Pricing Strategies

We introduce three types of adaptive pricing strategies, each of which makes very different demands on the required level of informational and computational power of agents, and some of which allow for the possibility that information about buyers and other sellers may be costly or even impossible to obtain. The pricing strategies which we consider are:

GT

The game-theoretic strategy is designed to reproduce the game-theoretic equilibrium computed in the previous section, provided that it is adopted by all sellers. It makes use of full information about the buyer population, as well as complete information about competitors' prices or pricing strategies. In essence, a game-theoretic agent assumes that all other agents abide by the prescribed game-theoretic strategy, and based on this assumption, it computes its own equilibrium price.

Recall that the game-theoretic equilibrium requires that one seller set its price at as computed in Eq. 11, while the remaining sellers all charge the monopolistic price v. This computation fails to address the question of which seller should volunteer to charge the low price . To ensure that there is exactly one such seller, the GT price-setting algorithm determines whether any other seller is currently charging a price that is equal to (to within some very small tolerance). If not, it sets its price to ; otherwise, it sets its price to v.

MY

The myoptimal  (myopically optimal) strategy [10, 11, 15] makes use of information about all the buyer characteristics that factor into the buyer demand function, as well as the competitors' prices, but makes no attempt to account for competitors' pricing strategies. Instead, it is based on the assumption of static expectations: even if one seller is contemplating a price change under myoptimal pricing, this seller does not assume that this will elicit a response from its competitors; instead it assumes that competitors' prices will remain fixed.

The myoptimal seller s uses all of the available information and the assumption of static expectations to perform an exhaustive search for the price that maximizes its expected profit . In our simulations, we compute according to Eqs. 7 and 8. The optimal price is guaranteed to be either the valuation v or below some competitor's price, where is the price quantum, or the smallest amount by which one seller may undercut another, set to 0.002 in these simulations. This limits the search for to S possible values.

DF

The derivative-following strategy is far less informationally intensive than either the myoptimal or the game-theoretic pricing strategies. In particular, this strategy can be used in the absence of any knowledge or assumptions about one's competitors or the buyer demand function. A derivative follower simply experiments with incremental increases (or decreases) in its price, continuing to move its price in the same direction until the observed profitability level falls, at which point the direction of movement is reversed. The price increment is chosen randomly from a uniform distribution; the maximum possible increment in the simulations described in this paper is 0.02.