of Networks
Strategic Formation
Lecture 10
We know
People make choices thinking
about what others are doing
We know
People make choices thinking
about what others are doing
our social relationships
have an important effect on
how we behave
We know
People make choices thinking
about what others are doing
our social relationships
have an important effect on
how we behave
Our networks are valuable,
they are the capital we use
to achieve our goals
Network Formation
In many social settings, our
relationships are not given
Network Formation
In many social settings, our
relationships are not given
We decide with whom to link
Network Formation
In many social settings, our
relationships are not given
We decide with whom to link
In this class we will study
how networks are formed by
strategic decision-makers
Aim Lecture 10
To Understand
The basic of network strategic formation
Simple cases of how to model network formation
The relation between individual incentives & social
welfare from a network perspective (emergence)
+
+
+
Some basic intuition
Some basic intuition
Costs & Benefits
Actors choose links
Contrasts incentives & Social efficiency
Some basic intuition
Costs & Benefits
Actors choose links
Contrasts incentives & Social efficiency
Nodes as actors making choices
Some basic intuition
Costs & Benefits
There are costs and benefits associated with each network
Actors choose links
Contrasts incentives & Social efficiency
Nodes as actors making choices
Some basic intuition
Costs & Benefits
There are costs and benefits associated with each network
Actors choose links
Contrasts incentives & Social efficiency
Nodes as actors making choices
We can also call them agents, players, people, countries, etc...
Some basic intuition
Costs & Benefits
There are costs and benefits associated with each network
Actors choose links
Contrasts incentives & Social efficiency
Nodes as actors making choices
We can also call them agents, players, people, countries, etc...
We will contrast the incentives individuals have to form
relationships with what’s best for society
How to model choices
Incentives to form and severe links
How to model choices
Incentives to form and severe links
Is consensus needed? (undirected/directed)
What happens on the network?
Are links adjustable in intensity?
Can they coordinate changes in the network?
How to model choices
Incentives to form and severe links
Is consensus needed? (undirected/directed)
Does somebody has to say yes to me to relate with her?
What happens on the network?
Are links adjustable in intensity?
Can they coordinate changes in the network?
How to model choices
Incentives to form and severe links
Is consensus needed? (undirected/directed)
Does somebody has to say yes to me to relate with her?
What happens on the network?
Are links adjustable in intensity?
Can they coordinate changes in the network?
Citations networks vs. friendships or alliances
How to model choices
Incentives to form and severe links
Is consensus needed? (undirected/directed)
Does somebody has to say yes to me to relate with her?
What happens on the network?
Are links adjustable in intensity?
Can they coordinate changes in the network?
Citations networks vs. friendships or alliances
I’ll form a new alliance with you but only if we can form an
alliance with someone else at the same time
How to model choices
Incentives to form and severe links
Is consensus needed? (undirected/directed)
Does somebody has to say yes to me to relate with her?
What happens on the network?
Are links adjustable in intensity?
Can they coordinate changes in the network?
Citations networks vs. friendships or alliances
I’ll from a new alliance with you but only if we can form an
alliance with someone else at the same time
What’s generating value in the network? where? Costs & benefits?
How to model choices
Incentives to form and severe links
Is consensus needed? (undirected/directed)
Does somebody has to say yes to me to relate with her?
What happens on the network?
Are links adjustable in intensity?
Can they coordinate changes in the network?
Citations networks vs. friendships or alliances
I’ll from a new alliance with you but only if we can form an
alliance with someone else at the same time
What’s generating value in the network? where? Costs & benefits?
Only whether a relationship exists or not? How intense is it?
Questions that arise
We will address some of them
Which networks are likely to form?
Are some networks more stable than others?
We will address some of them
Which networks are likely to form?
Are they the right ones from society’s perspective?
Are some networks more stable than others?
Questions that arise
We will address some of them
Which networks are likely to form?
Are they the right ones from society’s perspective?
Are some networks more stable than others?
if not, how different are they?
Questions that arise
We will address some of them
Which networks are likely to form?
Are they the right ones from society’s perspective?
Are some networks more stable than others?
if not, how different are they?
How likely is it that changes can occur in certain networks?
New people coming in? Creating new relationships?
Questions that arise
Representation
of strategic network formation
(Jackson & Wollinsky, 1996)
Representation
of strategic network formation
(Jackson & Wollinsky, 1996)
Payoffs:
The network g generates some payoffs to a given individual i
Representation
of strategic network formation
Payoff to i if the network is gui(g)
(Jackson & Wollinsky, 1996)
Payoffs:
The network g generates some payoffs to a given individual i
Representation
of strategic network formation
Payoff to i if the network is gui(g)
(Jackson & Wollinsky, 1996)
Payoffs:
The network g generates some payoffs to a given individual i
For simplicity:
We are going to look at undirected network formation
Representation
of strategic network formation
Payoff to i if the network is gui(g)
(Jackson & Wollinsky, 1996)
Payoffs:
The network g generates some payoffs to a given individual i
For simplicity:
We are going to look at undirected network formation
We could look at directed, weighted, etc.
Modeling
Incentives & Equilibrium
Modeling
Incentives & Equilibrium
is modeled as a game where
The network:
Modeling
Incentives & Equilibrium
is modeled as a game where
The network:
Each agent announces who they wish to link with
Modeling
Incentives & Equilibrium
is modeled as a game where
The network:
Each agent announces who they wish to link with
& a link forms if and only if both agents name each other
Modeling
Incentives & Equilibrium
is modeled as a game where
The network:
What is a Nash equilibrium in this game?
Each agent announces who they wish to link with
& a link forms if and only if both agents name each other
Equilibrium Networks
Nash equilibrium
Equilibrium Networks
Nash equilibrium
A situation where nobody can gain by
changing his/her actions (announcements)
Equilibrium Networks
Nash equilibrium
Given the actions (announcements) of
other individuals
A situation where nobody can gain by
changing his/her actions (announcements)
for undirected networks
Problem of Nash
mutual agreement to form a link
Problem of Nash
for undirected networks
mutual agreement to form a link
If they are separated, each gets a value of 0 and if together 1.
Example (i & j):
for undirected networks
Example (i & j):
If they are separated, each gets a value of 0 and if together 1.
They play a game of simultaneous announcement
mutual agreement to form a link
Problem of Nash
for undirected networks
If they are separated, each gets a value of 0 and if together 1.
They play a game of simultaneous announcement
If i thinks j won’t announce, she
might as well not announce
Example (i & j):
mutual agreement to form a link
Problem of Nash
for undirected networks
i
j
0
0
Case 1: Neither announces is a Nash equilibrium
If they are separated, each gets a value of 0 and if together 1.
They play a game of simultaneous announcement
Example (i & j):
If i thinks j won’t announce, she
might as well not announce
mutual agreement to form a link
Problem of Nash
for undirected networks
ii
jj
1
1
0
0
Case 1: Neither announces is a Nash equilibrium
If they are separated, each gets a value of 0 and if together 1.
They play a game of simultaneous announcement
Case 2: Both announce is a Nash equilibrium
Example (i & j):
If i thinks j won’t announce, she
might as well not announce
mutual agreement to form a link
Problem of Nash
Pairwise Stability
Modeling Incentives
A network (N,g) is pairwise stable if
ii
jj
1
1
0
0
Pairwise Stability
Modeling Incentives
A network (N,g) is pairwise stable if
ii
jj
1
1
0
0
No actor gains from severing a link (one person can do it)
No two actor gain from forming a link (at least one is better off)
Pairwise Stability
Modeling Incentives
A network (N,g) is pairwise stable if
ii
jj
1
1
0
0
Relationship must be beneficial to be maintained
No actor gains from severing a link (one person can do it)
No two actor gain from forming a link (at least one is better off)
Pairwise Stability
Modeling Incentives
A network (N,g) is pairwise stable if
ii
jj
1
1
0
0
Relationship must be beneficial to be maintained
Beneficial relationship are pursued when available
No actor gains from severing a link (one person can do it)
No two actor gain from forming a link (at least one is better off)
Some Notation
A network (N,g) is pairwise stable if
Pairwise Stability
Some Notation
A network (N,g) is pairwise stable if
No agent gains from severing a link (one person can do it)
ui(g) ≥ ui(g-ij) for i and ij in g
Pairwise Stability
Some Notation
A network (N,g) is pairwise stable if
No agent gains from severing a link (one person can do it)
ui(g) ≥ ui(g-ij) for i and ij in g
No two agents gain from forming a link (at least one is better off)
ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g
Pairwise Stability
Some Notation
A network (N,g) is pairwise stable if
No agent gains from severing a link (one person can do it)
ui(g) ≥ ui(g-ij) for i and ij in g
ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g
It’s still a very weak concept
Pairwise Stability
No two agents gain from forming a link (at least one is better off)
Some Notation
A network (N,g) is pairwise stable if
No agent gains from severing a link (one person can do it)
ui(g) ≥ ui(g-ij) for i and ij in g
ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g
It’s still a very weak concept
Only looks at pairs of individuals
Pairwise Stability
No two agents gain from forming a link (at least one is better off)
Some Notation
A network (N,g) is pairwise stable if
No agent gains from severing a link (one person can do it)
ui(g) ≥ ui(g-ij) for i and ij in g
ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g
It’s still a very weak concept
Only looks at pairs of individuals
One link at a time
Pairwise Stability
No two agents gain from forming a link (at least one is better off)
Some Notation
Pairwise Stability
A network (N,g) is pairwise stable if
No agent gains from severing a link (one person can do it)
ui(g) ≥ ui(g-ij) for i and ij in g
ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g
It’s still a very weak concept
Only looks at pairs of individuals
One link at a time
(It’s a minimum)
No two agents gain from forming a link (at least one is better off)
Back to our example
ii
jj
1
1
0
0
Back to our example
ii
jj
1
1
0
0
Relationship must be beneficial to be maintained
Beneficial relationship are pursued when available
Back to our example
ii
jj
1
1
0
0
Relationship must be beneficial to be maintained
Beneficial relationship are pursued when available
Which is the pairwise stable
situation (network)?
Back to our example
ii
jj
1
1
0
0
Relationship must be beneficial to be maintained
Beneficial relationship are pursued when available
Which is the pairwise stable
situation (network)?
Back to our example
ii
jj
1
1
0
0
Relationship must be beneficial to be maintained
Beneficial relationship are pursued when available
Which is the pairwise stable
situation (network)?
Although both are Nash equilibria
Remember
Lave & March
Remember
Lave & March
Models
Are a simplified version of the world
Remember
Lave & March
Models
Are a simplified version of the world
Models are created by speculating about
the process that could have produced
the observed outcomes
Collaboration Networks
Pairwise Stability
0 0
0 0
Think of situations in which we
collaborate with others (i.e.,
friendships, projects, inter-firm R&D)
The more collaborations you have the
better for you
&
But
The more collaborations your
collaborators have the worse for you
Negative Externalities
Collaboration Networks
Pairwise Stability
0 0
0 0
0 3
0 3
if 2 actors are
related, each gets
3 out of it.
Collaboration Networks
Pairwise Stability
0 0
0 0
0 3
0 3
Will this situation tend to change
or is it likely to be stable?
if 2 actors are
related, each gets
3 out of it.
Collaboration Networks
Pairwise Stability
0 0
0 0
0 3
0 3
3 3
3 3
The two other actors can
be better if they relate
Collaboration Networks
Pairwise Stability
0 0
0 0
0 3
0 3
3 3
3 3
3.25 3.25
2 2
NEGATIVE EXTERNALITIES
But now, the new connection benefits directly
the linked actors & affects negatively &
indirectly the existing neighbors
Collaboration Networks
Pairwise Stability
0 0
0 0
0 3
0 3
3 3
3 3
3.25 3.25
2 2
Think about the attention you get from your
parents if you are alone or if you have to
share it with your brothers & sisters
NEGATIVE EXTERNALITIES
Collaboration Networks
Pairwise Stability
0 0
0 0
0 3
0 3
3 3
3 3
3.25 3.25
2 2
2.5 2.5
2.5 2.5
Everyone has incentives to
create a new connection
without intending to
harm their neighbors
Think about Schelling’s Segregation
Collaboration Networks
Pairwise Stability
0 0
0 0
0 3
0 3
3 3
3 3
3.25 3.25
2 2
2.5 2.5
2.5 2.5
2.78 2
2 2.78
Collaboration Networks
Pairwise Stability
0 0
0 0
0 3
0 3
3 3
3 3
3.25 3.25
2 2
2.5 2.5
2.5 2.5
2.78 2
2 2.78
2.33 2.33
2.33 2.33
Until the
networks is
complete
Collaboration Networks
Pairwise Stability
0 0
0 0
0 3
0 3
3 3
3 3
3.25 3.25
2 2
2.5 2.5
2.5 2.5
2.78 2
2 2.78
2.33 2.33
2.33 2.33
Pairwise
Stable
Stability & Efficiency
Think about this two networks
Stability & Efficiency
Think about this two networks
3 3
3 3
Each could have gotten
3 & society 12
Stability & Efficiency
Think about this two networks
3 3
3 3
Each got 2.33 & society
9.32
2.33 2.33
2.33 2.33
Pairwise
Stable
Stability & Efficiency
Think about this two networks
3 3
3 3
Each got 2.33 & society
9.32
2.33 2.33
2.33 2.33
Pairwise
Stable
Efficient
Not stable to individual incentives
Efficiency
A network is efficient if the total
sum of all the utilities from all the
players is the maximal one can
achieve
The situation in which society as a whole is better off
But still some can be in very bad shape
Notation:
A network g is efficient if:
g maximizes ∑ui(g’)
Emergence
3 3
3 3
Although individuals do not
intend to harm their neighbors
2.33 2.33
2.33 2.33
Efficiency
Pursuing personal incentives leads to
social inefficiency
Their actions have implications
for other people they are not
necessarily taking into account
From our friends’ friends
Positive Externalities
Other Effects
In different settings
I get indirect benefits the more friends my friends have
Think about popularity, transmission of
valuable information, access to jobs
We will cover some of this in other lectures
Some Notation
Positive Externalities
uk(g+ij)≥uk(g) if ij not in g, for every k≠i,j
Everyone is equal or better with the new link
Negative Externalities
uk(g+ij)≤uk(g) if ij not in g, for every k≠i,j
At least someone is worse with the new link
Checklist
Strategic network formation assumes actors are
rational decision makers
Externalities from relationships influence the
networks that are likely to be formed
Social efficiency can be affected by individual
incentives
+
+
+
Questions?

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SN- Lecture 10

  • 2. We know People make choices thinking about what others are doing
  • 3. We know People make choices thinking about what others are doing our social relationships have an important effect on how we behave
  • 4. We know People make choices thinking about what others are doing our social relationships have an important effect on how we behave Our networks are valuable, they are the capital we use to achieve our goals
  • 5. Network Formation In many social settings, our relationships are not given
  • 6. Network Formation In many social settings, our relationships are not given We decide with whom to link
  • 7. Network Formation In many social settings, our relationships are not given We decide with whom to link In this class we will study how networks are formed by strategic decision-makers
  • 8. Aim Lecture 10 To Understand The basic of network strategic formation Simple cases of how to model network formation The relation between individual incentives & social welfare from a network perspective (emergence) + + +
  • 10. Some basic intuition Costs & Benefits Actors choose links Contrasts incentives & Social efficiency
  • 11. Some basic intuition Costs & Benefits Actors choose links Contrasts incentives & Social efficiency Nodes as actors making choices
  • 12. Some basic intuition Costs & Benefits There are costs and benefits associated with each network Actors choose links Contrasts incentives & Social efficiency Nodes as actors making choices
  • 13. Some basic intuition Costs & Benefits There are costs and benefits associated with each network Actors choose links Contrasts incentives & Social efficiency Nodes as actors making choices We can also call them agents, players, people, countries, etc...
  • 14. Some basic intuition Costs & Benefits There are costs and benefits associated with each network Actors choose links Contrasts incentives & Social efficiency Nodes as actors making choices We can also call them agents, players, people, countries, etc... We will contrast the incentives individuals have to form relationships with what’s best for society
  • 15. How to model choices Incentives to form and severe links
  • 16. How to model choices Incentives to form and severe links Is consensus needed? (undirected/directed) What happens on the network? Are links adjustable in intensity? Can they coordinate changes in the network?
  • 17. How to model choices Incentives to form and severe links Is consensus needed? (undirected/directed) Does somebody has to say yes to me to relate with her? What happens on the network? Are links adjustable in intensity? Can they coordinate changes in the network?
  • 18. How to model choices Incentives to form and severe links Is consensus needed? (undirected/directed) Does somebody has to say yes to me to relate with her? What happens on the network? Are links adjustable in intensity? Can they coordinate changes in the network? Citations networks vs. friendships or alliances
  • 19. How to model choices Incentives to form and severe links Is consensus needed? (undirected/directed) Does somebody has to say yes to me to relate with her? What happens on the network? Are links adjustable in intensity? Can they coordinate changes in the network? Citations networks vs. friendships or alliances I’ll form a new alliance with you but only if we can form an alliance with someone else at the same time
  • 20. How to model choices Incentives to form and severe links Is consensus needed? (undirected/directed) Does somebody has to say yes to me to relate with her? What happens on the network? Are links adjustable in intensity? Can they coordinate changes in the network? Citations networks vs. friendships or alliances I’ll from a new alliance with you but only if we can form an alliance with someone else at the same time What’s generating value in the network? where? Costs & benefits?
  • 21. How to model choices Incentives to form and severe links Is consensus needed? (undirected/directed) Does somebody has to say yes to me to relate with her? What happens on the network? Are links adjustable in intensity? Can they coordinate changes in the network? Citations networks vs. friendships or alliances I’ll from a new alliance with you but only if we can form an alliance with someone else at the same time What’s generating value in the network? where? Costs & benefits? Only whether a relationship exists or not? How intense is it?
  • 22. Questions that arise We will address some of them Which networks are likely to form? Are some networks more stable than others?
  • 23. We will address some of them Which networks are likely to form? Are they the right ones from society’s perspective? Are some networks more stable than others? Questions that arise
  • 24. We will address some of them Which networks are likely to form? Are they the right ones from society’s perspective? Are some networks more stable than others? if not, how different are they? Questions that arise
  • 25. We will address some of them Which networks are likely to form? Are they the right ones from society’s perspective? Are some networks more stable than others? if not, how different are they? How likely is it that changes can occur in certain networks? New people coming in? Creating new relationships? Questions that arise
  • 26. Representation of strategic network formation (Jackson & Wollinsky, 1996)
  • 27. Representation of strategic network formation (Jackson & Wollinsky, 1996) Payoffs: The network g generates some payoffs to a given individual i
  • 28. Representation of strategic network formation Payoff to i if the network is gui(g) (Jackson & Wollinsky, 1996) Payoffs: The network g generates some payoffs to a given individual i
  • 29. Representation of strategic network formation Payoff to i if the network is gui(g) (Jackson & Wollinsky, 1996) Payoffs: The network g generates some payoffs to a given individual i For simplicity: We are going to look at undirected network formation
  • 30. Representation of strategic network formation Payoff to i if the network is gui(g) (Jackson & Wollinsky, 1996) Payoffs: The network g generates some payoffs to a given individual i For simplicity: We are going to look at undirected network formation We could look at directed, weighted, etc.
  • 32. Modeling Incentives & Equilibrium is modeled as a game where The network:
  • 33. Modeling Incentives & Equilibrium is modeled as a game where The network: Each agent announces who they wish to link with
  • 34. Modeling Incentives & Equilibrium is modeled as a game where The network: Each agent announces who they wish to link with & a link forms if and only if both agents name each other
  • 35. Modeling Incentives & Equilibrium is modeled as a game where The network: What is a Nash equilibrium in this game? Each agent announces who they wish to link with & a link forms if and only if both agents name each other
  • 37. Equilibrium Networks Nash equilibrium A situation where nobody can gain by changing his/her actions (announcements)
  • 38. Equilibrium Networks Nash equilibrium Given the actions (announcements) of other individuals A situation where nobody can gain by changing his/her actions (announcements)
  • 39. for undirected networks Problem of Nash mutual agreement to form a link
  • 40. Problem of Nash for undirected networks mutual agreement to form a link If they are separated, each gets a value of 0 and if together 1. Example (i & j):
  • 41. for undirected networks Example (i & j): If they are separated, each gets a value of 0 and if together 1. They play a game of simultaneous announcement mutual agreement to form a link Problem of Nash
  • 42. for undirected networks If they are separated, each gets a value of 0 and if together 1. They play a game of simultaneous announcement If i thinks j won’t announce, she might as well not announce Example (i & j): mutual agreement to form a link Problem of Nash
  • 43. for undirected networks i j 0 0 Case 1: Neither announces is a Nash equilibrium If they are separated, each gets a value of 0 and if together 1. They play a game of simultaneous announcement Example (i & j): If i thinks j won’t announce, she might as well not announce mutual agreement to form a link Problem of Nash
  • 44. for undirected networks ii jj 1 1 0 0 Case 1: Neither announces is a Nash equilibrium If they are separated, each gets a value of 0 and if together 1. They play a game of simultaneous announcement Case 2: Both announce is a Nash equilibrium Example (i & j): If i thinks j won’t announce, she might as well not announce mutual agreement to form a link Problem of Nash
  • 45. Pairwise Stability Modeling Incentives A network (N,g) is pairwise stable if ii jj 1 1 0 0
  • 46. Pairwise Stability Modeling Incentives A network (N,g) is pairwise stable if ii jj 1 1 0 0 No actor gains from severing a link (one person can do it) No two actor gain from forming a link (at least one is better off)
  • 47. Pairwise Stability Modeling Incentives A network (N,g) is pairwise stable if ii jj 1 1 0 0 Relationship must be beneficial to be maintained No actor gains from severing a link (one person can do it) No two actor gain from forming a link (at least one is better off)
  • 48. Pairwise Stability Modeling Incentives A network (N,g) is pairwise stable if ii jj 1 1 0 0 Relationship must be beneficial to be maintained Beneficial relationship are pursued when available No actor gains from severing a link (one person can do it) No two actor gain from forming a link (at least one is better off)
  • 49. Some Notation A network (N,g) is pairwise stable if Pairwise Stability
  • 50. Some Notation A network (N,g) is pairwise stable if No agent gains from severing a link (one person can do it) ui(g) ≥ ui(g-ij) for i and ij in g Pairwise Stability
  • 51. Some Notation A network (N,g) is pairwise stable if No agent gains from severing a link (one person can do it) ui(g) ≥ ui(g-ij) for i and ij in g No two agents gain from forming a link (at least one is better off) ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g Pairwise Stability
  • 52. Some Notation A network (N,g) is pairwise stable if No agent gains from severing a link (one person can do it) ui(g) ≥ ui(g-ij) for i and ij in g ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g It’s still a very weak concept Pairwise Stability No two agents gain from forming a link (at least one is better off)
  • 53. Some Notation A network (N,g) is pairwise stable if No agent gains from severing a link (one person can do it) ui(g) ≥ ui(g-ij) for i and ij in g ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g It’s still a very weak concept Only looks at pairs of individuals Pairwise Stability No two agents gain from forming a link (at least one is better off)
  • 54. Some Notation A network (N,g) is pairwise stable if No agent gains from severing a link (one person can do it) ui(g) ≥ ui(g-ij) for i and ij in g ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g It’s still a very weak concept Only looks at pairs of individuals One link at a time Pairwise Stability No two agents gain from forming a link (at least one is better off)
  • 55. Some Notation Pairwise Stability A network (N,g) is pairwise stable if No agent gains from severing a link (one person can do it) ui(g) ≥ ui(g-ij) for i and ij in g ui(g+ij) ≥ ui(g) implies uj(g+ij) < uj(g) for ij not in g It’s still a very weak concept Only looks at pairs of individuals One link at a time (It’s a minimum) No two agents gain from forming a link (at least one is better off)
  • 56. Back to our example ii jj 1 1 0 0
  • 57. Back to our example ii jj 1 1 0 0 Relationship must be beneficial to be maintained Beneficial relationship are pursued when available
  • 58. Back to our example ii jj 1 1 0 0 Relationship must be beneficial to be maintained Beneficial relationship are pursued when available Which is the pairwise stable situation (network)?
  • 59. Back to our example ii jj 1 1 0 0 Relationship must be beneficial to be maintained Beneficial relationship are pursued when available Which is the pairwise stable situation (network)?
  • 60. Back to our example ii jj 1 1 0 0 Relationship must be beneficial to be maintained Beneficial relationship are pursued when available Which is the pairwise stable situation (network)? Although both are Nash equilibria
  • 62. Remember Lave & March Models Are a simplified version of the world
  • 63. Remember Lave & March Models Are a simplified version of the world Models are created by speculating about the process that could have produced the observed outcomes
  • 64. Collaboration Networks Pairwise Stability 0 0 0 0 Think of situations in which we collaborate with others (i.e., friendships, projects, inter-firm R&D) The more collaborations you have the better for you & But The more collaborations your collaborators have the worse for you Negative Externalities
  • 65. Collaboration Networks Pairwise Stability 0 0 0 0 0 3 0 3 if 2 actors are related, each gets 3 out of it.
  • 66. Collaboration Networks Pairwise Stability 0 0 0 0 0 3 0 3 Will this situation tend to change or is it likely to be stable? if 2 actors are related, each gets 3 out of it.
  • 67. Collaboration Networks Pairwise Stability 0 0 0 0 0 3 0 3 3 3 3 3 The two other actors can be better if they relate
  • 68. Collaboration Networks Pairwise Stability 0 0 0 0 0 3 0 3 3 3 3 3 3.25 3.25 2 2 NEGATIVE EXTERNALITIES But now, the new connection benefits directly the linked actors & affects negatively & indirectly the existing neighbors
  • 69. Collaboration Networks Pairwise Stability 0 0 0 0 0 3 0 3 3 3 3 3 3.25 3.25 2 2 Think about the attention you get from your parents if you are alone or if you have to share it with your brothers & sisters NEGATIVE EXTERNALITIES
  • 70. Collaboration Networks Pairwise Stability 0 0 0 0 0 3 0 3 3 3 3 3 3.25 3.25 2 2 2.5 2.5 2.5 2.5 Everyone has incentives to create a new connection without intending to harm their neighbors Think about Schelling’s Segregation
  • 71. Collaboration Networks Pairwise Stability 0 0 0 0 0 3 0 3 3 3 3 3 3.25 3.25 2 2 2.5 2.5 2.5 2.5 2.78 2 2 2.78
  • 72. Collaboration Networks Pairwise Stability 0 0 0 0 0 3 0 3 3 3 3 3 3.25 3.25 2 2 2.5 2.5 2.5 2.5 2.78 2 2 2.78 2.33 2.33 2.33 2.33 Until the networks is complete
  • 73. Collaboration Networks Pairwise Stability 0 0 0 0 0 3 0 3 3 3 3 3 3.25 3.25 2 2 2.5 2.5 2.5 2.5 2.78 2 2 2.78 2.33 2.33 2.33 2.33 Pairwise Stable
  • 74. Stability & Efficiency Think about this two networks
  • 75. Stability & Efficiency Think about this two networks 3 3 3 3 Each could have gotten 3 & society 12
  • 76. Stability & Efficiency Think about this two networks 3 3 3 3 Each got 2.33 & society 9.32 2.33 2.33 2.33 2.33 Pairwise Stable
  • 77. Stability & Efficiency Think about this two networks 3 3 3 3 Each got 2.33 & society 9.32 2.33 2.33 2.33 2.33 Pairwise Stable Efficient Not stable to individual incentives
  • 78. Efficiency A network is efficient if the total sum of all the utilities from all the players is the maximal one can achieve The situation in which society as a whole is better off But still some can be in very bad shape Notation: A network g is efficient if: g maximizes ∑ui(g’)
  • 79. Emergence 3 3 3 3 Although individuals do not intend to harm their neighbors 2.33 2.33 2.33 2.33 Efficiency Pursuing personal incentives leads to social inefficiency Their actions have implications for other people they are not necessarily taking into account
  • 80. From our friends’ friends Positive Externalities Other Effects In different settings I get indirect benefits the more friends my friends have Think about popularity, transmission of valuable information, access to jobs We will cover some of this in other lectures
  • 81. Some Notation Positive Externalities uk(g+ij)≥uk(g) if ij not in g, for every k≠i,j Everyone is equal or better with the new link Negative Externalities uk(g+ij)≤uk(g) if ij not in g, for every k≠i,j At least someone is worse with the new link
  • 82. Checklist Strategic network formation assumes actors are rational decision makers Externalities from relationships influence the networks that are likely to be formed Social efficiency can be affected by individual incentives + + +