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Structural Tractability of Shapley and Banzhaf Values in Allocation Games

AAAI Conferences

Allocation games are coalitional games defined in the literature as a way to analyze fair division problems of indivisible goods. The prototypical solution concepts for them are the Shapley value and the Banzhaf value. Unfortunately, their computation is intractable, formally #P-hard. Motivated by this bad news, structural requirements are investigated which can be used to identify islands of tractability. The main result is that, over the class of allocation games, the Shapley value and the Banzhaf value can be computed in polynomial time when interactions among agents can be formalized as graphs of bounded treewidth. This is shown by means of technical tools that are of interest in their own and that can be used for analyzing different kinds of coalitional games. Tractability is also shown for games where each good can be assigned to at most two agents, independently of their interactions.


Maximal Cooperation in Repeated Games on Social Networks

AAAI Conferences

Standard results on and algorithms for repeated games assume that defections are instantly observable. In reality, it may take some time for the knowledge that a defection has occurred to propagate through the social network. How does this affect the structure of equilibria and algorithms for computing them? In this paper, we consider games with cooperation and defection. We prove that there exists a unique maximal set of forever-cooperating agents in equilibrium and give an efficient algorithm for computing it. We then evaluate this algorithm on random graphs and find experimentally that there appears to be a phase transition between cooperation everywhere and defection everywhere, based on the value of cooperation and the discount factor. Finally, we provide a condition for when the equilibrium found is credible, in the sense that agents are in fact motivated to punish deviating agents. We find that this condition always holds in our experiments, provided the graphs are sufficiently large.


On the Aggregation of Argumentation Frameworks

AAAI Conferences

We study the problem of aggregation of Dung's abstract argumentation frameworks. Some operators for this aggregation have been proposed, as well as some rationality properties for this process. In this work we study the existing operators and new ones that we propose in light of the proposed properties, highlighting the fact that existing operators do not satisfy a lot of these properties. The conclusions are that on one hand none of the existing operators seem fully satisfactory, but on the other hand some of the properties proposed so far seem also too demanding.


On the Boundary of (Un)decidability: Decidable Model-Checking for a Fragment of Resource Agent Logic

AAAI Conferences

This choice, which is also related to the finitary and infinitary The model-checking problem for Resource Agent semantics of [Bulling and Farwer, 2010], stipulates whether Logic is known to be undecidable. We review existing in every model, agents always have a choice of doing nothing (un)decidability results and identify a significant (executing an idle action) that produces and consumes fragment of the logic for which model checking no resources [Alechina et al., 2014]. Apart from the technical is decidable. We discuss aspects which makes convenience for model-checking (intuitively it implies model checking decidable and prove undecidability that any strategy to satisfy a next or until formula only needs of two open fragments over a class of models in to ensure the relevant subformula becomes true after finitely which agents always have a choice of doing nothing.


A Dictatorship Theorem for Cake Cutting

AAAI Conferences

We consider discrete protocols for the classical Steinhaus cake cutting problem. Under mild technical conditions, we show that any deterministic strategy-proof protocol for two agents in the standard Robertson-Webb query model is dictatorial, that is, there is a fixed agent to which the protocol allocates the entire cake. For n > 2 agents, a similar impossibility holds, namely there always exists an agent that gets the empty piece (i.e. no cake). In contrast, we exhibit randomized protocols that are truthful in expectation and compute approximately fair allocations.


A Privacy Preserving Algorithm for Multi-Agent Planning and Search

AAAI Conferences

To engage diverse agents in cooperative behavior, it is important, even necessary, to provide algorithms that do not reveal information that is private or proprietary.A number of recent planning algorithms enable agents to plan together for shared goals without disclosing information about their private state and actions. But these algorithms lack clear and formal privacy guarantees: the fact that they do not require agents to explicitly reveal private information, does not imply that such information cannot be deduced. The main contribution of this paper is an enhanced version of the distributed forward-search planning framework of Nissim and Brafman that reveals less information than the original algorithm, and the first, to our knowledge, discussion and formal proof of privacy guarantees for distributed planning and search algorithms.


Ranked Voting on Social Networks

AAAI Conferences

They pinpoint families of voting rules that exhibit robustness: they are accurate in the limit with respect to a wide Classic social choice theory assumes that votes are range of noise models, which govern the way noisy votes are independent (but possibly conditioned on an underlying generated, given the ground truth [Caragiannis et al., 2013; objective ground truth). This assumption 2014]. is unrealistic in settings where the voters are connected While these results are promising, they rely on a crucial via an underlying social network structure, modeling assumption: votes are independent. This assumption as social interactions lead to correlated votes. We is clearly satisfied in some settings -- when votes are establish a general framework -- based on random submitted by computer Go programs [Jiang et al., 2014], say.


Truthful Cake Cutting Mechanisms with Externalities: Do Not Make Them Care for Others Too Much!

AAAI Conferences

We study truthful mechanisms in the context of cake cutting when agents not only value their own pieces of cake but also care for the pieces assigned to other agents. In particular, agents derive benefits or costs from the pieces of cake assigned to other agents. This phenomenon is often referred to as positive or negative externalities. We propose and study the following model: given an allocation, externalities of agents are modeled as percentages of the reported values that other agents have for their pieces. We show that even in this restricted class of externalities, under some natural assumptions, no truthful cake cutting mechanisms exist when externalities are either positive or negative. However, when the percentages agents get from each other are small, we show that there exists a truthful cake cutting mechanism with other desired properties.


A Scalable Interdependent Multi-Issue Negotiation Protocol for Energy Exchange

AAAI Conferences

To address We present a novel negotiation protocol to facilitate this challenge, Alam et al. [2013b] presented a protocol to energy exchange between off-grid homes that facilitate negotiation over energy exchange. Their protocol are equipped with renewable energy generation and restricts the type and number of offers such that negotiation electricity storage. Our protocol imposes restrictions leads to a subgame perfect Nash equilibrium (SPNE). However, over negotiation such that it reduces the complex their protocol only allows point-to-point communication interdependent multi-issue negotiation to one and relies on a fully connected network topology (i.e., where agents have a strategy profile in subgame each home is connected to all other homes in the community) perfect Nash equilibrium. We show that our protocol whereby the number of connections and messages exchanged; is concurrent, scalable and; under certain conditions; grow quadratically with the number of connected leads to Pareto-optimal outcomes.


Efficient, Private, and eps-Strategyproof Elicitation of Tournament Voting Rules

AAAI Conferences

Voting is commonly used as a method for aggregating information in crowdsourcing and human computation. In many settings, one would like to use voting rules which can be efficiently elicited, preserve voter privacy, and are robust to strategic manipulation. In this paper, we give algorithms which elicit approximate winners in a way which provably satisfies all three of these requirements simultaneously. Our results hold for tournament voting rules, which we define to be the voting rules which can be expressed solely as a function of the table of pairwise comparisons containing the number of voters preferring one candidate to another. Tournament voting rules include many common voting rules such as the Borda, Copeland, Maximin, Nanson, Baldwin, Kemeny-Young, Ranked Pairs, Cup, and Schulze voting rules. Our results significantly expand the set of voting rules for which efficient elicitation was known to be possible and improve the known approximation factors for epsilon-strategyproof voting in the regime where the number of candidates is large.