Equilibria in secure strategies in the Bertrand-Edgeworth duopoly

This paper analyzes the Bertrand-Edgeworth duopoly model using a solution concept of Equilibrium in Secure Strategies (EinSS), which describes cautious behavior in noncooperative games. The concept is suitable for studying games where the threats of other players represent an important factor in the decision-making process. We demonstrate that, in some cases where the Bertrand-Edgeworth price duopoly admits no Nash-Cournot equilibria, there exists a unique EinSS with both players choosing an identical equilibrium price lower than the monopoly price. The difference between these prices can be interpreted as an additional reduction in price that allows the players to secure themselves against the mutual threats of undercutting. We formulate and prove a criterion for the EinSS existence.