Reshef Meir

The Cost of Stability in Coalitional Games

A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the core --the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external payments. We consider a scenario where an external party, which 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 their coalition(s). The sum of this payment plus the actual gains of the coalition(s) may then be divided among the agents so as to promote stability. We define the cost of stability (CoS) as the minimal external payment that stabilizes the game. We provide general bounds on the cost of stability in several classes of games, and explore its algorithmic properties. To develop a better intuition for the concepts we introduce, we provide a detailed algorithmic study of the cost of stability in weighted voting games, a simple but expressive class of games which can model decision-making in political bodies, and cooperation in multiagent settings. Finally, we extend our model and results to games with coalition structures.

Complexity of strategic behavior in multi-winner elections

Although recent years have seen a surge of interest in the computational aspects of social choice, no specific attention has previously been devoted to elections with multiple winners, e.g., elections of an assembly or committee. In this paper, we characterize the worst-case complexity of manipulation and control in the context of four prominent multiwinner voting systems, under different formulations of the strategic agents goal.

A local-dominance theory of voting equilibria

We suggest a new model for strategic voting based on local dominance, where voters consider a set of possible outcomes without assigning probabilities to them. We prove that voting equilibria under the Plurality rule exist for a broad class of local dominance relations. Furthermore, we show that local dominance-based dynamics quickly converge to an equilibrium if voters start from the truthful state, and we provide weaker convergence guarantees in more general settings. Using extensive simulations of strategic voting on generated and real profiles, we show that emerging equilibria replicate widely known patterns of human voting behavior such as Duvergers law, and that they generally improve the quality of the winner compared to non-strategic voting.

Subsidies, stability, and restricted cooperation in coalitional games

Cooperation among automated agents is becoming increasingly important in various artificial intelligence applications. Coalitional (i.e., cooperative) game theory supplies conceptual and mathematical tools useful in the analysis of such interactions, and in particular in the achievement of stable outcomes among self-interested agents. Here, we study the minimal external subsidy required to stabilize the core of a coalitional game. Following the Cost of Stability (CoS) model introduced by Bachrach et al. [2009a], we give tight bounds on the required subsidy under various restrictions on the social structure of the game. We then compare the extended core induced by subsidies with the least core of the game, proving tight bounds on the ratio between the minimal subsidy and the minimal demand relaxation that each lead to stability.

The Cost of Stability in Network Flow Games

The core of a cooperative game contains all stable distributions of a coalitions gains among its members. However, some games have an empty core, with every distribution being unstable. We allow an external party to offer a supplemental payment to the grand coalition, which may stabilize the game, if the payment is sufficiently high. We consider the cost of stability (CoS)--the minimal payment that stabilizes the game. We examine the CoS in threshold network flow games (TNFGs), where each agent controls an edge in a flow network, and a coalition wins if the maximal flow it can achieve exceeds a certain threshold. We show that in such games, it is coNP-complete to determine whether a given distribution (which includes an external payment) is stable. Nevertheless, we show how to bound and approximate the CoS in general TNFGs, and provide efficient algorithms for computing the CoS in several restricted cases.

Mechanism design on discrete lines and cycles

We study strategyproof (SP) mechanisms for the location of a facility on a discrete graph. We give a full characterization of SP mechanisms on lines and on sufficiently large cycles. Interestingly, the characterization deviates from the one given by Schummer and Vohra (2004) for the continuous case. In particular, it is shown that an SP mechanism on a cycle is close to dictatorial, but all agents can affect the outcome, in contrast to the continuous case. Our characterization is also used to derive a lower bound on the approximation ratio with respect to the social cost that can be achieved by an SP mechanism on certain graphs. Finally, we show how the representation of such graphs as subsets of the binary cube reveals common properties of SP mechanisms and enables one to extend the lower bound to related domains.

Minimal subsidies in expense sharing games

A key solution concept in cooperative game theory is the core. The core of an expense sharing game contains stable allocations of the total cost to the participating players, such that each subset of players pays at most what it would pay if acting on its own. Unfortunately, some expense sharing games have an empty core, meaning that the total cost is too high to be divided in a stable manner. In such cases, an external entity could choose to induce stability using an external subsidy. We call the minimal subsidy required to make the core of a game non-empty the Cost of Stability (CoS), adopting a recently coined term for surplus sharing games. We provide bounds on the CoS for general, subadditive and anonymous games, discuss the special case of Facility Games, as well as consider the complexity of computing the CoS of the grand coalition and of coalitional structures.

Strategic Voting Behavior in Doodle Polls

Finding a common time slot for a group event is a daily conundrum and illustrates key features of group decision-making. It is a complex interplay of individual incentives and group dynamics. A participant would like the final time to be convenient for her, but she is also expected to be cooperative towards other peoples preferences. We combine large-scale data analysis with theoretical models from the voting literature to investigate strategic behaviors in event scheduling. We analyze all Doodle polls created in the US from July-September 2011 (over 340,000 polls), consisting of both hidden polls (a user cannot see other responses) and open polls (a user can see all previous responses). By analyzing the differences in behavior in hidden and open polls, we gain unique insights into strategies that people apply in a natural decision-making setting. Responders in open polls are more likely to approve slots that are very popular or very unpopular, but not intermediate slots. We show that this behavior is inconsistent with models that have been proposed in the voting literature, and propose a new model based on combining personal and social utilities to explain the data.

Algorithms for strategyproof classification

The strategyproof classification problem deals with a setting where a decision maker must classify a set of input points with binary labels, while minimizing the expected error. The labels of the input points are reported by self-interested agents, who might lie in order to obtain a classifier that more closely matches their own labels, thereby creating a bias in the data; this motivates the design of truthful mechanisms that discourage false reports. In this paper we give strategyproof mechanisms for the classification problem in two restricted settings: (i) there are only two classifiers, and (ii) all agents are interested in a shared set of input points. We show that these plausible assumptions lead to strong positive results. In particular, we demonstrate that variations of a random dictator mechanism, that are truthful, can guarantee approximately optimal outcomes with respect to any family of classifiers. Moreover, these results are tight in the sense that they match the best possible approximation ratio that can be guaranteed by any truthful mechanism. We further show how our mechanisms can be used for learning classifiers from sampled data, and provide PAC-style generalization bounds on their expected error. Interestingly, our results can be applied to problems in the context of various fields beyond classification, including facility location and judgment aggregation.

Playing the Wrong Game: Smoothness Bounds for Congestion Games with Behavioral Biases

In many situations a player may act so as to maximize a perceived utility that is not exactly her utility function, but rather some other, biased, utility. Examples of such biased utility functions are common in behavioral economics, and include risk attitudes, altruism, present-bias and so on. When analyzing a game, one may ask how inefficiency, measured by the Price of Anarchy (PoA) is a?ected by the perceived utilities. The smoothness method [16, 15] naturally extends to games with such perceived utilities or costs, regardless of the game or the behavioral bias. We show that such biasedsmoothness is broadly applicable in the context of nonatomic congestion games. First, we show that on series-parallel networks we can use smoothness to yield PoA bounds even for diverse populations with di?erent biases. Second, we identify various classes of cost functions and biases that are smooth, thereby substantially improving some recent results from the literature.