDo not lend to strangersWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
3/73Slide4
Social Network: Question
Consider a social network, which is a graphNodes: peopleEdges: friendshipWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
4/73
Alice
Carol
Bob
“How many people should buy an
IKEA
toolkit for everyone to use
it
?”Slide5
Social Optimal Decision
The answer is at least peopleSocially 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)
5/73
Bob
“Does everyone want to stick to
their current decisions?”
AliceSlide6
Individually Optimal DecisionThe answer is NoIndividually optimal: everyone best responses to others’ decisions
Socially inefficient (suboptimal): 4 purchases happen when 2 are enoughWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)6/73
Alice
BobSlide7
Social InefficiencyIndividually optimal outcome with 6 purchases
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)7/73
Dan
Carol
“How can we prevent this social inefficiency?”Slide8
Moving toward Social OptimumWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
8/73“How can we make people to stick with this socially optimal outcome?”
Recall the
socially optimal outcome
Bob
AliceSlide9
Imposing Access Costs
Renters pay a
cost
for getting
permanent
accessAccess cost is half the price of a toolkit
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
9
/73
“Does everyone want to stick to
their current decisions?”
Bob
AliceSlide10
Socially & Individually Optimal
The answer is
Yes
Alice & Bob:
are
paid more than the priceThe 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)
10
/73
Bob
AliceSlide11
Goal and ApproachesGoal: To examine incentives to buy sharable goodsApproaches:
game-theoretic models with equilibrium analysis and simulationsQuestions: Q1. How socially inefficient 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)11/73
Sharable good game (SGG)
Sharable good game
with access cost (SGG-AC)Slide12
Road Map
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)12/73
Concepts in Game Theory
Game-theoretic Models
Sharable Good Game
Sharable Good Game with Access Cost
Simulation
ConclusionSlide13
Road MapWhy You Should Charge Your Friends for Borrowing Your Stuff (by
Kijung Shin)13/73
Concepts in Game Theory <<
Game-theoretic Models
Sharable Good Game
Sharable Good Game with Access Cost
Simulation
ConclusionSlide14
Concept: GameA normal-form game consists of
Players : entities who make decisionsStrategy set : possible strategies that each player can takeOutcome: 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)
14
/73Slide15
Example: Prisoner’s DilemmaPlayers: two men who are charged with a crimeStrategy set: {cooperate, defect}cooperate: stay silent
defect: talk to the police and admit their crimeUtility:both cooperate: both will be jailed for 1 yearboth defect: both will be jailed for 6 yearsone defects and the other cooperates: one who defects will be freed while the other will be jailed for 9 yearsWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
15/73Slide16
Example: Prisoner’s DilemmaWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
16/73-1, -1-9, 0
0,
-9
-6
,
-6
Cooperate
Defect
Cooperate
Defect
Player 2’s strategy
Player 1’s strategy
Utility of
Player 1
Utility of
Player 2Slide17
Concept: Nash EquilibriumNash 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)
17
/73
current strategy of player
other players’ current strategies (FIXED)
possible strategy
of player
Slide18
Utility of Player 1Utility of Player 2
Example: Nash EquilibriumClaim: (Defect, Defect) is an NE in Prisoner’s DilemmaWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)18/73
-1, -1
-9, 0
0, -9
-6, -6
Cooperate
Defect
Cooperate
Defect
Player 2’s Strategy
Player 1’s StrategySlide19
-1, -1
-9, 00, -9-6,
-6Cooperate
Defect
Cooperate
Defect
Example: Nash Equilibrium
Claim:
(Defect, Defect)
is an NE in Prisoner’s Dilemma
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
19
/73
if Player 1 changes its strategy
Player 2’s Strategy
Player 1’s StrategySlide20
-1, -1
-9, 0-6, -6Example: Nash EquilibriumClaim: (Defect, Defect) is an NE in Prisoner’s Dilemma
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
20/73
0,
-9
Cooperate
Defect
Cooperate
Defect
if Player2 changes its strategy
Player 2’s Strategy
Player 1’s StrategySlide21
Example: Nash EquilibriumClaim: (Defect, Defect) is an NE in Prisoner’s Dilemma
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)21/73-1, -1-9, 0
0, -9
-6, -6
Cooperate
Defect
Cooperate
Defect
Player 2’s Strategy
Player 1’s StrategySlide22
Example: Nash EquilibriumClaim: (Cooperate, Cooperate) is not an NE
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)22/73-1, -1-9, 0
0, -9
-6, -6
Cooperate
Defect
Cooperate
Defect
Player 2’s Strategy
Player 1’s StrategySlide23
Example: Nash EquilibriumClaim: (Cooperate, Cooperate) is not an NE
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)23/73-1, -1
-9, 0
0, -9
-6, -6
Cooperate
Defect
Cooperate
Defect
-9
,
0
if Player 2 changes its strategy
Player 2’s Strategy
Player 1’s StrategySlide24
Concept: Social OptimumSocial welfare in an outcomesum of utilities of all players in the outcomeSocial optimum
: an outcome where social welfare is maximizedGenerally, Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)24/73social optimum Nash equilibrium
Slide25
Example: Social OptimumClaim: (Cooperate, Cooperate) is a social optimum
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)25/73-1 + -1= -2-9 + 0
= -9
0 -9
= -9
-6 -6
= -12
Cooperate
Defect
Cooperate
Defect
Player 2’s Strategy
Player 1’s StrategySlide26
Example: Social OptimumNash equilibrium
social optimum Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)26/73-1, -2
-9, 0
0, -9
-6, -6
Cooperate
Defect
Cooperate
Defect
Player 2’s Strategy
Player 1’s Strategy
Social
optimum
Nash equilibriumSlide27
Game Theory Concepts: SummaryNash equilibrium: an outcome where each user best responds to others’ strategiesSocial welfare: sum of utilities of all players
Social optimum: an outcome where the social welfare is maximizedWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)27/73Slide28
Road Map
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)28/73
Concepts in Game Theory
Game-theoretic Models
Sharable Good Game <<
Sharable Good Game with Access Cost
Simulation
ConclusionSlide29
Sharable Good Game (SGG)Consider a good sharable with friendsPlayers: nodes in a social networkStrategy 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)
29/73
)
owner
underprivileged
free rider (friends of the owner)Slide30
Nash Equilibrium: Conditionsno underprivileged nodesunderprivileged 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)30/73Utility comparison:free rider > owner > underprivileged
underprivileged
owner
owner
free riderSlide31
Nash Equilibrium: ExistenceProof: The following algorithm always gives an NEWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)31
/73Theorem [Existence of NEs in SGG]:In any social network, there exists a Nash Equilibrium.initialize the strategy of every node to “not buy” repeat until there is no underprivileged nodechoose an underprivileged node
change its strategy to “buy”
“Do Nash equilibria exist
in every social network?”Slide32
Proof of ExistenceWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)32/73
initialize the strategy of every node to “not buy” repeat until there is no underprivileged nodechoose an underprivileged node change its strategy to “buy”
Underprivileged
DetailSlide33
Proof of Existence (cont.)Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)33/73
Underprivileged
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”
DetailSlide34
Proof of Existence (cont.)Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)34/73
Free riders
Underprivileged
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”
Detail
UnderprivilegedSlide35
Proof of Existence (cont.)Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)35/73
initialize the strategy of every node to “not buy” repeat until there is no underprivileged nodechoose an underprivileged node change its strategy to “buy”
Free riders
Underprivileged
Detail
Underprivileged
UnderprivilegedSlide36
Proof of Existence (cont.)Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
36/73The outcome is a Nash Equilibriumno underprivileged nodesthis is the termination conditionowners have no owner friends new owners are chosen among underprivileged nodesinitialize the strategy of every node to “not buy” repeat until there is no underprivileged node
choose an underprivileged node change its strategy to “buy”
DetailSlide37
Nash Equilibrium: Non-uniquenessWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
37/73“Is there a unique Nash equilibriumin every social network?”Slide38
Nash Equilibrium: Non-uniquenessWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
38/73Theorem [Non-uniqueness of NEs in SGG]:There can be multiple Nash equilibria with different social welfareExample:
NE with social welfare
NE with social welfare
Social OptimumSlide39
Measuring InefficiencyIn every NE and social optima
no underprivileged nodeevery node gets benefit from a goodUse # owners to measure inefficiency of NEsWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
39/73
benefit
# nodes
price
# owners
Fixed
FixedSlide40
Measuring Inefficiency (cont.)Given a social network,Given a social network,Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
40/73# owners in a social optimum# owners in the NEinefficiency of an NE
:= PoA
(Price of Anarchy)
maximum inefficiency
over all NEs
PoS
(Price of Stability)
:=
minimum
inefficiency
over all NEs
:=
Slide41
Worst-case AnalysisWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)41/73
Example :…
…
Theorem
[Worst-case Analysis in SGG]
:
There exists a social network with
nodes
where
both
PoA
and
PoS
are
Slide42
Worst-case Analysis (cont.)Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)42/73
Theorem [Worst-case Analysis in SGG]:There exists a social network with nodes where both PoA and PoS are
Example :
…
…
…
…
…
social optimum
(
owners)
least efficient NE
(
owners)
most efficient NE
(
owners)
…
Slide43
Reason of InefficiencyA Nash equilibrium is inefficient whennodes with many friends free ridenodes with few friends buy a goodWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
43/73…
…
…
…
…
social optimum
(
owners)
most efficient NE
(
owners)
least efficient NE
(
owners)
…
“How can we incentivize nodes
with many friends to buy a good?”Slide44
Summary of SGGDefinition:Players: nodes in a social networkStrategy set: “buy”, “not buy”
Utility: free rider > owner > underprivilegedNash Equilibrium: always exists but not uniqueEfficiency of Nash Equilibria:both best and worst NEs can be highly inefficientWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)44/73Slide45
Road MapWhy You Should Charge Your Friends for Borrowing Your Stuff (by
Kijung Shin)45/73
Concepts in Game Theory
Game-theoretic Models
Sharable Good Game
Sharable Good Game with Access Cost <<
Simulation
ConclusionSlide46
SGG with Access Cost (SGG-AC)Consider a good sharable with friendsPlayers: nodes in a social networkStrategy set: buy a good ( ) or not buy ( )
rent a good from a friend by paying an access cost ( ) to the friendWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)46/73
)
owner
renter
renter
underprivilegedSlide47
Utility in SGG-ACUtility: 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)
47
/73
owner
renter
renter
underprivileged
Utility comparison:
rich owner > renter > poor owner > underprivilegedSlide48
Nash Equilibrium: ConditionsWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
48/73
no
underprivileged
nodes
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
Utility comparison:
rich owner > renter > poor owner > underprivileged
poor owner
poor owner
renterSlide49
Existence and Non-uniquenessWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)49/73
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
Example :Slide50
Measuring Inefficiency: ReviewGiven a social network,Given a social network,Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
50/73# owners in a social optimum# owners in the NEinefficiency of an NE
:=
PoA
(Price of Anarchy)
maximum
inefficiency over all NEs
PoS
(Price of Stability)
:=
minimum
inefficiency
over all NEs
:=
Slide51
Worst-case Analysis: PoAWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
51/73Theorem [Worst-case PoA Analysis in SGG-AC]:There exists a social network with nodes where PoA is
Example :
…
…
Worst
NEs
in SGG-AC are as
inefficient
as those in SGGSlide52
Worst-case Analysis: PoAWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
52/73social optimum( owners)
…
…
…
…
least efficient NE
(
owners)
Theorem
[Worst-case
PoA
Analysis in SGG-AC]
:
There exists a social network with
nodes
where
PoA
is
Slide53
Worst-case Analysis: PoSWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
53/73Theorem [Worst-case PoS Analysis in SGG-AC]:If (i.e.,
), then
PoS is
in every network.
If
,
b
est
NEs
are
socially optimal.
Proof Sketch:
w
e designed an algorithm that
starts from a social optimum
reaches a Nash equilibrium
without increasing the number of ownersSlide54
Worst-case Analysis: PoSWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
54/73Theorem [Worst-case PoS Analysis in SGG-AC]:If (i.e.,
), then
PoS is
in every network.
social optimum,
Nash equilibrium
…
…
Example
:
…
…
Slide55
Worst-case Analysis: PoSWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
55/73Theorem [Worst-case PoS Analysis in SGG-AC]:If PoS
is in every social network.
If
,
PoS
is
in every social network
There exists a social network where
PoS
is
Detail
(i.e., the number of nodes)
PoS
in SGG-AC
PoS
in SGG with
Slide56
Worst-case Analysis: PoSWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
56/73DetailTheorem [Worst-case
PoS Analysis in SGG-AC]:If
PoS
is
in every social network.
If
,
PoS
is
in every social network
There exists a social network where
PoS
is
…
…
Example
:Slide57
Worst-case Analysis: PoSWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
57/73Theorem [Worst-case PoS Analysis in SGG-AC]:If PoS
is in every social network.
If
,
PoS
is
in every social network
There exists a social network where
PoS
is
Detail
social optimum
(
owners)
…
…
…
…
most efficient NE
(T owners)
Slide58
Summary of Theoretic AnalysisWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
58/73PoAPoSSGG
SGG-AC
if
otherwise
PoA
PoS
SGG
SGG-AC
Introducing access costs
(SGG
SGG-AC)
:
Does not reduce inefficiency of worst NEs:
Does reduce inefficiency of best NEs:
or
“How inefficient are other NEs,
which are neither best nor worst?”Slide59
Summary of SGG-ACDefinition:Players: nodes in a social network
Strategy set: “buy”, “rent with an access cost”, “no buy no rent”Utility: rich owner > renter > poor owner > underprivilegedNash Equilibrium: always exists but not uniqueEfficiency of Nash Equilibria:best NEs are always efficient (socially optimal if )worst NEs can be highly inefficient
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
59
/73Slide60
Road MapWhy You Should Charge Your Friends for Borrowing Your Stuff (by
Kijung Shin)60/73
Concepts in Game Theory
Game-theoretic Models
Sharable Good Game
Sharable Good Game with Access Cost
Simulation <<
ConclusionSlide61
Why Simulation?Complement our theoretical analysisReal social networks:Karate club (34 nodes, 78 edges)Hamsterster (1,858 nodes, 12,534 edges)Advogato (5,155 nodes, 51,127 edges)
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)61/73Nash EquilibriaSocial NetworkTheoretical analysis
best and worst NEshypothetical social networks
Simulation
realistic NEs
real
social networksSlide62
Simulation MethodUse best-response dynamics to obtain 1,000 NEs
Measure the average inefficiency of the 1,000 NEsWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)62/73
randomly initialize strategies
repeat
for each
node
change its strategy to a
best response
until
an NE is reached
Theorem:
Always terminates
# owners in a social optimum
# owners in the NE
inefficiency
of an NE
:=Slide63
Simulation ResultsAverage (social) inefficiencyWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
63/73GamesSGG
SGG-AC
Access cost
1
2
5
10
Karate Club
Hamsterster
Advogato
Games
SGG
SGG-AC
Access cost
1
2
5
10
Karate Club
Hamsterster
AdvogatoSlide64
Simulation Results: SGGAverage social inefficiencyWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
64/73SGG
SGG-AC
Access cost
1
2
5
10
Karate Club
Hamsterster
Advogato
SGG
SGG-AC
Access cost
1
2
5
10
Karate Club
Hamsterster
Advogato
- In SGG (without access cost), inefficiency was
Slide65
Simulation Results: SGG-ACAverage social inefficiencyWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
65/73SGG
SGG-AC
Access cost
1
2
5
10
Karate Club
Hamsterster
Advogato
SGG
SGG-AC
Access cost
1
2
5
10
Karate Club
Hamsterster
Advogato
- In SGG (without access cost), inefficiency was
- In SGG-AC with a proper access cost, inefficiency was
Slide66
Simulation Results: Proper CostAverage social inefficiencyWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
66/73SGG
SGG-AC
Access cost
1
2
5
10
Karate Club
Hamsterster
Advogato
SGG
SGG-AC
Access cost
1
2
5
10
Karate Club
Hamsterster
Advogato
Inefficiency was minimized when
(i.e.,
)
Theorem
PoS
is minimized when
Slide67
Summary of SimulationComplements our theoretical analysisanalyze realistic Nash Equilibriause real social networks
Supports our theoretical analysisinefficiency decreases by access costs: inefficiency is minimized when (i.e.,
)
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
67
/73Slide68
Road MapWhy You Should Charge Your Friends for Borrowing Your Stuff (by
Kijung Shin)68/73
Concepts in Game Theory
Game-theoretic Models
Sharable Good Game
Sharable Good Game with Access Cost
Simulation
Conclusion <<Slide69
SummaryGoal: To examine incentives to buy sharable goodsApproaches:
game-theoretic models with equilibrium analysis and simulationsFindings: individually optimal purchases can be harmful to societyaccess costs significantly reduce social inefficiencyproper access cost lies between 1/3 and 1/2 of the priceWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)69/73
Sharable good game (SGG)
Sharable good game
with access cost (SGG-AC)Slide70
Actionable ConclusionHard to mandate access costs at a societal level IKEA toolkits, DVDs, etc.Feasible at the level of an organization Example: University researchers share expensive lab equipment
mandating access costs might reduce costWhy You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)70/73Slide71
Future Work: CoalitionTake coalitions of nodes into accountAnalyze coalition-proof equilibriaE.g., “strong Nash equilibria”
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)71/73Slide72
Related WorkShin et al [2017] – the full paperconsider goods sharable with nodes within distance
Bramoulle and Kranton [2007]strategy is the amount of contribution to a public goodElliott and Golub [2013]consider directed and weighted graphsAllouch [2015]consider both private goods and public goods Jackson and Zenou [2014]survey on games on networks Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)
72/73Slide73
Thank YouPaper: http://www.cs.cmu.edu/~kijungs/papers/sggIJCAI2017.pdfEmail: kijungs@cs.cmu.edu
Why You Should Charge Your Friends for Borrowing Your Stuff (by Kijung Shin)73/73