The Economics of Being "Nice"

If utopia were something that existed, it would probably be a situation where blogs with titles like these ceased to exist, for people wouldn’t really want an answer to this question. That, however, would not bode too well for me, because then either no one would read this (assuming some readership now) for my writing would be regarded hyperbole and ergo not warrant any flicker of interest. On second thought, utopia would probably deter me from harbouring such ideas in the first place, so the very reason this (this being the words that I am writing now) exists, is the inherent absence of utopia.
At several points in my life I have succumbed to decadent thoughts, those which propel me to wonder-“ Is being ‘nice’ the right strategy?”. I use the word strategy here because I am a fledgling in the world of game theory and having been recently enamoured by Nash Equilibrium, and seduced by the world of strategies and concepts of the like, I feel this propelling urge to appease my narcissistic side. Having managed to successfully drift away from the topic I promised to dive into at the very inception of this endeavour, I think any further procrastination albeit comic relief attempts might warrant a change in the title.
Let us assume that being “nice” or “not nice” are the two strategies that two individuals have.
Let the names of these individuals/players be “ Phelangie” and “Phoebe”

Whereby in (x,y) we have payoffs of Phleangie (x) and Phoebe (y).The payoffs are written so assuming that when a player plays a nice strategy and in turn gets a not nice strategy he gives all the benefit to the player receiving the “nice” behaviour award. Also, when both players choose “not nice” strategies, then the payoff is in negative as the society as a whole also suffers from the absence of “nice” behaviour.
Assuming this is a one shot game and both the players act simultaneously, we can elaborate as follows:
If Phoebe plays nice, Phelangie would chose strategy not nice so as to get a payoff of 20.
If Phoebe plays not nice, Phelangie would play strategy nice to get a pay off of 0.
If Phelangie plays Nice, Phoebe would play strategy Not Nice to get a pay off of 20.
If Phelangie plays Not Nice, Phoebe would play a strategy of nice get a payoff of 0.
We get 2 Nash Equilbriums stating that Phelangie and Phoebe would play the following Strategies:
Phoebe-Nice, Phelangie-Not Nice (20,0)
Phoebe-Not Nice, Phelangie-Nice (0,20)
So economics clearly states that there is NO rationale for people to be nice to each other simultaneously.
Maybe this is what explains when on any given day, a stranger smiles at you, the lady in the bus gives you her seat, your friends bring over flowers when you are feeling unwell, and someone says something nice to you while you have nothing to offer except a frown.
Converse: Stop wondering why others aren’t exhibiting the “nice” behaviour you dish out their way. :P

PS: I am new to this. Corrections are welcome. However, I must warn you, a correction may prompt me to ask you for help with economics homework.