What are 'Symmetric Agents' vs. 'Asymmetric Agents'? Here is a contextual example from Landry et. al. 2006 :


  We concentrate on an economy with n symmetric agents who
  derive utility from consuming a numeraire good, yi, a public good
  at level G, and (possibly) from their own contribution bi to the
  public good. Each agent faces a budget constraint yi  bi  w and
  derives ex post utility according to  
  
  (1) $   Ui = u(yi) + \Theta h(G)  + \gamma f(bi)$
“Symmetric agents” generally means that all the agents have the same payoff function and the same information set. In this case, it’s the function you’ve specified. It’s often the case that, because symmetric agents will all respond the same way, they can be replaced with a single representative agent, in contrast to heterogenous agent models.