Efficient Defection: Overage-Proportional Rationing Attains the Cooperative Frontier
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arXiv
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| Format: | Preprint |
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2025
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| author | Lengyel, Florian |
| author_facet | Lengyel, Florian |
| contents | We study a noncooperative $n$-player game of slack allocation in which each player $j$ has entitlement $L_j>0$ and chooses a claim $C_j\ge0$. 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 $α$-power family, the linear rule ($α=1$) 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Defection: Overage-Proportional Rationing Attains the Cooperative Frontier Lengyel, Florian Theoretical Economics Optimization and Control 91B32, 91A10 (Primary) 91B26, 91A12, 91B15 (Secondary) We study a noncooperative $n$-player game of slack allocation in which each player $j$ has entitlement $L_j>0$ and chooses a claim $C_j\ge0$. 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 $α$-power family, the linear rule ($α=1$) 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. |
| title | Efficient Defection: Overage-Proportional Rationing Attains the Cooperative Frontier |
| topic | Theoretical Economics Optimization and Control 91B32, 91A10 (Primary) 91B26, 91A12, 91B15 (Secondary) |
| url | https://arxiv.org/abs/2509.07145 |