Equilibrium in secure strategies in the Bertrand–Edgeworth duopoly

We analyze the Bertrand–Edgeworth duopoly model using a solution concept of Equilibrium in Secure Strategies (EinSS), which provides a model of cautious behavior in non-cooperative games. It is suitable for studying games, in which threats of other players are an important factor in the decision-making. We show that in some cases when Nash–Cournot equilibrium does not exist in the price duopoly of Bertrand–Edgeworth there is a unique EinSS, in which both players choose the same equilibrium price lower than the monopoly price. The difference between these prices can be interpreted as an additional reduction in price, which allows players to secure themselves against mutual threats of undercutting. We formulate and prove a criterion for the EinSS existence.