This paper deals with the equilibria of games when the agents have multiple objectives and, therefore, their utilities cannot be represented by a single value, but by a vector containing the various dimensions of the utility. Our approach allows the incorporation of partial information about the preferences of the agents into the model, and permits the identification of the set of equilibria in accordance with this information. We also propose an additional conservative criterion which can be applied in this framework in order to predict the results of interaction.The potential application of the theoretical results is shown with an analysis of a mixed oligopoly in which the agents value additional objectives other than their own benefit. These objectives are related to social welfare and to the profit of the industry. The flexibility of our approach provides a general theoretical framework for the analysis of a wide range of strategic economic models.

We present a unified approach to study the problem of the commons for agents with other‐regarding preferences. This situation is modeled as a game with vector‐valued utilities. Several types of agents are characterized depending on the importance assigned to the components of their utility functions. We obtain the set of equilibria of the game with two types of agents, pro‐social and pro‐self, and some refinements of this set for conservative agents. The most relevant result is that only a pro‐social agent is required to avoid the tragedy of the commons, regardless of the behavior of the rest of the agents.

Abstract. Power-adjustable spectacle lenses, based on the Alvarez-Lohmann principle, can be used to provide affordable spectacles for subjective refractive errors measurement and its correction. A new mechanical frame has been designed to maximize the advantages of this technology. The design includes a mechanism to match the interpupillary distance with that of the optical centers of the lenses. The frame can be manufactured using low cost plastic injection molding techniques. A prototype has been built to test the functioning of this mechanical design. C 2011 Society of Photo-Optical Instrumentation Engineers (SPIE).

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