What Are Game Theory and Bargaining Theory?

Game Theory - How I Would Define It
Game theory considers economic scenarios with the following properties:
•Two or more 'economic actors' - that is, two or more firms, individuals, political parties, etc.
•Each individual economic actor has a set of decisions they can make - what price to charge, how much to save, whether to move right or left, etc.
•Each individual economic actor has a 'goal' or payoff, such as profit maximization, maximize happiness, minimize loss, etc.
•The decisions made by one economic actor not only affects her payoff, but the payoff of one or more other economic actors
Game theory is a particularly useful tool for understanding why firms and individuals make the decisions they do, and how the decisions made by one individual affects others.
Game Theory - Some Alternative Points of View
Here are a few definitions that should help you answer the question "What are Game Theory and Bargaining Theory?":
The best definition of Game Theory I've seen is contained in the Economists "Dictionary of Economics". In part it states: "Much of economic theory is concerned with the process and conditions under which individuals or firms maximize their own benefits or minimize their own costs in markets in which their individual actions do not materially influence others (perfect competition). There are, however, many cases in which economic decisions are made in situations of conflict, where one party's actions induces a reaction from others. An example is wage bargaining between employers and unions. A more simple case is the of duopoly, in which the price set by one seller will be based on his view of that set by the other in reply. The mathematical theory of games has been applied to economics to help elucidate problems of this kind."
The Game Theory Society
A group of academic game theorists called the Game Theory Society defines game theory as: "Game theory studies strategic interaction in competitive and cooperative environments. Only fifty years old, it has already revolutionized economics, and is spreading rapidly to a wide variety of fields. It develops general mathematical formulas and algorithms to identify optimal strategies and to predict the outcome of interactions."
Bargaining Theory and Evolutionary Game Theory
Bargaining Theory deals with a more narrow class of problems than Game Theory, but many economists tend to use the terms interchangably. Both bargaining theory and game theory can be broken into various subfields, most notably evolutionary game theory. The Economics Glossary gives the following definition for Evolutionary Game Theory: "Evolutionary game theory describes game models in which players choose their strategies through a trial-and-error process in which they learn over time that some strategies work better than others."