Maria Polukarov

Cooperative games with overlapping coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions-or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure.

Coalition structure generation over graphs

We give the analysis of the computational complexity of coalition structure generation over graphs. Given an undirected graph

Cooperative Equilibria in Iterated Social Dilemmas

The implausibility of the extreme rationality assumptions of Nash equilibrium has been attested by numerous experimental studies with human players. In particular, the fundamental social dilemmas such as the Traveler’s dilemma, the Prisoner’s dilemma, and the Public Goods game demonstrate high rates of deviation from the unique Nash equilibrium, dependent on the game parameters or the environment in which the game is played. These results inspired several attempts to develop suitable solution concepts to more accurately explain human behaviour. In this line, the recently proposed notion of cooperative equilibrium [5, 6], based on the idea that players have a natural attitude to cooperation, has shown promising results for single-shot games. In this paper, we extend this approach to iterated settings. Specifically, we define the Iterated Cooperative Equilibrium (ICE) and show it makes statistically precise predictions of population average behaviour in the aforementioned domains. Importantly, the definition of ICE does not involve any free parameters, and so it is fully predictive.

New Results on Equilibria in Strategic Candidacy

We consider a voting setting where candidates have preferences about the outcome of the election and are free to join or leave the election. The corresponding candidacy game, where candidates choose strategically to participate or not, has been studied in very few papers, mainly by Dutta et al. [5,6], who showed that no non-dictatorial voting procedure satisfying unanimity is candidacy-strategyproof, or equivalently, is such that the joint action where all candidates enter the election is always a pure strategy Nash equilibrium. They also showed that for voting trees, there are candidacy games with no pure strategy equilibria. However, no results were known about other voting rules. Here we prove several such results. Some are positive (a pure strategy Nash equilibrium is guaranteed for Copeland and the uncovered set, whichever is the number of candidates, and for all Condorcet-consistent rules, for 4 candidates). Some are negative, namely for plurality and maximin.

Random Order Congestion Games

We introduce a new class of games called random order congestion games (ROCGs). In an ROCG, each player has a task that can be carried out by any element of a set of resources, and each resource executes its assigned tasks in a random order. The aim of each player is to minimize his expected cost, which is the sum of the fixed costs over the set of his utilized resources and the expected cost of his task execution. The cost of a players task execution is determined by the earliest time his task is completed, and thus it might be beneficial for him to assign his task to several resources. We prove the existence of pure strategy Nash equilibria in ROCGs. Moreover, we present a polynomial time algorithm for finding such an equilibrium in a given ROCG.

Taxed congestion games with failures

In this paper, we introduce and study Taxed Congestion Games with Failures [TCGFs], extending congestion games with failures [CGFs] to consider costly task submission. We define TCGFs, and prove that TCGFs possess a pure strategy Nash-equilibrium. Moreover, we provide an efficient algorithm for the computation of such equilibrium. We also provide a specialized, simpler, algorithm for the case in which all resources are identical.

Redistribution of VCG payments in public project problems

Redistribution of VCG payments has been mostly studied in the context of resource allocation. This paper focuses on another fundamental model--the public project problem. In this scenario, the VCG mechanism collects in payments up to

On the Impact of Strategy and Utility Structures on Congestion-Averse Games

\frac{n-1}{n}

Optimal payments in dominant-strategy mechanisms for single-parameter domains

of the total value of the agents. This collected revenue represents a loss of social welfare. Given this, we study how to redistribute most of the VCG revenue back to the agents. Our first result is a bound on the best possible efficiency ratio, which we conjecture to be tight based on numerical simulations. Furthermore, the upper bound is confirmed on the case with 3 agents, for which we derive an optimal redistribution function. For more than 3 agents, we turn to heuristic solutions and propose a new approach to designing redistribution mechanisms.

Asynchronous Congestion Games

Recent results regarding games with congestion-averse utilities (or, congestion-averse games--CAGs) have shown they possess some very desirable properties. Specifically, they have pure strategy Nash equilibria, which may be found in polynomial time. However, these results were accompanied by a very limiting assumption that each player is capable of using any subset of its available set of resources. This is often unrealistic--for example, resources may have complementarities between them such that a minimal number of resources is required for any to be useful. To remove this restriction, in this paper we prove the existence and tractability of a pure strategy equilibrium for a much more general setting where each player is given a matroid over the set of resources, along with the bounds on the size of a subset of resources to be selected, and its strategy space consists of all elements of this matroid that fit in the given size range. Moreover, we show that if a player strategy space in a given CAG does not satisfy these matroid properties, then a pure strategy equilibrium need not exist, and in fact the determination of whether or not a game has such an equilibrium is NP-complete. We further prove analogous results for each of the congestion-averse conditions on utility functions, thus showing that current assumptions on strategy and utility structures in this model cannot be relaxed anymore.