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. the bargaining process between the union and the firm. Two players : a firm and a monopoly union

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Wages and employment in a unionized firm

wages and employment in a unionized firm

a repeated game of complete and perfect information

Microeconomics presentation – Spring 2008

Virginia Silvestri


The bargaining process between the union and the firm
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:

STAGEI the monopoly union chooses w

STAGE II the firm observes w, then chooses L

STAGE III payoffs are realized


The bargaining process between the union and the firm1
the bargaining process between the union and the firm

firm’s objective:

max

union’s objective:

max


working by backward induction...

STAGE II

STAGE I

the solution (L*,w*) is the NE of the one-shot game


One shot game equilibrium leontief 1946
one-shot game equilibriumLeontief (1946)

the unique NE of the one-shot game is clearly inefficient


Infinitely repeated version of the game espinosa and rhee 1989
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


Infinitely repeated version of the game
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.


Infinitely repeated version of the game1
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-δ)Πc ≥ Πd + δ/(1-δ)ΠNE


Infinitely repeated version of the game2
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 δ≥ (Πd– Πc) / (Πd – ΠNE) = δ*

the cooperative outcome is sustainable at the equilibrium


Infinitely repeated version of the game3
infinitely repeated version of the game

in general it will exist a value of δ* in [0,1] such that

if δ* ≤ δ ≤ 1 the fully efficient solution can be sustained in a SPNE

if 0 < δ < δ* the SPNE solution lies between the fully efficient and the fully inefficient solution

if δ = 0the NE of the static game is the only possible SPNE equilibrium of the game


Infinitely repeated version of the game4
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


Implications
implications

  • Policy: laws to increase the employment level

  • Fluctuating demand

  • Depressed industries

  • Firm’s bargaining power


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