Technical Note—Risk Sensitivity and Firm Power: Price Competition with Mean²-Variance Profit Objective Under Multinomial Logit Demand

This paper is the first in the literature to address a risk-sensitive price competition under the multinomial logit choice model, with each participating firm maximizing a risk-adjusted profit objective. We find that, at equilibrium, a subset of firms earns a positive profit, whereas others are driven to zero profit, contrasting with the risk-neutral equilibrium in which all firms earn a positive profit regardless of quality and cost. We identify a power index—the ratio of effective product attractiveness to risk sensitivity—and show that the set of profitable firms is power index ordered. Risk aversion drives firms toward a more aggressive equilibrium pricing strategy and intensifies competition. However, the relative profit impact across firms is not monotone; although high risk aversion handicaps a firm, moderate risk aversion may place a firm at an advantage over an otherwise equivalent competitor that is less risk sensitive, contrary to intuition. In an equilibrium with market entry cost, we show that the set of active firms at equilibrium follows a generalized power index order that depends on entry cost. Furthermore, although the power index is decreasing in risk aversion, the generalized power index may initially be increasing in risk aversion.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2466.