wages and employment in a unionized firm

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wages and employment in a unionized firm

• a repeated game of complete and perfect
  information

Microeconomics presentation Spring
2008 Virginia Silvestri
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the bargaining process between the union and the
firm

• Two players
• a firm and a monopoly union
• Structure of the game at each period t
• STAGE I the monopoly union chooses w
• STAGE II the firm observes w, then chooses L
• STAGE III payoffs are realized

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the bargaining process between the union and the
firm
firms objective
max
unions objective
max
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working by backward induction...
STAGE II
STAGE I
the solution (L,w) is the NE of the one-shot
game
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one-shot game equilibriumLeontief (1946)
the unique NE of the one-shot game is clearly
inefficient
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infinitely repeated version of the game(Espinosa
and Rhee 1989)
when repetition is taken into account, the loss
from noncooperation builds up! the firm and the
union can have incentives strong enough to
implicitly create a strategy to deter deviations
from the cooperative outcome and reach a Pareto
superior outcome as a SPNE of the game, provided
that the threats are credible

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infinitely repeated version of the game

• trigger strategy
• (wt,Lt)(wc,Lc) cooperative outcome
• if in the previous stage the firm (or the
  union) has choosen Lc (or wc), in the next stage
  the union (or the firm) will choose wc (or Lc)
• if any defection is observed, they will revert
  to the NE outcome (wNE,LNE) forever.

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infinitely repeated version of the game
we can obtain an equilibrium solution
(wc,Lc)?(wNE,LNE) only if the incentive
constraints of the firm and the union are
satisfied
Incentive Constraint gain from cooperation
gain from deviation (present values)
ICu Uc UNE 0 ICf
1/(1-d)?c ?d d/(1-d)?NE
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infinitely repeated version of the game

• the only constraint which is relevant to the
  sustainability of the cooperative solution at the
  equilibrium (wc,Lc) is ICf
• if d (?d ?c) / (?d ?NE) d

the cooperative outcome is sustainable at the
equilibrium
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infinitely repeated version of the game
in general it will exist a value of d in 0,1
such that
if d d 1 the fully efficient solution
can be sustained in a SPNE if 0 lt d lt d the
SPNE solution lies between the fully efficient
and the fully inefficient solution if d 0
the NE of the static game is the only
possible SPNE equilibrium of the game
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infinitely repeated version of the game

• conclusion

a typical wage contract can support a
near-efficient outcome as long as each agent
believes that the game will continue with high
enough probability
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implications

• Policy laws to increase the employment level
• Fluctuating demand
• Depressed industries
• Firms bargaining power