Perhaps it's not surprising that game theory is childishly simple and fiendishly complex all at once. Essentially it deals with decisions and their consequences when you are not simply up against 'chance'. Morton D Davis' book does exactly what it says on the cover, although an appreciation of simple probability and statistics will help at one or two points.
Beginning with "the two-person, zero-sum game with equilibrium points" (which sounds very technical, but is actually the simplest form), the book traverses a number of different "game" formats. In a zero-sum game, one player's benefit relates directly to another's cost, and there is a conservation law at play somewhere in the background (for example, a fixed some of money at stake between two players, or the total number of votes available in a two-party election). In a non-zero-sum game, the costs and benefits are not conserved and the options become more complex. There are many examples of this form, such as military arms races, price wars and market share between businesses. The longest chapter in the book is devoted to this subject, including the famed Prisoner's Dilemma. At this point the book is as much about psychology as mathematics; there is no one "correct" solution, but we way up the options subjectively, assigning hidden values to avoid the dilemma. Finally there is a chapter on the n-person game, which again rarely has unambiguous solutions. This chapter includes some interesting comments on electoral systems and voting power.
The book is dry in places, but generally is quite readable. There is an obvious American bias in the text, both in writing style and in the nature of the examples (and in the description "the House of Lords in England" [my italics]). Each chapter (other than the introduction) begins with a set of problems, which is different from the usual problems at the end approach, but works quite well in attempting to get you to think about the issues, which can be very complex indeed.