It is well established in game theory that when all players in a game cooperate, their welfare is higher than in the absence of cooperation, but that when only some players cooperate, all players may be worse off than under non-cooperation. Rog off has applied this result to international policy coordination, arguing that cooperation among monet- ary authorities may be sub-optimal if it cannot be extended to the interaction within each country between the authorities and private agents.

In Discussion Paper No. 258, Research Fellow Carlo Carraro and Programme Director Francesco Giavazzi dispute Rogoff's result in a symmetric two-country model with a representative firm, union and central bank in each country. The existence of nominal contracts is a crucial assumption in Carraro and Giavazzi's model: it gives central bankers the power to affect real variables, and it makes the game sequential by constraining one set of players, the unions, to move first. The actual behaviour of productivity is known to the firms and central banks before they make their decisions, but not to the unions, who set wages in period zero so as to stabilize employment around its natural rate, based on the price level (rationally) expected to prevail in period one.
Firms are passive players, seeking to maximize profits given wages and productivity. Central banks minimize both domestic price fluctuations and the difference between domestic employment and a target value above the natural rate. The inefficiency of the natural rate of output in each country is the motivation for the game: if the natural rates of output were socially optimal, central bankers would have no incentive to affect the real variables. Each central bank sets the money stock given domestic nominal wages and knowledge of how domestic firms will react.

Given the level of wages, central banks then decide whether or not to cooperate in period one, and choose the optimal level of the money stock. Under cooperation, they form a coalition and maximize a joint objective function. Carraro and Giavazzi demonstrate that both central banks achieve a larger pay-off under cooperation, whatever the wages set by the unions in period zero. A superior equilibrium can only be achieved if the central banks could precommit not to cooperate. The authors then introduce productivity shocks. They show that if the central banks can decide period by period, having observed wages and real shocks, whether or not to cooperate, the only equilibrium is the cooperative one. If, however, real shocks are `small', this is dominated by the outcome under a precommitment not to form coalitions.
These results seem to provide an argument for designing `institutions' that make credible countries' commitment not to cooperate for example cancelling routine OECD or Gn meetings. The argument is similar to the view that in a closed economy the central bank's discretion should be restricted by law. Carraro and Giavazzi nevertheless argue in favour of discretion in international economic policy-making. Tying the hands of the central bank may not be optimal in a stochastic world; and even in a deterministic world where rules may be desirable, they should be directed at limiting central banks' power to create surprise inflation, rather than at forcing them not to cooperate internationally. The authors conclude that nom- inal wage rigidity cannot be used to prove that international cooperation may be counterproductive. A different explanation, suggested by Charles Bean, is asymmetric information; another direction is to raise the number of players, introducing two policy-makers in each country or raising the number of countries

Can International Policy Coordination Really be Counterproductive?
Carlo Carraro and Francesco Giavazzi

Discussion Paper No. 258, August 1988 (IM)