In Massively Open Online Courses (MOOCs) TA resources are limited; most MOOCs use peer assessments to grade assignments. Students have to divide up their time between working on their own homework and grading others. If there is no risk of being caught and penalized, students have no reason to spend any time grading others Course staff want to incentivize students to balance their time between course work and peer grading. They may do so by auditing students, ensuring that they perform grading correctly. One would not want students to invest too much time on peer grading, as this would result in poor course performance. We present the first model of strategic auditing in peer grading, modeling the student's choice of effort in response to a grader's audit levels as a Stackelberg game with multiple followers. We demonstrate that computing the equilibrium for this game is computationally hard. We then provide a PTAS in order to compute an approximate solution to the problem of allocating audit levels. However, we show that this allocation does not necessarily maximize social welfare; in fact, there exist settings where course auditor utility is arbitrarily far from optimal under an approximately optimal allocation. To circumvent this issue, we present a natural condition that guarantees that approximately optimal TA allocations guarantee approximately optimal welfare for the course auditors.

A key challenge in solving extensive-form games is dealing with large, or even infinite, action spaces. In games of imperfect information, the leading approach is to find a Nash equilibrium in a smaller abstract version of the game that includes only a few actions at each decision point, and then map the solution back to the original game. However, it is difficult to know which actions should be included in the abstraction without first solving the game, and it is infeasible to solve the game without first abstracting it. We introduce a method that combines abstraction with equilibrium finding by enabling actions to be added to the abstraction at run time. This allows an agent to begin learning with a coarse abstraction, and then to strategically insert actions at points that the strategy computed in the current abstraction deems important. The algorithm can quickly add actions to the abstraction while provably not having to restart the equilibrium finding. It enables anytime convergence to a Nash equilibrium of the full game even in infinite games. Experiments show it can outperform fixed abstractions at every stage of the run: early on it improves as quickly as equilibrium finding in coarse abstractions, and later it converges to a better solution than does equilibrium finding in fine-grained abstractions.

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.

This paper explores a PAC (probably approximately correct) learning model in cooperative games. Specifically, we are given m random samples of coalitions and their values, taken from some unknown cooperative game; can we predict the values of unseen coalitions? We study the PAC learnability of several well-known classes of cooperative games, such as network flow games, threshold task games, and induced subgraph games. We also establish a novel connection between PAC learnability and core stability: for games that are efficiently learnable, it is possible to find payoff divisions that are likely to be stable using a polynomial number of samples.

A simple mechanism for allocating indivisible resources is sequential allocation in which agents take turns to pick items. We focus on possible and necessary allocation problems, checking whether allocations of a given form occur in some or all mechanisms for several commonly used classes of sequential allocation mechanisms. In particular, we consider whether a given agent receives a given item, a set of items, or a subset of items for natural classes of sequential allocation mechanisms: balanced, recursively balanced, balanced alternation, and strict alternation. We present characterizations of the allocations that result respectively from the classes, which extend the well-known characterization by Brams and King [2005] for policies without restrictions. In addition, we examine the computational complexity of possible and necessary allocation problems for these classes.

We consider the computational complexity of computing welfare maximizing partitions for fractional hedonic games — a natural class of coalition formation games that can be succinctly represented by a graph. For such games, welfare maximizing partitions constitute desirable ways to cluster the vertices of the graph. We present both intractability results and approximation algorithms for computing welfare maximizing partitions.

We study the adjustment and use of the Max-sumalgorithm for solving Asymmetric Distributed ConstraintOptimization Problems (ADCOPs). First, we formalize asymmetric factor-graphs and apply the different versions of Max-sum to them. Apparently, in contrast to local search algorithms, most Max-sum versions perform similarly when solving symmetric and asymmetric problems and some even perform better on asymmetric problems. Second, we prove that the convergence properties of Max-sum ADVP (an algorithm that was previously found to outperform other Max-sum versions) and the quality of the solutions it produces are dependent on the order between nodes involved in each constraint, i.e., the inner constraint order (ICO). A standard ICO allows to reproduce the properties achieved for symmetric problems, and outperform previously proposed local search ADCOP algorithms. Third, we demonstrate that a non-standard ICO can be used to balance exploration and exploitation, resulting in the best performing Max-sum version on both symmetric and asymmetric standard benchmarks.

As part of the ongoing effort of designing secure DCOP algorithms, we propose P-Max-Sum, the first private algorithm that is based on Max-Sum. The proposed algorithm has multiple agents preforming the role of each node in the factor graph, on which the Max-Sum algorithm operates. P-Max-Sum preserves three types of privacy: topology privacy, constraint privacy, and assignment/decision privacy.By allowing a single call to a trusted coordinator, P-Max-Sum also preserves agent privacy. The two main cryptographic means that enable this privacy preservation are secret sharing and homomorphic encryption. Our experiments on structured and realistic problems show that the overhead of privacy preservation in terms of runtime is reasonable.

Parallel Test Paper Generation ( k -TPG) is a biobjective distributed resource allocation problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified criteria.Generating high-quality parallel test papers is challenging due to its NP-hardness in maximizing the collective objective functions.In this paper, we propose a Collective Biobjective Optimization (CBO) algorithm for solving k -TPG. CBO is a multi-step greedy-based approximation algorithm, which exploits the submodular property for biobjective optimization of k -TPG.Experiment results have shown that CBO has drastically outperformed the current techniques in terms of paper quality and runtime efficiency.

Distributed constraint optimization (DCOP) is an important framework for coordinated multiagent decision making. We address a practically useful variant of DCOP, called resource-constrained DCOP (RC-DCOP), which takes into account agents' consumption of shared limited resources. We present a promising new class of algorithm for RC-DCOPs by translating the underlying coordination problem to probabilistic inference. Using inference techniques such as expectation-maximization and convex optimization machinery, we develop a novel convergent message-passing algorithm for RC-DCOPs. Experiments on standard benchmarks show that our approach provides better quality than previous best DCOP algorithms and has much lower failure rate. Comparisons against an efficient centralized solver show that our approach provides near-optimal solutions, and is significantly faster on larger instances.