Dear Andrew,

The book "Industrial Organization Theory and Practice," by Don Waldman and Elizabeth Jensen, Third Edition, 2007 has examples of the sort you are looking for. I attach two pages with one monopolist and an a potential entrant that has three Nash equilibria.

Hope this helps

Thanks Lall for your response. I have found that it is difficult to construct a simple algebraic example that obviates the extensive form representation to show multiple Nash Equilibria in a continuous context but yet preserve economic logic.

Hi Andrew,

I may have found an example for you; it is illustrated in the link.  It is a relatively simple example.  If you are seeking a real-world example, then this may miss your target; however, it would not be too challenging to add some realism to it.  I hope this helps.

Rob    

https://www.economics.utoronto.ca/osborne/2x3/tutorial/COURNX.HTM

Thanks Rob but I have actually been in contact with Prof Osborne before (Osborne and Rubinstein is a must read on game theory basics) The example as he says has "a unique Nash equilibrium".  However I am looking for the case of a NON UNIQUE or Multiple Nash Equilibrium in a Cournot Duopoly. That however seems to be elusive.  Thanks for your help and I do apologise that I was not precise.

Thanks

Hi Andrew,

You Definitely do not need to apologize, especially for my mistake; your question clearly states both "equilibria" and "multiple."  What could be more clear? In fact, that was what first came to mind until I ran across the piece for which I created the link and then in my haste I did not reread your question carefully before posting.  

If I find the reference I originally wanted, I will post it.  If I recall correctly, the  prices (and output) of the firms move down and up through a bounded range of prices.  It has intrigued me since I first encountered it.  With prices seemingly constantly in motion, yet in a predictable manner and within a bounded range, it creates a paradoxical example of a quasi-equilibrium-like situation in a broad sense. If that is not what you are after, let me know and I will stop looking.

At least I now have a fresh example of an oxymoron (e.g., non-stable equilibrium) to add to my list of economics-related oxymora.  Thanks again for your gentle correction of my mistake.

In fact I found an example of multiple Nash Equilibria as the intersection of reaction functions.  I have the hard copy book but its a little difficult to scan so here is it taken from google books.

Fudenberg, D. and Tirole J. Game theory Boston: MIT Press, 1991 page 25.

As you can see there are a 3 intersections of the tworeaction functions I would like the equation of this curve. (B,C and D) and assuming the second order conditions for a profit maximum is satisfied at each intersection then there would be three Nash equilibria. In particular, Fudenberg and Tirole unfortunately said (page 24) "we spare the reader the derivation of such reaction functions from a specification of the cost and demand functions". Unfortunately to be able to replicate this diagram, I would like to know the analytical specifications of these lamniscate/figure of 8/devil's curve reaction functions.