Leadership and Peer Effects in an Organization.

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Leadership and Peer Effects in an Organization.

• Penélope Hernández
• Gonzalo Olcina
• Raúl Toral

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LEADERSHIP AND PEER EFFECTS IN AN ORGANIZATION

• Agents might have an incentive to conform to the
  views of others (specially, of leaders).
• Economic theory focusses on monetary or material
  incentives for agents with given preferences.
• But we know from psychology and sociology that
  preferences might change. And we also know which
  are the sources for change.
• Therefore, perhaps is cheaper for the Principal
  to make the agents behave as the Principal wants
  by socializing them to the rightpreferences,
  instead of providing them the rigth monetary
  incentives.

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LEADERSHIP AND PEER EFFECTS IN AN ORGANIZATION

• Agency theory many times you cannot use money to
  align incentives.
• In these cases, aligning preferences might be a
  useful alternative. (See for instance, the army,
  a religious organization, a revolutionary
  party).
• The Principal can make the agents conform to his
  views through indoctrination or socialization,
  provided he is perceived as a leader by the
  agents.
• However, this source of preference change (or
  preference formation) competes with other sources
  also very well-documented in the psychological
  and sociological literature. For instance, the
  inertia of your idiosyncratic preferences.
• And, specially relevant in an organization, are
  endogenous social norms, that is, social norms of
  behavior established by your peers.

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LEADERSHIP AND PEER EFFECTS IN AN ORGANIZATION

• PRINCIPAL
• He has an ideal accion for each agent-
• N-AGENTS Every agent chooses an action xit, and
  has an ideal action sit a preference .

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LEADERSHIP AND PEER EFFECTS IN AN
ORGANIZATIONPrincipal

• P has some ideal organization composition or
  vector of preferred actions si one for each agent
  i that we assume time independent and also
  exogenous.
• P can invest in costly socialization trying to
  instill this "corporate culture" in all the
  agents of the organization.

All the ideal actions are different
All the ideal actions coincide
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LEADERSHIP AND PEER EFFECTS IN AN ORGANIZATION
Agents

• Each agent i has her ideal action sit at stage t
  and chooses an action xit. When an agent makes a
  decision on xit her behavior is driven by two
  competing motives
• She wants her behavior to agree
• with her personal ideal action sit
• 
  
• 
  2) She wants also her behavior to
• 
  be as close as possible to the
• 
  average behavior of her peers.

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The N-player game

• Research in sociology and psychology indicate
  that individuals want to minimize the social
  distance between themselves and the social norms
  established by their peers.
• And also that there are costs (that might be
  psychological or material) associated with the
  distance between your actual behavior and your
  ideal behavior (see specially, the notion of
  "identity" of Akerlof and Kranton, 2000).
• The parameter ?i describes the taste for
  conformity and measures the intensity of the
  social (endogenous) norm.
• This is the standard way to model conformity and
  social norms in economics (see, among others,
  Akerlof, 1980, Bernheim, 1994, Gillen, 1994,
  Kandel and Lazear, 1992, Akerlof, 1997, Kandori,
  2000, Huck, Kübler and Weibull, 2006, Fischer and
  Huddart, 2008...).

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LEADERSHIP AND PEER EFFECTS IN AN ORGANIZATION

• Ideal actions or preferences of the agents evolve
  over time.
• There are two sources of preference change.
• On the one hand, there exists a costly corporate
  socialization effort exerted by P trying to
  transform the ideal action of each agent sit to
  the ideal action for P,
• On the other hand, each agent's ideal action
  changes in the direction of actual behavior
  (self-persuasion or cognitive dissonance).
• These are in essence two psychological sources
• Follow the leader
• Self-consistence
• FORMALLY

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LEADERSHIP AND PEER EFFECTS IN AN ORGANIZATION
The preferred action of agent i evolves subject
to two forces

• The socialization effort of the corporation dit,
  trying to instill in the agent i the "ideal
• The way to model purposeful socialization effort
  of a "cultural parent" is similar to others in
  the literature (see, for example, Bisin and
  Verdier, 2001 or for the case of a continuos
  trait or preference, Panebianco, 2009, Pichler,
  2009).

• When this socialization effort does not succeed,
  the preference of agent i changes in the
  direction of his actual (Nash equilibrium)
  behavior with an intensity ?.
• The second source for preference change,
  self-consistency, has a robust psychological
  foundation and has been widely used in this
  discipline. (In economics, see for instance,
  Kuran, 1995 and Kuran and Sandholm , 2007).

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Related Literature

• We have already mentioned the economics
  literature on conformity and endogenous social
  norms.
• Literature on Peer effects and Social Networks
  (for example, Cabrales, Calvó-Armengol and Zenou,
  2009)
• There are a few works analyzing corporate culture
  in a dynamic model. See, Kandori, 2000 and Rob
  and Zemsky, 2002.
• These are effort models and their main goal is
  to analyze the interplay between norms and
  monetary incentives. But none of them includes
  the possibility for the firm of investing in
  socialization.
• Cultural transmission literature.
• Cordes, Richerson, McElreath and Strimling, 2006
  analyze how an entrepreneur can shape human
  behavior within a firm. They model it as biased
  transmission of cultural contents via social
  learning process.

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We are interested in the long-run outcomes of
this dynamics and in particular in the ability of
P to fully instill the corporate culture in the
members of the organization.

• Dynamics
• Principal wants to maximize in each period t
• Utility of player i

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Questions

• Under what conditions (if any) the ideal
  preference of each agent coincides in the steady
  state of the dynamics with the ideal action of
  the Principal for all i?
• In case there is no perfect convergence to the
  preferred actions of P, we want to know how
  different parameters influence a measure of the
  success of P.

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1. Solving the N-player game

• Pure Strategy Nash Equilibrium. Best- Response
  functions

Homogeneous case
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2. Computing the steady state

• Given
• Maximum
• Steady states

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• Does the principal succeed in imposing the
  preferred action?
• Answer? Only if
  (homogenous case).
• Which is the action Si taken by the agent?
• Solve a third degree equation
• Self-consistency equation
• Degree of success

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RESULT

• - If P has the same ideal action for all the
  organization, then in the unique steady state of
  the dynamics, P succeeds in instilling this ideal
  action.
• - But, if P has different ideal actions for the
  agents, then there is not a steady state where P
  succeeds.

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FURTHER RESEARCH

• - boundaries of the organization (a single or
  separate organizations?).
• - team initial composition (recruitment).
• - robustness (exogenous shock on the preferred
  actions).
• - a forward looking Principal.
• - an effort model.

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SIMULATIONS
Iterate basic evolution equations
Initial conditions
0
-e
e
(
)
(
)
Sit0
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Parameters N100, ?1, ß2, ?0.5 e, d,
Focus on -Time evolution of -Degree of
success
-Heterogeneity of population
-Average socialization effort
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s
t-1/2
t-1
sx
t
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t-1/2
sx
t
22
s
t-1/2
sx
23
s
e10
e1
t
24
e10
e1
t
25
s
t
26
s
sx
t
27
s
sx
t
28
N100
s
d
29
N1000
s
d
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FURTHER RESEARCH

• Include time-dependent ideals.
• Heterogenous agents with different ?i .
• A single organization or separate organizations
  the boundaries of organizations.
• More economic structure an effort model.
  Analysis of the interaction between monetary
  incentives and socialization.

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THANKS!