Game theory: A 3-way Prisoner's Dilemma with no Nash Equilibrium

quixotecoyote · 26th February 2009, 04:15 AM

I'll explain in detail later what I'm looking for and why (eta: if anyone wants to know), but if anyone happens to know of an example of a Prisoner's Dilemma variant or any similar exercise (Inspector/Worker) with more than 2 players that does not result in a Nash Equilibrium, it would save me a lot of headaches.

Folly · 26th February 2009, 01:56 PM

More context or qualifications? Otherwise, I'm going to suggest that the answer is "No, no one can provide you with a game without a Nash equilibrium." Imperfect recall? Only pure strategies?

quixotecoyote · 26th February 2009, 02:04 PM

D'oh!

That may be the reason for no replies.

I meant variants with no pure-strategy Nash equilibrium.

I'm trying to work some kinks out of the methodology for a study I'm doing. I pulled one example out of "Game Theory" by Fudenberg & Triole, but ideally I'd like a variant where all players have the choice to co-operate or defect.

In Fudenberg & Triole's example, each player had two choices, but player three's choice axis was inverted. When player 3 co-operated, players 1 and 2 were worse off.

That would be ideal, but I'm fishing for any examples.

Folly · 26th February 2009, 03:33 PM

Sorry. Not off the top of my head

. I could probably come up with a bunch of randomly chosen payoffs, but it sounds like you want more than a game with a bunch of arbitrary outcomes...

quixotecoyote · 26th February 2009, 03:39 PM

Originally Posted by Folly

Sorry. Not off the top of my head

. I could probably come up with a bunch of randomly chosen payoffs, but it sounds like you want more than a game with a bunch of arbitrary outcomes...

That's right. I'm trying to come up with an (at least) 3-player game where each player has the choice to co-operate and defect, yet will not have a pure-strategy equilibrium. I thought I had it figured it out, but then I realized I had the matrices all wrong.

INRM · 1st March 2009, 08:48 AM

What's a prisoner's dilemma

Terry · 1st March 2009, 08:54 AM

Prisoner's Dilemma^WP

Professor Yaffle · 1st March 2009, 08:54 AM

Originally Posted by INRM

What's a prisoner's dilemma

http://lmgtfy.com/?q=prisoner%27s+dilemma

26th February 2009, 04:15 AM	#1
quixotecoyote Howling to glory I go Join Date: Jun 2006 Posts: 9,621	Game theory: A 3-way Prisoner's Dilemma with no Nash Equilibrium I'll explain in detail later what I'm looking for and why (eta: if anyone wants to know), but if anyone happens to know of an example of a Prisoner's Dilemma variant or any similar exercise (Inspector/Worker) with more than 2 players that does not result in a Nash Equilibrium, it would save me a lot of headaches.
	__________________ If people needed video games to live, a national single payer plan to fund those purchases would be a great idea. Last edited by quixotecoyote; 26th February 2009 at 04:19 AM.

26th February 2009, 01:56 PM	#2
Folly Thinker Join Date: Oct 2003 Posts: 243	More context or qualifications? Otherwise, I'm going to suggest that the answer is "No, no one can provide you with a game without a Nash equilibrium." Imperfect recall? Only pure strategies?
Folly Thinker Join Date: Oct 2003 Posts: 243	Last edited by Folly; 26th February 2009 at 01:57 PM. Reason: added suggested contexts

26th February 2009, 02:04 PM	#3
quixotecoyote Howling to glory I go Join Date: Jun 2006 Posts: 9,621	D'oh! That may be the reason for no replies. I meant variants with no pure-strategy Nash equilibrium. I'm trying to work some kinks out of the methodology for a study I'm doing. I pulled one example out of "Game Theory" by Fudenberg & Triole, but ideally I'd like a variant where all players have the choice to co-operate or defect. In Fudenberg & Triole's example, each player had two choices, but player three's choice axis was inverted. When player 3 co-operated, players 1 and 2 were worse off. That would be ideal, but I'm fishing for any examples.
	__________________ If people needed video games to live, a national single payer plan to fund those purchases would be a great idea.

26th February 2009, 03:33 PM	#4
Folly Thinker Join Date: Oct 2003 Posts: 243	Sorry. Not off the top of my head . I could probably come up with a bunch of randomly chosen payoffs, but it sounds like you want more than a game with a bunch of arbitrary outcomes...
Folly Thinker Join Date: Oct 2003 Posts: 243

26th February 2009, 03:39 PM	#5
quixotecoyote Howling to glory I go Join Date: Jun 2006 Posts: 9,621	Originally Posted by Folly Sorry. Not off the top of my head . I could probably come up with a bunch of randomly chosen payoffs, but it sounds like you want more than a game with a bunch of arbitrary outcomes... That's right. I'm trying to come up with an (at least) 3-player game where each player has the choice to co-operate and defect, yet will not have a pure-strategy equilibrium. I thought I had it figured it out, but then I realized I had the matrices all wrong.
	__________________ If people needed video games to live, a national single payer plan to fund those purchases would be a great idea. Last edited by quixotecoyote; 26th February 2009 at 03:40 PM.

1st March 2009, 08:48 AM	#6
INRM Philosopher Join Date: Jul 2002 Posts: 5,490	What's a prisoner's dilemma
INRM Philosopher Join Date: Jul 2002 Posts: 5,490

1st March 2009, 08:54 AM	#7
Terry Zeitgeist-impaired Technical Moderator Join Date: Jun 2003 Location: logged in to the server Posts: 6,450	Prisoner's Dilemma^WP

1st March 2009, 08:54 AM	#8
Professor Yaffle Butterbeans and Breadcrumbs Join Date: Jan 2007 Location: Emily's shop Posts: 15,360	Originally Posted by INRM What's a prisoner's dilemma http://lmgtfy.com/?q=prisoner%27s+dilemma
	__________________ I think you'll find it's a little bit more complicated than that. My blog "Well I think I've made it abundantly clear in this thread I have no idea what I'm talking about..." - truethat