Abstract
In two-action generalized polymatrix games, Nash equilibria are support-type-symmetric, i.e., determined by supports for each type of player. We show that such a property does not generalize straightforwardly for games with at least three actions or where interaction weights have different signs (neither all positive nor negative). A non-trivial condition on interaction weights must be satisfied, which may go unnoticed as it is trivially satisfied for: (i) two-action games, (ii) conformity games, and (iii) congestion games. We derive this condition and the corresponding simplified analytic equation for mixed strategies.

Abstract
We study an evolutionary dynamics for the contributions by agents to a common/public good in a generalized version of Baliga and Maskin's environmental protection model. The dynamical equilibria consist of three scenarios: a single agent contributing to preserve the good with its optimal contribution level, and all the other agents being free-riders: a group of agents with the same optimal contribution level contributing to preserve the good, and all the other agents being free-riders; one where no agents contribute. The dynamics of the contributions can be complex but we prove that each trajectory converges to the equilibrium associated to the single agent (or group of agents) with the highest preference for the good that are contributing since the beginning. We note that while the aggregate contribution is below the optimal contribution level of the agent with the smallest preference for the good, then the aggregate contribution is increasing and there is no free-riding. Hence, if the optimal contribution level of the agent with the smallest preference is enough to not exhaust the good too quickly and the optimal contribution level of the agent with the greatest preference is enough to preserve the good, then, in spite of the appearance of free-riding in the contributions, the good might not be exhausted.

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Abstract
Reasoning about spatial information is fundamental in natural language to fully understand relationships between entities and/or between events. However, the complexity underlying such reasoning makes it hard to represent formally spatial information. Despite the growing interest on this topic, and the development of some frameworks, many problems persist regarding, for instance, the coverage of a wide variety of linguistic constructions and of languages. In this paper, we present a proposal of integrating ISO-Space into a ISO-based multilayer annotation scheme, designed to annotate news in European Portuguese. This scheme already enables annotation at three levels, temporal, referential and thematic, by combining postulates from ISO 24617-1, 4 and 9. Since the corpus comprises news articles, and spatial information is relevant within this kind of texts, a more detailed account of space was required. The main objective of this paper is to discuss the process of integrating ISO-Space with the existing layers of our annotation scheme, assessing the compatibility of the aforementioned parts of ISO 24617, and the problems posed by the harmonization of the four layers and by some specifications of ISO-Space. © European Language Resources Association (ELRA).