All of Life is a Game- The Art of Decision Making III

Sometimes you have to make a choice with consequences you have to live with forever.

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So this article is gonna be about the everyday games we play, the people we play them with and the outcomes we see, which none of us might have intended. So first... what exactly is a game?? According to me, a game is just a sequence of decision making situations between us and any number of people, in which our choices affect them and theirs affect us. Add to that the fundamental underlying assumption of any game which is: we will  make our best possible move and we also know that our opponents are gonna make their best possible move too. I mean to say that we are sane/ rational  players and so are our opponents. A classic game : Take Dave and Henry- two sane men locked up in  different jails for the same crime. Each of these men face two choices- either confess crime or claim not guilty. If both confess, each get 3 years of prison time and if none confess, each gets 2 years of prison time. Lets say if one confesses and the other pleads innocence, the one who confessed will only get 1 year of jail time while the other will be 5 years behind bars. 

Puzzle (A): Lets say you are Dave's lawyer, what would you suggest him to do?? Confess or remain silent??

Another classic example of a game: Rock Paper Scissors. I am sure all of us have played this when young. We know rock beats scissors which beats paper which in-turn beats rock. Lets turn this into a betting game between you and me. Every time I win, I get Re.1 from you and vice- versa. If both of us show the same item, then it is a draw. Now we know, for every turn, we are faced with three choices: rock, paper, scissors. I know, if I play one item for every turn, lets say I play paper in every turn, or lets say paper is my strategy, then you would learn that paper is my strategy after 2 or 3 turns and would start playing scissors or rather would make scissors your strategy and beat me every turn thereafter. Hence I will not be playing the same strategy in every turn because I am as much game savvy as you are.

Puzzle (B): Is it possible for both of us to win this game?? Will there ever be a win- win situation in such a game?? If yes, why? If no, why?

Another example: A football match between Real Madrid and FC Barcelona. Lets say Real decide to go on an offense and Barça decide to go on a defense. So for Real, its about maximizing the minimum gain  possible even with Barça's defense and for Barça, it is about minimizing the maximum loss possible even with Real's offense. Let's say Real has 2 offense strategies, A and B and Barça has 2 defense strategies C and D. Lets say over the years, Real has found that strategy A is best when Barça plays strategy C and strategy B is best when Barça plays strategy D. So assuming the basic principle of Game Theory that each coach chooses the best strategy for his team assuming the fact that the rival coach is also choosing the best strategy for his team, how is this game going to turn out to be.

Puzzle (C): Is the game going to go on in circles? Can there be a pure strategy for both teams- which if they adhere to throughout the game will yield them the best outcome turn after turn?

Actually the problem with the above example is that the game is not strictly determined, meaning that there is simply no 'SINGLE best possible move (strategy)' for either of the teams, irrespective of the move (strategy) of the opponent team. So when exactly can we call a game to be strictly determined? Lets say there is this one strategy for both Real and Barça which yields their best offense and best defense respectively. So such a strategy or a saddle point (as we call it in mathematical terms), is the optimal strategy for both teams. Such a saddle point if has a value of 0, then the game is said to be 'fair'. If it has a value >0 or <0 then it is 'biased/ unfair' to either of the teams. 

Makes me ever wonder, practical life has no 0 valued saddle points. Sad truth. But is it ever possible to find the optimal strategy to solve such a game. Well, you are not off the hook, yet!