I have some problems in understanding the VCG (Vickrey-Clarke-Groves) mechanism in game theory. Actually the bid for player $j$ is defined as:
$p_j$ = (optimal welfare for the other players if player $j$ is not participating) - (welfare of the other players by the choosen outcome). Ofc. this can be formulated mathematically, but would need a lot of notations.
Now I have an example, where I would like to know the VGC outcome:
Consider a purchase of 800 kWh electrical energy. There are 6 providers, where player 1 and 2 offers each 800kWh at 50€, player 3-6 offers each 200kWh to 0€.
Now players 3-6 win the auction, and each one charges now:
$$p_j=(50€ + 0€ + 0€ + 0€)-(0€ + 0€ + 0€)=50€$$
So the buyer pays a total of 200€ for the 800kWh.
Is this the correct VGC outcome here?