Efficient Defection: Overage-Proportional Rationing Attains the Cooperative Frontier

Abstract

We study a noncooperative $n$-player game of slack allocation in which each player $j$ has entitlement $L_j>0$ and chooses a claim $C_j\ge 0$. Let $v_j=(C_j-L_j{)}_{+}$ (overage) and $s_j=(L_j-C_j{)}_{+}$ (slack); set $X={\sum }_j{v}_j$ and $I={\sum }_j{s}_j$. At the end of the period an overage-proportional clearing rule allocates cooperative surplus $I$ to defectors in proportion to $v_j$; cooperators receive $C_j$. We show: (i) the selfish outcome reproduces the cooperative payoff vector $(L_1,\dots ,L_n)$; (ii) with bounded actions, defection is a weakly dominant strategy; (iii) within the $\hat{I}\pm$-power family, the linear rule ($\hat{I}\pm =1$) is the unique boundary-continuous member; and (iv) the dominant-strategy outcome is Strong Nash under transferable utility and hence coalition-proof (Bernheim et al., 1987). We give a policy interpretation for carbon rationing with a penalty collar.

10 pages. Corrections to the boundary allocation in Appendix A to preserve budget balance; clarification of the dominant strategy result; bounded-actions paragraph added; aggregate-identity discussion tightened