A new concept of equilibrium in secure strategies (EinSS) in non-cooperative games is presented. The EinSS coincides with the Nash Equilibrium when Nash Equilibrium exists and postulates the incentive of players to maximize their profit under the condition of security against actions of other players. The new concept is illustrated by a number of matrix game examples and compared with

other closely related theoretical models. We prove the existence of equilibrium in secure strategies in two classic games that fail to have Nash equilibria. On an infinite line we obtain the solution in secure strategies of the classic Hotelling’s price game (1929) with a restricted reservation price and linear transportation costs. New type of monopolistic equilibria in secure strategies are discovered in the Tullock Contest (1967, 1980) of two players.

We present a comprehensive model of household economic decision covering both fully cooperative and non-cooperative cases as well as semi-cooperative cases, varying with income distribution and a parameter vector θ representing degrees of individual autonomy with respect to the public goods. In this model, the concept of “household θ-equilibrium” is introduced through the reformulation of the Lindahl equilibrium for Nashimplementation and its extension to semi-cooperation. Existence is proved and some generic properties derived.

An example is given to illustrate. Finally, a particular decomposition of the pseudo-Slutsky matrix is derived and the testability of the various models discussed.

In the framework of a ﬁrst-price private-value auction, we study the seller as a player in a game with the buyers in which he has private information about their realized valuations. We ask whether the seller can beneﬁt by using his private information strategically. We ﬁnd that in fact, depending upon his information, available signals, and his commitment power, he may indeed increase his revenue by strategic transmission of his information.