Voluntary Contribution to Multiple Public Projects

M.A.L. Koster, J.H. Reijnierse, M. Voorneveld

Research output: Working paperDiscussion paperOther research output

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Abstract

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
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages29
Volume1999-88
Publication statusPublished - 1999

Publication series

NameCentER Discussion Paper
Volume1999-88

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Voluntary contributions
Public project
Strong Nash equilibrium
Welfare function
Financing
Utility function
Best response
Reward
Coordination games
Cooperative game
Strategic games

Keywords

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

Cite this

Koster, M. A. L., Reijnierse, J. H., & Voorneveld, M. (1999). Voluntary Contribution to Multiple Public Projects. (CentER Discussion Paper; Vol. 1999-88). Tilburg: Microeconomics.
Koster, M.A.L. ; Reijnierse, J.H. ; Voorneveld, M. / Voluntary Contribution to Multiple Public Projects. Tilburg : Microeconomics, 1999. (CentER Discussion Paper).
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Koster, MAL, Reijnierse, JH & Voorneveld, M 1999 'Voluntary Contribution to Multiple Public Projects' CentER Discussion Paper, vol. 1999-88, Microeconomics, Tilburg.

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

Tilburg : Microeconomics, 1999. (CentER Discussion Paper; Vol. 1999-88).

Research output: Working paperDiscussion paperOther research output

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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

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KW - cooperative games

KW - coordination games

KW - potential games

KW - utili- tarian welfare function

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Koster MAL, Reijnierse JH, Voorneveld M. Voluntary Contribution to Multiple Public Projects. Tilburg: Microeconomics. 1999. (CentER Discussion Paper).