A solution of the externality problem using strategic matching (Q1184962)

The authors formalize a sort of Coasean compensation mechanism; the present approach is related to earlier papers of the authors. Formally, given actors \(i=1,\dots,n\), actions \(x_ i\geq 0\) and payoffs \(u_ i(x_ 1,\dots,x_ n)\), the problem of implementing a Pareto-optimal payoff system (i.e. one maximizing \(\sum_ i u_ i(x_ 1,\dots,x_ n))\) is studied. This is done by means of 2-steps games in which the actors choose compensation factors \(b_{ij}\) (i.e. \(i\) chooses all \(b_{ij}\)) and then choose their ``flat'' actions \(a_ i\); the actual choice of \(x_ i\) is then given by \(x_ i:=a_ i+\sum_{j\neq i} b_{ij}a_ j\). The authors study subgame perfect equilibria in such games \((b_{ij}=(\partial u_ i/\partial x_ j)/(\partial u_ j/\partial x_ i)\) for \(x\) in equilibrium). Special emphasis is given to the case of \(n=2\).