Price Update

By the definition of a pricebot, each of the pricebot algorithms, game-theoretic, myopically-optimal, derivative-following, and q-learning ultimately calculate a price [1]. In a given population in which there is more than one pricebot, regardless of the algorithm being used, the pricebots can update their prices in one of two ways. Either all of the pricebots update their prices, and then all of the pricebots update their profits (simultaneous update); or one pricebot updates its price, and then all of the pricebots update their profits, and then another pricebot updates its price, and then all of the pricebots update their profits, and so on (sequential update). With sequential update, pricebots can update their prices in either a fixed or a random order. We have chosen to have the pricebots update their prices in a fixed order when updating sequentially.

With simultaneous update we see the following,

for (g generations)
{
for (r rounds)
{
//
// ALL pricebots update price
// ALL pricebots receive profits
//
}
//
// evolve population
//
}

Whereas with sequential update and a fixed order of update we see, for s pricebots we see,

for (g generations)
{
for (r rounds)
{
//
// ONE pricebot updates price: pricebot 1
// ONE pricebot receives profits: pricebot 1
//
//
// ONE pricebot updates price: pricebot 2
// ONE pricebot receives profits: pricebot 2
//
//
// ...
//
//
// ONE pricebot updates price: pricebot s
// ONE pricebot receivess profits: pricebot s
//
}
//
// evolve population
//
}

The important difference between the two types of updating is that different information is available to a pricebot updating its price depending on whether simultaneous or sequential updating is being used [1,2]. In simultaneous updating, no pricebot is allowed to know the price any other pricebot has chosen for the round. In sequential updating, since the pricebots update their prices in a fixed order, when it comes time for pricebot i to update its price, i knows the prices and corresponding profits for the current round for pricebots 1 through i-1.