A note on the growth of the dimension in complete simple games

The remoteness from a simple game to a weighted game can be measured by the concept of the dimension or the more general Boolean dimension. It is known that both notions can be exponential in the number of voters. For complete simple games it was only recently shown that the dimension can also be exponential. Here we show that this is also the case for complete simple games with two types of voters and for the Boolean dimension of general complete simple games, which was posed as an open problem.Comment: 9 page

A Three-Dimensional Voting System in Hong Kong

The voting system in the Legislative Council of Hong Kong (Legco) is sometimes unicameral and sometimes bicameral, depending on whether the bill is proposed by the Hong Kong government. Therefore, although without any representative within Legco, the Hong Kong government has certain degree of legislative power --- as if there is a virtual representative of the Hong Kong government within the Legco. By introducing such a virtual representative of the Hong Kong government, we show that Legco is a three-dimensional voting system. We also calculate two power indices of the Hong Kong government through this virtual representative and consider the $C$-dimension and the $W$-dimension of Legco. Finally, some implications of this Legco model to the current constitutional reform in Hong Kong will be given

Familiars: representing Facebook users’ social behaviour through a reflective playful experience

In this paper, we describe the design and development of a social game called Familiars. Inspired by the daemons in Pullman’s “Dark Material” trilogy, Familiars are animal companions that sit on your Facebook profile and change into different animal forms based on your social activity within the social network of Facebook. . Familiars takes advantage of the powerful capabilities of the developers platform of Facebook to build a multi-dimensional picture of a player’s state based on social activity, facial expression analysis on photographs and suggestions from friends. This rich information is then distilled and presented to the player in the form of animal that the familiar chooses to take. We show how the types of animals and personalities were associated in a cross-cultural user study, and present quantitative results from the social behaviours of the players within the game in addition to qualitative data gathered from questionnaire responses

Fixed-Dimensional Energy Games are in Pseudo-Polynomial Time

We generalise the hyperplane separation technique (Chatterjee and Velner, 2013) from multi-dimensional mean-payoff to energy games, and achieve an algorithm for solving the latter whose running time is exponential only in the dimension, but not in the number of vertices of the game graph. This answers an open question whether energy games with arbitrary initial credit can be solved in pseudo-polynomial time for fixed dimensions 3 or larger (Chaloupka, 2013). It also improves the complexity of solving multi-dimensional energy games with given initial credit from non-elementary (Br\'azdil, Jan\v{c}ar, and Ku\v{c}era, 2010) to 2EXPTIME, thus establishing their 2EXPTIME-completeness.Comment: Corrected proof of Lemma 6.2 (thanks to Dmitry Chistikov for spotting an error in the previous proof

Cooperation through social influence

We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which a team (or coalition) of players succeeds if it is able to convince enough agents to participate in the task (to vote in favor of a decision). We take the linear threshold model as the influence model. We show first the expressiveness of influence games showing that they capture the class of simple games. Then we characterize the computational complexity of various problems on influence games, including measures (length and width), values (Shapley-Shubik and Banzhaf) and properties (of teams and players). Finally, we analyze those problems for some particular extremal cases, with respect to the propagation of influence, showing tighter complexity characterizations.Peer ReviewedPostprint (author’s final draft