Today, at the University of Cape Town, I began to teach an undergraduate course in game theory.  The course is a broad-based introduction to game theory for students across the university's faculties: from humanities, to commerce, to engineering and the built environment.  We instruct with the textbook Games of Strategy (3rd ed) by Dixit, Reiley and Skeath.  The book is a good, broad-based and intuitive introduction to game theory, with mathematical formalisation that is accessible to the majority of students who have done basic calculus.  However, producing problem sets is difficult year-on-year as many of the problems are similar and students often share information across the university network.  I mean that literally: they share their solutions of old problem sets so that their friends can download the solutions and hand them in as 'their' solutions.

Consequently, in an attempt to expand the number of resources I have for problem sets, I have found a number of other books useful for finding additional problems, especially some problems outside of economics.  I have several goals for the course, one of which is to ensure that the students have many problems that they can work on in order to prepare for the mid-term test and the exam.  I have found a problem-oriented approach to work quite well and, as far as I understand it, research demonstrates that this is a good way to approach a course like introductory game theory. Nevertheless, I also hope to convey most of the intuitions in accessible and commonsensical situations.  I have lectured the course a few times before and I am looking forward to lecturing it again after this hiatus (the last time I lectured it was for the summer term in early 2007). 

Here is a list of the books I have found useful so far:
Binmore, Ken (2007) Playing for Real - Gets a bit complex for the course I will teach, but has some good examples that one can adapt quite easily for problem sets.  The book is an updated version of Binmore's earlier (1991) Fun and Games.
Miller, James (2003) Game Theory at Work: How to use game theory to outthink and outmaneuver your competition - written for the businessperson wanting to understand the basics of game theory, this book has many examples that can be adapted to create problem set questions.  The book could have been better edited and better conceived in parts, but it does give many typical problems in different settings that can be useful for someone producing problem sets.
McCarty Nolan and Adam Meirowitz (2007) Political Game Theory: An Introduction - this book has several basic examples with added complexity that make for good problem set questions.  Moreover, it has problem sets at the end of chapters that can be used quite easily for problem sets. The book itself is a bit too formal for the 2nd year course that I am teaching, but I think that it could probably be used quite easily in a higher level undergraduate or Honours-level course where the mathematical formalisation would not be a problem for students.
Rasmusen, Eric (2006) Games and Information: An Introduction to Game Theory - Rasmusen uses a number of definitions and approaches that I would not use when teaching game theory, nevertheless he has many interesting and fun examples in his textbook that can be put into problem sets for a course like mine.  Rasmusen also gets a bit too mathematical and caught up in definitions that I would not want to use. 
Romp, Graham (1997) Game Theory: Introduction and Applications is targeted at advanced undergraduate and early graduate students. Consequently, the book as a whole gets too complex for my course, but several of the examples in the introductory chapters as well as 'dumbed down' versions of the applications can make good problems for an introductory game theory course.  
Straffin, Philip D. (1996) Game Theory and Strategy is also a bit too mathematical for the needs of my course.  Nevertheless, it also has some good examples of zero sum and non-zero sum two-person games that can be easily introduced into an easier course.  The N-person games stuff is interesting, but too in depth for the way in which we approach games with many players. 
Gibbons, Robert (1992) Game Theory for Applied Economists is again too mathematical for the course I am teaching, but it has numerous examples and problems that can be adapted to an easier and more intuitively directed course. 

Overall, looking at all of these books has reinforced how Dixit, Reiley and Skeath is a great book for an introductory game theory course. Most of the books claim to be introductory, but aren't really, they're introductory if you've done sufficient calculus and economics, but not introductory in the sense that most second year students in an cross-faculty course would be able to deal with them. Instead they are pitched at an advanced undergraduate or introductory graduate level where there seems to be a lot of competition for that kind of book.  I'm surprised that more authors haven't tried to take the path that Dixit, Reiley and Skeath have by finding a less formal way to approach game theory and hook students into an area of study that has such potential, notwithstanding its flaws (see Hargreaves-Heap and Varoufakis' Game Theory: A Critical Introduction or some of the passages in Gintis's Game Theory Evolving). 

Books I'm not using:
Osborne and Rubinstein - A Course in Game Theory - Too much mathematics in an inaccessibly written way.  
Binmore, Ken - Game Theory: A Very Short Introduction - Though this is meant to be a book for the layperson and I thought I might get some useful examples from it, I got the sense that someone would have had to study a fair amount of economics to make head or tail of it.  Not useful.
Gibbons (1992) A Primer in Game Theory - Too mathematical and too brief, I'd use this for an advanced undergraduate course.
Gintis, Herbert (2009) Game Theory Evolving (2nd Edition) - More focused on evolutionary game theory, which I'd love to teach, but is outside the ambit of this course also requires more math than 2nd years will have. 

There are many other books that I haven't begun to look at or study, especially some of the more advanced Micro texts that would be unnecessary for a course such as this.  I also know that Dixit and Nalebuff have two good books - The Art of Strategy and Thinking Strategically - but I don't have those to hand and therefore did not want to comment on them.