### Abstract

Original language | English |
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Place of Publication | Tilburg |

Publisher | Microeconomics |

Number of pages | 29 |

Volume | 1999-88 |

Publication status | Published - 1999 |

### Publication series

Name | CentER Discussion Paper |
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Volume | 1999-88 |

### Fingerprint

### Keywords

- public goods
- cooperative games
- coordination games
- potential games
- utili- tarian welfare function

### Cite this

*Voluntary Contribution to Multiple Public Projects*. (CentER Discussion Paper; Vol. 1999-88). Tilburg: Microeconomics.

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**Voluntary Contribution to Multiple Public Projects.** / Koster, M.A.L.; Reijnierse, J.H.; Voorneveld, M.

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Voluntary Contribution to Multiple Public Projects

AU - Koster, M.A.L.

AU - Reijnierse, J.H.

AU - Voorneveld, M.

N1 - Pagination: 29

PY - 1999

Y1 - 1999

N2 - The problem of financing a set of public goods (facilities, projects) by private contri- butions is studied. The corresponding cooperative game, the realization game, is shown to be convex. For the noncooperative setting we study a realization scheme that induces a strategic game. This contribution game is shown to be best-response equivalent with a coordination game in which the payoff to all players is the utilitarian collective welfare function, i.e., the sum of the utility functions of the players. Several equilibrium proper- ties are derived: no money is wasted in an equilibrium; a player whose necessary projects are not all realized does not contribute. Strategy profiles maximizing utilitarian welfare are strong Nash equilibria of the contribution game. Each strong Nash equilibrium corre- sponds to a core element of the realization game in a natural way. It is shown that there is a one-to-one correspondence between the set of strong Nash equilibria of the contribution game and the largest set of core elements of the realization game, that is consistent with maximizing the number of players with non-zero payoffs. It is precisely the subset of the core according to which rewards zero indicate null players

AB - The problem of financing a set of public goods (facilities, projects) by private contri- butions is studied. The corresponding cooperative game, the realization game, is shown to be convex. For the noncooperative setting we study a realization scheme that induces a strategic game. This contribution game is shown to be best-response equivalent with a coordination game in which the payoff to all players is the utilitarian collective welfare function, i.e., the sum of the utility functions of the players. Several equilibrium proper- ties are derived: no money is wasted in an equilibrium; a player whose necessary projects are not all realized does not contribute. Strategy profiles maximizing utilitarian welfare are strong Nash equilibria of the contribution game. Each strong Nash equilibrium corre- sponds to a core element of the realization game in a natural way. It is shown that there is a one-to-one correspondence between the set of strong Nash equilibria of the contribution game and the largest set of core elements of the realization game, that is consistent with maximizing the number of players with non-zero payoffs. It is precisely the subset of the core according to which rewards zero indicate null players

KW - public goods

KW - cooperative games

KW - coordination games

KW - potential games

KW - utili- tarian welfare function

M3 - Discussion paper

VL - 1999-88

T3 - CentER Discussion Paper

BT - Voluntary Contribution to Multiple Public Projects

PB - Microeconomics

CY - Tilburg

ER -