Utility maximization problem in the context of "Sonnenschein–Mantel–Debreu theorem"

In economics, a consumer's indirect utility function${\displaystyle v(p,w)}$ gives the consumer's maximal attainable utility when faced with a vector ${\displaystyle p}$ of goods prices and an amount of income ${\displaystyle w}$. It reflects both the consumer's preferences and market conditions.

This function is called indirect because consumers usually think about their preferences in terms of what they consume rather than prices. A consumer's indirect utility ${\displaystyle v(p,w)}$ can be computed from their utility function ${\displaystyle u(x),}$ defined over vectors ${\displaystyle x}$ of quantities of consumable goods, by first computing the most preferred affordable bundle, represented by the vector ${\displaystyle x(p,w)}$ by solving the utility maximization problem, and second, computing the utility ${\displaystyle u(x(p,w))}$ the consumer derives from that bundle. The resulting indirect utility function is

The term Homo economicus, or economic man, is the portrayal of humans as agents who are consistently rational and narrowly self-interested, and who pursue their subjectively defined ends optimally. It is a wordplay on Homo sapiens, used in some economic theories and in pedagogy.

In game theory, Homo economicus is often (but not necessarily) modelled through the assumption of perfect rationality. It assumes that agents always act in a way that maximize utility as a consumer and profit as a producer, and are capable of arbitrarily complex deductions towards that end. They will always be capable of thinking through all possible outcomes and choosing that course of action which will result in the best possible result.