Risk Seeking

Risk seeking describes an individual's attitude toward risk. A person is considered risk-seeking when they prefer to engage in a lottery rather than accept its expected value with certainty. In such cases, the individual assigns greater utility to the lottery's expected outcome than to the utility of its expected monetary value. In other words, given a lottery (a random variable) with two possible outcomes, X₁ and X₂, occurring with probabilities p₁ and p₂ respectively, the condition for risk-seeking behavior is expressed by the following inequality:

On the left-hand side of the inequality is the utility of the expected value of the lottery. On the right-hand side is the expected utility derived from participating in the lottery. A risk-seeking individual finds the gamble more attractive than the guaranteed outcome, even when both options have the same expected monetary value. Graphically, this preference is represented by a convex utility function, as shown below:

The diagram displays the utility function of the expected value (red curve) and the expected utility function (blue line). A risk-seeking individual experiences higher satisfaction (utility) from winning a sum through a gamble than from receiving the same amount with certainty. For instance, for a given monetary outcome R_x, the utility U_x associated with winning via lottery (i.e., under uncertainty) is greater than the utility U_c associated with receiving the same amount risk-free. As clearly shown in the graph, U_x (with risk) exceeds U_c (without risk), despite both being tied to the same monetary value R_x.

Corollary. An individual exhibits risk-seeking behavior when the expected value of a lottery is lower than its certainty equivalent. If the two values coincide, the individual is said to be risk neutral.