Automated analysis of weighted voting games

Weighted voting games (WVGs) are an important mechanism for modeling scenarios where a group of agents must reach agreement on some issue over which they have different preferences. However, for such games to be effective, they must be well designed. Thus, a key concern for a mechanism designer is to structure games so that they have certain desirable properties. In this context, two such properties are PROPER and STRONG. A game is PROPER if for every coalition that is winning, its complement is not. A game is STRONG if for every coalition that is losing, its complement is not. In most cases, a mechanism designer wants games that are both PROPER and STRONG. To this end, we first show that the problem of determining whether a game is PROPER or STRONG is, in general, NP-hard. Then we determine those conditions (that can be evaluated in polynomial time) under which a given WVG is PROPER and those under which it is STRONG. Finally, for the general NP-hard case, we discuss two different approaches for overcoming the complexity: a deterministic approximation scheme and a randomized approximation method

Exogenous coalition formation in the e-marketplace based on geographical proximity

This paper considers a model for exogenous coalition formation in e-marketplaces. Using the informational advantage e-retailer creates coalitions of customers based on geographical proximity. Most of the literature regards this process as endogenous: a coalition leader bundles eventual purchases together in order to obtain a better bargaining position. In contrast - and in response to what is being observed in business practice - we analyse a situation in which an existing e-retailer exogenously forms customers' coalitions. Results of this study are highly encouraging. Namely, we demonstrate that even under highly imperfect warehouse management schemes leading to contagion eects, suggested combined delivery service may oer signifficant efficiency gains as well as opportunities for Pareto-improvement.Coalition formation, e-commerce, multi-agent systems, consumer satisfaction, demand planning, warehouse management.

The Computational Difficulty of Bribery in Qualitative Coalitional Games

Qualitative coalitional games (QCG) are representations of coalitional games in which self interested agents, each with their own individual goals, group together in order to achieve a set of goals which satisfy all the agents within that group. In such a representation, it is the strategy of the agents to find the best coalition to join. Previous work into QCGs has investigated the computational complexity of determining which is the best coalition to join. We plan to expand on this work by investigating the computational complexity of computing agent power in QCGs as well as by showing that insincere strategies, particularly bribery, are possible when the envy-freeness assumption is removed but that it is computationally difficult to identify the best agents to bribe.Bribery, Coalition Formation, Computational Complexity

Boolean Hedonic Games

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player's preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.Comment: This paper was orally presented at the Eleventh Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2014) in Bergen, Norway, July 27-30, 201

Online Automated Synthesis of Compact Normative Systems

Peer reviewedPostprin

Hard and soft equilibria in Boolean games

A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify games in order to eliminate such undesirable equilibria, for example through the use of subsidies and taxation, or by allowing players to undergo a preplay negotiation phase. In this paper, we consider the effect of such transformations in Boolean games with costs, where players are primarily motivated to seek the satisfaction of some goal, and are secondarily motivated to minimise the costs of their actions. The preference structure of these games allows us to distinguish between hard and soft equilibria, where hard equilibria arise from goal-seeking behaviour, and cannot be eliminated from games by, e.g., taxes or subsidies, while soft equilibria are those that arise from the desire of agents to minimise costs. We investigate several mechanisms which allow groups of players to form coalitions and eliminate undesirable equilibria from the game, even when taxes or subsidies are not a possibility

The Computational Difficulty of Bribery in Qualitative Coalitional Games

Qualitative coalitional games (QCG) are representations of coalitional games in which self interested agents, each with their own individual goals, group together in order to achieve a set of goals which satisfy all the agents within that group. In such a representation, it is the strategy of the agents to find the best coalition to join. Previous work into QCGs has investigated the computational complexity of determining which is the best coalition to join. We plan to expand on this work by investigating the computational complexity of computing agent power in QCGs as well as by showing that insincere strategies, particularly bribery, are possible when the envy-freeness assumption is removed but that it is computationally difficult to identify the best agents to bribe