Analogies between phase transitions in potential games and quantum phase transitions

Potential games at population level has a very natural analogy with statistical mechanical systems. Here we show that there are clear analogies between quantum phase transitions at zero temperature and phase transitions in potential games being played by fully rational players. Such phase transitions are brought about by tuning parameters which change the payoff matrix either directly (as in classical games) or indirectly through continuous change in strategies (as in quantum games). The phase transitions take the system from one Nash equilibrium to another; these Nash equilibria (NE) are, in a sense, refined as only the ones that correspond to global maxima of the potential are selected in the thermodynamic limit (infinite number of players). We observe that the types of the phase transitions depend on the states involved in the transition process: while transitions involving two symmetric NE are discontinuous, the transitions between a symmetric and an antisymmetric NE are continuous.