The field of decision theory is vast and there are many examples of real-world problems to choose from. We present an example from viral marketing, a small snippet from the epinions.com database. Viral marketing is based on the premise that members of a social network influence each other’s purchasing decisions. The goal is then to select the best set of people to market to, such that the overall profit is maximized by propagation of influence through the network. We modeled this problem using the state predicates Buys(x) and Trusts(x1, x2), and the action predicate MarketTo(x). The utility function is represented by the unit clauses Buys(x) (with positive utility, representing profits from sales) and MarketTo(x) (with negative utility, representing the cost of marketing). The topology of the social network is specified by an evidence database of Trusts(x1, x2) atoms. The core of the model consists of two formulas:
0.6 Buys(x1) ^ Trusts(x2, x1) => Buys(x2) 0.8 MarketTo(x) => Buys(x)
The weight of Formula 1 represents how strongly x1 influences x2, and the weight of Formula 2 represents how strongly users are influenced by marketing. In addition, the model includes the unit clause:
-2:20 Buys(x)
with a utility of 20 (see above). The negative weight represents the fact that most users do not buy most products. In addition, we include the action predicate:
:-1 MarketTo(x)
We perform maximum expected utility (MEU) inference with the following command:
infer -i marketing.mln -e trust.db -r marketing.result -q MarketTo -ow Buys -decision
The output contains the maximum utility achieved and the optimal assignment of action atoms.