Nash Equilibrium: Good and Bad Outcomes

Towards the end of 2024, I left the 9 to 5 routine given my financial goals were achieved.  It felt great not needing to hug my phone to sleep and waking up at whatever godly (or ungodly) hour desired.  Fast forward six months, the retirement routine became mundane.  I needed to find meaningful use of my newly found time.  Between street and league soccer, writing a book, exotic getaways, relocation back to my adopted home country, all the while taking on advisory gigs with interesting companies, life seemed like a handful.  Somehow, I managed to find time to study various topics of interest.  One topic that really caught on was game theory.  

Learning game theory was a self-improvement initiative.  I wanted a life broader horizon and be better equipped when when dealing with others.  My definition of game theory is the study of interactive decision making of more than one party, where the outcome of each particpant or player depends on the actions of all.  Applications of this subject are widespread in economics, business and more.  

Perhaps the most renowned example of game theory is Prisoner's Dilemma.   I assume my readers are familar with the case.  What most don't know however, is that Prisoner's Dilemma is also kind of Nash Equilibrium.   Nash Equilibrium, in simple terms, states that a player will continue with the chosen strategy without deviation, after taking into consideration the opponent's strategy.  Expressed mathematically, it is: 

where is the set of all possible strategies for player , and . Let be a strategy profile, a set consisting of one strategy for each player, where denotes the strategies of all the players except .  is player i's payoff as a function of the strategies.

Nash Equilirium can be good or bad.  In a good equilibrium, all players have a strong incentive to cooperate to achieve a mutually desirable outcome.  It may not be the best outcome for the individual per se, but is nonetheless a desirable outcome.  An example of this is a couple dueling to watch the program of thier choice on TV.  The husband wants to watch the the basketball game live, but the wife wants to catch the final episode of The Squid Game on Netflix.  Four distinct outcomes come to mind: 
  1. Both watch The Squid Game - Wife wins, husband loses.  Happy wife, happy life, right?
  2. Both watch the basketball game - Wife loses, husband wins.  Husband gets the couch that night 
  3. Turn off the TV - both loses.  Husband gets the couch that night
  4. Both watch Top Gun, an altnerative program they would enjoy together - both wins.  Happily ever after? 
It is not difficult to spot that possibility #4 is the good equilibrium, whereas #3 is bad.  In fact, Prisoner's Delimma also leads to a bad equilibrium when both prisoners betray each other to do what is best for themselves.  This seemingly inevitable outcome is a result of lack of communication among the participants.  Whereas the happy couple was able to discuss options, the prisoners were interrogated in secluded cells.  The lack of information sharing among the prisoners led them down the betrayal path.  If they were allowed to cooperate, they would both have less jail time which meant good equilibrium.  

Game theory has many applications in real-life.  Ever wondered why a KFC is closely placed next to a McDonald's?  Or why do big retailers almost always offer discounts around the same time of the year?  These everyday questions have everyday answers supported by game theory.  I am only a third of the way into my reading materials.  But my appetite has been fully wetted.  Looking forward to more sharing when the learning deepens. 


- PTS

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