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

[quixotecoyote]

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]

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]

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]

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]

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]

What's a prisoner's dilemma

[Terry]

Prisoner's Dilemma

[Professor Yaffle]

What's a prisoner's dilemma

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