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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 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 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 equilibriumLeontief (1946) the unique NE of the one-shot game is clearly inefficient
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 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 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 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 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 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 • Policy: laws to increase the employment level • Fluctuating demand • Depressed industries • Firm’s bargaining power