Algorithmic and complexity aspects of simple coalitional games

Simple coalitional games are a fundamental class of cooperative games and voting games which are used to model coalition formation, resource allocation and decision making in computer science, artificial intelligence and multiagent systems. Although simple coalitional games are well studied in the domain of game theory and social choice, their algorithmic and computational complexity aspects have received less attention till recently. The computational aspects of simple coalitional games are of increased importance as these games are used by computer scientists to model distributed settings. This thesis fits in the wider setting of the interplay between economics and computer science which has led to the development of algorithmic game theory and computational social choice. A unified view of the computational aspects of simple coalitional games is presented here for the first time. Certain complexity results also apply to other coalitional games such as skill games and matching games. The following issues are given special consideration: influence of players, limit and complexity of manipulations in the coalitional games and complexity of resource allocation on networks. The complexity of comparison of influence between players in simple games is characterized. The simple games considered are represented by winning coalitions, minimal winning coalitions, weighted voting games or multiple weighted voting games. A comprehensive classification of weighted voting games which can be solved in polynomial time is presented. An efficient algorithm which uses generating functions and interpolation to compute an integer weight vector for target power indices is proposed. Voting theory, especially the Penrose Square Root Law, is used to investigate the fairness of a real life voting model. Computational complexity of manipulation in social choice protocols can determine whether manipulation is computationally feasible or not. The computational complexity and bounds of manipulation are considered from various angles including control, false-name manipulation and bribery. Moreover, the computational complexity of computing various cooperative game solutions of simple games in dierent representations is studied. Certain structural results regarding least core payos extend to the general monotone cooperative game. The thesis also studies a coalitional game called the spanning connectivity game. It is proved that whereas computing the Banzhaf values and Shapley-Shubik indices of such games is #P-complete, there is a polynomial time combinatorial algorithm to compute the nucleolus. The results have interesting significance for optimal strategies for the wiretapping game which is a noncooperative game defined on a network

Algorithmic and complexity aspects of simple coalitional games

Simple coalitional games are a fundamental class of cooperative games and voting games which are used to model coalition formation, resource allocation and decision making in computer science, artificial intelligence and multiagent systems. Although simple coalitional games are well studied in the domain of game theory and social choice, their algorithmic and computational complexity aspects have received less attention till recently. The computational aspects of simple coalitional games are of increased importance as these games are used by computer scientists to model distributed settings. This thesis fits in the wider setting of the interplay between economics and computer science which has led to the development of algorithmic game theory and computational social choice. A unified view of the computational aspects of simple coalitional games is presented here for the first time. Certain complexity results also apply to other coalitional games such as skill games and matching games. The following issues are given special consideration: influence of players, limit and complexity of manipulations in the coalitional games and complexity of resource allocation on networks. The complexity of comparison of influence between players in simple games is characterized. The simple games considered are represented by winning coalitions, minimal winning coalitions, weighted voting games or multiple weighted voting games. A comprehensive classification of weighted voting games which can be solved in polynomial time is presented. An efficient algorithm which uses generating functions and interpolation to compute an integer weight vector for target power indices is proposed. Voting theory, especially the Penrose Square Root Law, is used to investigate the fairness of a real life voting model. Computational complexity of manipulation in social choice protocols can determine whether manipulation is computationally feasible or not. The computational complexity and bounds of manipulation are considered from various angles including control, false-name manipulation and bribery. Moreover, the computational complexity of computing various cooperative game solutions of simple games in dierent representations is studied. Certain structural results regarding least core payos extend to the general monotone cooperative game. The thesis also studies a coalitional game called the spanning connectivity game. It is proved that whereas computing the Banzhaf values and Shapley-Shubik indices of such games is #P-complete, there is a polynomial time combinatorial algorithm to compute the nucleolus. The results have interesting significance for optimal strategies for the wiretapping game which is a noncooperative game defined on a network.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Visual complexity, player experience, performance and physical exertion in motion-based games for older adults

Motion-based video games can have a variety of benefits for the players and are increasingly applied in physical therapy, rehabilitation and prevention for older adults. However, little is known about how this audience experiences playing such games, how the player experience affects the way older adults interact with motion-based games, and how this can relate to therapy goals. In our work, we decompose the player experience of older adults engaging with motion-based games, focusing on the effects of manipulations of the game representation through the visual channel (visual complexity), since it is the primary interaction modality of most games and since vision impairments are common amongst older adults. We examine the effects of different levels of visual complexity on player experience, performance, and exertion in a study with fifteen participants. Our results show that visual complexity affects the way games are perceived in two ways: First, while older adults do have preferences in terms of visual complexity of video games, notable effects were only measurable following drastic variations. Second, perceived exertion shifts depending on the degree of visual complexity. These findings can help inform the design of motion-based games for therapy and rehabilitation for older adults

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

An Experiential Comparative Tool for Board Games

In the field of game studies, contemporary board games have until now remained relatively unexplored. The recent years have allowed us to witness the emergence of the occasional academic texts focusing on board games – such as Eurogames (Woods, 2012), Characteristics of Games (Elias et al. 2013), and most recently Game Play: Paratextuality in Contemporary Board Games (Booth, 2015). The mentioned authors all explore board games from diverse viewpoints but none of these authors present a viable and practical analytical tool to allow us to examine and differentiate one board game from another. In this vein, this paper seeks to present an analytical comparative tool intended specifically for board games. The tool builds upon previous works (Aarseth et al. 2003; Elias et al. 2012; and Woods 2012) to show how four categories – rules, luck, interaction and theme – can interact on different levels to generate diverse gameplay experiences. Such a tool allows to score games objectively and separately in each of the categories to create a combined gameplay experience profile for each board game. Following this, the paper proceeds to present numerous practical examples of contemporary board games and how it can be used from a design perspective and an analytical perspective alike

False-Name Manipulation in Weighted Voting Games is Hard for Probabilistic Polynomial Time

False-name manipulation refers to the question of whether a player in a weighted voting game can increase her power by splitting into several players and distributing her weight among these false identities. Analogously to this splitting problem, the beneficial merging problem asks whether a coalition of players can increase their power in a weighted voting game by merging their weights. Aziz et al. [ABEP11] analyze the problem of whether merging or splitting players in weighted voting games is beneficial in terms of the Shapley-Shubik and the normalized Banzhaf index, and so do Rey and Rothe [RR10] for the probabilistic Banzhaf index. All these results provide merely NP-hardness lower bounds for these problems, leaving the question about their exact complexity open. For the Shapley--Shubik and the probabilistic Banzhaf index, we raise these lower bounds to hardness for PP, "probabilistic polynomial time", and provide matching upper bounds for beneficial merging and, whenever the number of false identities is fixed, also for beneficial splitting, thus resolving previous conjectures in the affirmative. It follows from our results that beneficial merging and splitting for these two power indices cannot be solved in NP, unless the polynomial hierarchy collapses, which is considered highly unlikely

A Behavioral Approach to Learning in Economics - Towards an Economic Theory of Contingent Learning

In economics, adjustment of behavior has traditionally been treated as a "black box." Recent approaches that focus on learning behavior try to model, test, and simulate specific adjustment mechanisms in specific environments (mostly in games). Results often critically depend on distinctive assumptions, and are not easy to generalize. This paper proposes a different approach that aims to allow for more general conclusions in a methodologically more compatible way. It is argued that the introduction of the main determinants of learning behavior as situational restrictions into the standard economic model may be a fruitful way to capture some important aspects of human behavior that have often been omitted in economic theory. Based on a simple model of learning behavior (learning loop), robust findings from psychology are used to explain behavior adjustment, and to identify its determinants (contingent learning). An integrative methodology is proposed where the "black box" is not opened, but instead the factors that determine what happens inside, and the limits imposed by theses factors can be analyzed and used for model building. The paper concludes with testable hypotheses about learning behavior in the context of economics.microeconomics, game theory, learning theory, experiments