Games people play : 2

If you have missed the first part in the series, click here to read it

Zero-Sum and non-Zero-Sum Games It all started with the concept that a player wins at the expense of other's failure. This type of game is seen more commonly at our daily walk of life and in many instances, between two players only. A game of Ludo or a game of chess can essentially be considered as a zero-sum game because at the end, one player loses (-1) and the other player wins (+1), or it results in a draw (both 0), thereby making the algebraic sum to be zero. When a couple decides to go for a vacation and gets into an argument whether to go by train (husband) or flight (wife), this ensues a zero-sum game. If they go by flight, the husband wins (+1) and the wife loses (-1). If they go by train, the husband loses (-1) and the wife wins (+1). What if they compromise and go by train and return by flight, as would be the most amicable solution? This will result in husband scoring a zero (+0.5 for onward journey, -0.5 for return journey) and the wife scoring a zero too (-0.5 for onward journey, +0.5 for return journey).

However, most of life's practical scenarios cannot be easily rendered in terms of win-lose strategies. For example, in Stock Market if I make lot of money, that wouldn't be essentially at the cost of another share-holder. In Political Science, socialist doctrines believes that a person grows richer because wealth is extracted from some other person making him poorer, hence the national economy is a zero-sum game. The capitalist doctrines, as expected, believes the other way round. To them, the economics is a non-zero sum game because human enterprise actually creates new wealth far out of proportion to any transfers or resource depletion; and voluntary transactions address the preferential desires of both parties.

Strategies

There are so many simple and complex theories about strategies in zero-sum and non-zero sum games. Of course, none of such theories try to establish any rule, which when followed, will ensure a sure win. The reasons for existence of such strategies, and in general, the subject of The Game Theory itself, is to provide a good understanding and knowledge base for identifying games in real life and how to scientifically approach the problems, given all the risk and benefit probabilities that are available during the playing the game.

For example, if a strategy S dominates a strategy T if every outcome in S is at least as good as the corresponding outcome in T, and at least one outcome in S is strictly better than the corresponding outcome in T, the strategy S is considered to be a Dominant Strategy. If player 1 follows a strategy that guarantees that he will win at least N points and player 2 follows a strategy which guarantees player 1 will win no more than N, then N is called the value of the game. The whole game then centres around this value of the game and during the lifetime of the game, different strategies are followed.

A strategy is a comprehensive contingent plan of actions. Contingent – takes into account others’ actions for example. Comprehensive – means that every possible action of the game is considered - not just those that “seem likely” but also includes those that may not be reached.

In general, the Games Theory is not at all a branch of economics or abstract mathematics but a study of our real-world, complex problems trying to explore rational approach in solving them.

In my concluding post, we will explore the game of tic-tac-toe that would be an interesting way of understanding the concepts of strategies and how this could be used for forensic analysis.