  This paper considers the discounted criterion of nonzero-sum decentralized
stochastic games with prospect players. The state and action spaces are finite.
The state transition probability is nonstationary. Each player independently
controls their own Markov chain. The subjective behavior of players is
described by the prospect theory (PT). Compared to the average criterion of
stochastic games under PT studied firstly in 2018, we are concerned with the
time value of utility, i.e., the utility should be discounted in the future.
Since PT distorts the probability, the optimality equation that plays a
significant role in proving the existence of equilibrium does not exist. On the
other hand, the games change into Markov decision processes (MDPs) with
nonstationary payoff function when fixing others' stationary Markov strategies,
then the occupation measure and the linear programming of stationary MDPs are
no longer suitable. Therefore, we explore a new technique by constructing the
marginal distribution on the state-action pairs at any time, and establish the
existence of Nash equilibrium. When the initial state is given, there exists a
Markov Nash equilibrium. Furthermore, this novel technique can be extended to
the finite horizon criterion. Then, we present an algorithm to find a Markov
$\varepsilon$-equilibrium. Finally, the model is applied to a noncooperative
stochastic game among prosumers who can produce and consume energy in the smart
grid, and we give some simulation results.
