Need help for solution

[Emine Özge Yurdakurban]

Hello everyone, 

I need help with my public good game solution. I'm trying to find equilibrium, but I'm just confused. I'm doing FOCs and finding Nash, but it's not giving the optimal contribution level. FOC gives the beta equation in terms of N and alpha. I want to see the optimal contribution in Nash equilibrium. How can I find it? Why FOCs did not give the optimal contribution? Is there anybody who can help me? I have a complicated result that does not satisfy me. If anyone can help and if anyone wants to see it, please write to me. I'm waiting for your help. 

Thank you.

Best regards

[Kuzmics, Christoph (christoph.kuzmics@uni-graz.at)]

Hi Emine,

if you could tell us concisely the players, strategy sets, and payoff functions of your game, I am sure some of us can help with finding Nash equilibria of your game.

Best wishes,

Christoph

Christoph Kuzmics
https://homepage.uni-graz.at/de/christoph.kuzmics/
Professor of Microeconomics
School of Business, Economics, and Social Sciences
and Complexity of Life (COLIBRI)
University of Graz
blog: https://gametheory.life/

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Von: learning-evolutio...@googlegroups.com <learning-evolutio...@googlegroups.com> im Auftrag von Emine Özge Yurdakurban <eoyurd...@gmail.com>
Gesendet: Montag, 19. August 2024 11:12
An: Learning Evolution and Games Forum
Betreff: [Caution: Message contains Redirect URL] [LEG_Forum] Need help for solution

 

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[Berger, Ulrich]

Hi Emine,

 

player i’s utility function is linear in i’s own contribution, so setting its derivative equal to 0 just gives you the value of \alpha_i where this utility happens to be constant, i.e. independent of i’s own contribution, \alpha_i = (N-\beta) / (\beta(N-1)). For \alpha_i below this value, utility is linearly decreasing in own contribution, so contributing 0 is strictly dominant, while for \alpha_i above this value, utility is linearly increasing in own contribution, and contributing the whole endowment is optimal. So generically, in equilibrium all those who are altruistically enough contribute everything, while the others contribute nothing.

 

Best, Ulrich

 

_________________________________________

 

Univ.Prof. DDr. Ulrich BERGER

Department of Economics

WU Vienna University of Economics and Business

 

Department Volkswirtschaft

Wirtschaftsuniversität Wien

 

Welthandelsplatz 1/D4

1020 Wien

 

+43-1-31336-4562

ulrich...@wu.ac.at

https://www.wu.ac.at/en/economics/people/berger-u/

 

Von: learning-evolutio...@googlegroups.com <learning-evolutio...@googlegroups.com> Im Auftrag von Emine Özge Yurdakurban
Gesendet: Montag, 19. August 2024 11:13
An: Learning Evolution and Games Forum <learning-evolutio...@googlegroups.com>
Betreff: [LEG_Forum] Need help for solution

 

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