Efficient Equilibria in Polymatrix Coordination Games

We consider polymatrix coordination games with individual preferences where every player corresponds to a node in a graph who plays with each neighbor a separate bimatrix game with non-negative symmetric payoffs. In this paper, we study $\alpha$-approximate $k$-equilibria of these games, i.e., outcomes where no group of at most $k$ players can deviate such that each member increases his payoff by at least a factor $\alpha$. We prove that for $\alpha \ge 2$ these games have the finite coalitional improvement property (and thus $\alpha$-approximate $k$-equilibria exist), while for $\alpha < 2$ this property does not hold. Further, we derive an almost tight bound of $2\alpha(n-1)/(k-1)$ on the price of anarchy, where $n$ is the number of players; in particular, it scales from unbounded for pure Nash equilibria ($k = 1)$ to $2\alpha$ for strong equilibria ($k = n$). We also settle the complexity of several problems related to the verification and existence of these equilibria. Finally, we investigate natural means to reduce the inefficiency of Nash equilibria. Most promisingly, we show that by fixing the strategies of $k$ players the price of anarchy can be reduced to $n/k$ (and this bound is tight)

The Least-core and Nucleolus of Path Cooperative Games

Cooperative games provide an appropriate framework for fair and stable profit distribution in multiagent systems. In this paper, we study the algorithmic issues on path cooperative games that arise from the situations where some commodity flows through a network. In these games, a coalition of edges or vertices is successful if it enables a path from the source to the sink in the network, and lose otherwise. Based on dual theory of linear programming and the relationship with flow games, we provide the characterizations on the CS-core, least-core and nucleolus of path cooperative games. Furthermore, we show that the least-core and nucleolus are polynomially solvable for path cooperative games defined on both directed and undirected network

Impact of gameplay vs. reading on mental models of social-ecological systems: a fuzzy cognitive mapping approach

Climate change is a highly complex social-ecological problem characterized by system-type dynamics that are important to communicate in a variety of settings, ranging from formal education to decision makers to informal education of the general public. Educational games are one approach that may enhance systems thinking skills. This study used a randomized controlled experiment to compare the impact on the mental models of participants of an educational card game vs. an illustrated article about the Arctic social-ecological system. A total of 41 participants (game: n = 20; reading: n = 21) created pre- and post-intervention mental models of the system, based on a "fuzzy cognitive mapping" approach. Maps were analyzed using network statistics. Both reading the article and playing the game resulted in measurable increases in systems understanding. The group reading the article perceived a more complex system after the intervention, with overall learning gains approximately twice those of the game players. However, game players demonstrated similar learning gains as article readers regarding the climate system, actions both causing environmental problems and protecting the Arctic, as well as the importance of the base- and mid-levels of the food chain. These findings contribute to the growing evidence showing that games are important resources to include as strategies for building capacity to understand and steward sustainable social-ecological systems, in both formal and informal education

“Stickier” learning through gameplay: an effective approach to climate change education

As the impacts of climate change grow, we need better ways to raise awareness and motivate action. Here we assess the effectiveness of an Arctic climate change card game in comparison with the more conventional approach of reading an illustrated article. In-person assessments with control/reading and treatment/game groups (N = 41), were followed four weeks later with a survey. The game was found to be as effective as the article in teaching content of the impacts of climate change over the short term, and was more effective than the article in long-term retention of new information. Game players also had higher levels of engagement and perceptions that they knew ways to help protect Arctic ecosystems. They were also more likely to recommend the game to friends or family than those in the control group were likely to recommend the article to friends or family. As we consider ways to broaden engagement with climate change, we should include games in our portfolio of approaches

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

Bounds on the Cost of Stabilizing a Cooperative Game

This is the author accepted manuscript. The final version is available from the AI Access Foundation via the DOI in this record.A key issue in cooperative game theory is coalitional stability, usually captured by the notion of the core—the set of outcomes that are resistant to group deviations. However, some coalitional games have empty cores, and any outcome in such a game is unstable. We investigate the possibility of stabilizing a coalitional game by using subsidies. We consider scenarios where an external party that is interested in having the players work together offers a supplemental payment to the grand coalition, or, more generally, a particular coalition structure. This payment is conditional on players not deviating from this coalition structure, and may be divided among the players in any way they wish. We define the cost of stability as the minimum external payment that stabilizes the game. We provide tight bounds on the cost of stability, both for games where the coalitional values are nonnegative (profit-sharing games) and for games where the coalitional values are nonpositive (cost-sharing games), under natural assumptions on the characteristic function, such as superadditivity, anonymity, or both. We also investigate the relationship between the cost of stability and several variants of the least core. Finally, we study the computational complexity of problems related to the cost of stability, with a focus on weighted voting games.DFGEuropean Science FoundationNRF (Singapore)European Research CouncilHorizon 2020 European Research Infrastructure projectIsrael Science FoundationIsrael Ministry of Science and TechnologyGoogle Inter-University Center for Electronic Markets and AuctionsEuropean Social Fund (European Commission)Calabria Regio

Further sub-cycle and multi-cycle schedulling support for Bluespec Verilog

Bluespec is a hardware description language where all behaviour is expressed in rules that execute atomically. The standard compilation semantics for Bluespec enforce a particular mapping between rule firing and hardware clock cycles, such as a register only being updated by exactly one firing of at most one rule in any clock cycle. Also, the standard compiler does not introduce any additional state, such as credit-based or round-robin arbiters to guarantee fairness between rules over time. On the other hand, many useful hardware resources, such as complex ALUs and synchronous RAMs, are pipelined. Unlike typical high-level synthesis tools, in standard Bluespec such resources cannot be invoked using infix operators in expressions such as A[e] or e1*e2 since binding to specific instances and multi-clock cycle schedules are required. In this paper we extend the reference semantics of Bluespec to decouple it from clock cycles, allowing multiple updates to a register within one clock cycle and automatic instantiation of arbiters for multi-clock cycle behaviour. We describe the new semantic packing rules as extensions of our standard compilation rules and we report early results from an open-source, fully-functional implementation