War of Attrittion or, How Game Theory Can Make Me More Logical

A War of Attrition is a model in game theory which means to exploit the idea of competing members in a specific type of zero-sum game... let's back up a moment. What is Game Theory, and how can it make me a more logical thinker? this, if you are not familiar with game theory, is probably what is popping in your head right about now. Game Theory (G.T), at it's core, is the study of decision making; as such, it has many applications in the fields of economics (which very much adopted G.T. as a standard component to economic thought) and can be utilized in everyday thinking, especially in finance. Most models in G.T. are mathematical in nature, but that should not prohibit or discourage the novice mathematician from exploring it's fields. Many components in Game Theory can be expressed without mathematical quotients and for the sake of this site- we will rarely if ever be expressing G.T. inside the realm of quotients and variables. One core idea in G.T. is knowing what kind of game you are playing; one example of how important it is to know what game you are playing can be expressed like this: a con-man going to a bank for a loan. The banker meets with the con-man and might see a good portfolio, reassuring documents and a profitable reason to loan a man a sum, he believes he is playing 'game A'. But keep in mind, the con-man is playing a different game all together. While the banker might have thought he was getting a mutually beneficial deal, the con-man is playing his own game and more importantly knows so- that is why he has the advantage, he will take the loan and never repay it.
War of Attrition, which is a zero-sum game- a situation (or game) in which one's benefit or loss is exactly proportional to someone else's benefit or loss (ie where there is only one winner), but what is important in a War of Attrition is that every move taken before reaching your goal is costly. It is also generally the case that the costs issued are necessary to obtain your goal.
In actuality, the real life examples of this can be endless. For example, if one accepts the Peter Siris model for trading stocks, you would be looking at each trade as a small battle (or game) where you buying a stock and someone selling a stock are in direct competition- fighting over who is in the right. Siris' take on the situation is that there is always one loser and one winner. So say, even if "man X" bought acb Company at $5 a share and sells them to you at $25 a share and abc Co goes to $50 a share- man X lost that game. Now, most people looking at this believe that everyone won, "man X" made money and you made money; but Siris' view is that "man X" only sold his position because he believed it was not worth that and therefore would lose value soon. Since that did not happen he lost that battle.
Thanks to ĻiĻ Pië for Photo (Continued in Part II)