Game Theory

http://msl1.mit.edu/ESD10/block4/4.4_-_Game_Theory.pdf

Summary:

Game theory is the branch of decision theory concerned with interdependent decisions. Participants, or players, in a situation, or game, compete to achieve objectives with similar resources. The goal of game theory is not necessarily to "win," but rather to identify an optimal strategy. The sequence of moves a player uses is called a "strategy," and does not need to be wholly unique.

There are two categories of games: sequential and simultaneous. In sequential games, participants take turns acting. The basic strategic rule when applying game theory in this situation is to "look ahead and reason back." This starts with the last decision to be made, then working back through the problem to choose the course of action the other player would make until an initial decision needs made.


Simultaneous games require a more robust analysis due to their overall complexity. There is no "final move" per say in these games. In simultaneous games all possible combinations must be laid out. Players in this type of game should identify their dominate strategy and dominated strategy, the later should never be employed. Thus, the overall range of choices can be limited. Players then can go back to assess if there is another dominate strategy they can employ from the remain outcomes, as well as determine if there is another dominated strategy. This sequence can be replicated until a final strategy is reached, or if a dominate strategy is no longer evident.


In simultaneous games, comptitors without a clear dominate strategy should seek out equalibrium in relation to the other. Equilibrium is reached when both competitors do not have an incentive to change strategy.

What Is Game Theory And What Are Some Of Its Applications?

Saul I. Gass
Professor emeritus at the University of Maryland

Summary
After learning how to play the game tick-tack-toe, players typically discover a strategy of play that enables them to achieve at least a draw and potentially a win if the opponent makes a mistake. Sticking to that strategy ensures that the player will not lose. This illustrates the essential aspects of game theory.

Games with perfect information, such as tick-tack-toe, allow for the development of a pure strategy, an overall plan specifying moves to be taken in all eventualities that can arise. Games without perfect information (e.g. poker), however, offer a challenge because there is no pure strategy that ensures a win.

Players of games with imperfect information must then reconcile the questions: What is the optimal mix of strategies to play? How much do I expect to win?

Players must seek an equilibrium solution or a mixed set of strategies for each player, so that each player has no reason to deviate from that strategy, assuming all other players stick to their equilibrium strategy. This then creates the important generalization of a solution for game theory. All many-person non-cooperative finite strategy games have at least one equilibrium solution.

It is important to note, however, that for many competitive situations, game theory does not really solve the problem. Rather, game theory helps to illuminate the problem and offers players a different way of interpreting the competitive interactions and possible results. Game theory is a standard tool of analysis for professionals working the fields of operations research, economics, regulation, military, retail marketing, politics, conflict analysis, and many more.

Specific real-world situations include missile defense, sale price wars, NASCAR racing, military conflicts, conflict resolution, the stock market, telecommunications, elections and voting, and arbitration to name a few.