By: Pelle Nelissen

Using data from 35 Participatory Budgeting instances in Amsterdam, we empirically compare two different Participatory Budgeting rules: the greedy cost welfare rule and the Method of Equal Shares. We quantify how proportional, equal and fair the rules are and conclude that, for a small price in total voter satisfaction, the Method of Equal Shares performs better on all notions of fairness studied. We further provide a popular and a visual ex... more

Using data from 35 Participatory Budgeting instances in Amsterdam, we empirically compare two different Participatory Budgeting rules: the greedy cost welfare rule and the Method of Equal Shares. We quantify how proportional, equal and fair the rules are and conclude that, for a small price in total voter satisfaction, the Method of Equal Shares performs better on all notions of fairness studied. We further provide a popular and a visual explanation of the Method of Equal Shares. less

By: Fengzhuo Zhang, Vincent Y. F. Tan, Zhaoran Wang, Zhuoran Yang

We design and analyze reinforcement learning algorithms for Graphon Mean-Field Games (GMFGs). In contrast to previous works that require the precise values of the graphons, we aim to learn the Nash Equilibrium (NE) of the regularized GMFGs when the graphons are unknown. Our contributions are threefold. First, we propose the Proximal Policy Optimization for GMFG (GMFG-PPO) algorithm and show that it converges at a rate of $O(T^{-1/3})$ after... more

We design and analyze reinforcement learning algorithms for Graphon Mean-Field Games (GMFGs). In contrast to previous works that require the precise values of the graphons, we aim to learn the Nash Equilibrium (NE) of the regularized GMFGs when the graphons are unknown. Our contributions are threefold. First, we propose the Proximal Policy Optimization for GMFG (GMFG-PPO) algorithm and show that it converges at a rate of $O(T^{-1/3})$ after $T$ iterations with an estimation oracle, improving on a previous work by Xie et al. (ICML, 2021). Second, using kernel embedding of distributions, we design efficient algorithms to estimate the transition kernels, reward functions, and graphons from sampled agents. Convergence rates are then derived when the positions of the agents are either known or unknown. Results for the combination of the optimization algorithm GMFG-PPO and the estimation algorithm are then provided. These algorithms are the first specifically designed for learning graphons from sampled agents. Finally, the efficacy of the proposed algorithms are corroborated through simulations. These simulations demonstrate that learning the unknown graphons reduces the exploitability effectively. less

# Two-Sided Matching Markets: Impossibility Results on Existence of Efficient and Envy Free Solutions

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By: Thorben Tröbst, Vijay V Vazirani

The Hylland-Zeckhauser gave a classic pricing-based mechanism (HZ) for a one-sided matching market; it yields allocations satisfying Pareto optimality and envy-freeness (Hylland and Zeckhauser, 1979), and the mechanism is incentive compatible in the large (He et al., 2018). They also studied the exchange extension of HZ and gave an example showing that it may not even admit an equilibrium. In this paper, we consider two models of two sided ... more

The Hylland-Zeckhauser gave a classic pricing-based mechanism (HZ) for a one-sided matching market; it yields allocations satisfying Pareto optimality and envy-freeness (Hylland and Zeckhauser, 1979), and the mechanism is incentive compatible in the large (He et al., 2018). They also studied the exchange extension of HZ and gave an example showing that it may not even admit an equilibrium. In this paper, we consider two models of two sided matching markets: when utility functions are symmetric and when they are non-symmetric. We ask if these models always admit allocations satisfying the two basic properties of Pareto efficiency and envy freeness. Our results are negative. A corollary of the former result is a negative result for non-bipartite matching markets as well. less

By: Anna M. Maddux, Maryam Kamgarpour

We consider the problem of learning to play a repeated contextual game with unknown reward and unknown constraints functions. Such games arise in applications where each agent's action needs to belong to a feasible set, but the feasible set is a priori unknown. For example, in constrained multi-agent reinforcement learning, the constraints on the agents' policies are a function of the unknown dynamics and hence, are themselves unknown. Unde... more

We consider the problem of learning to play a repeated contextual game with unknown reward and unknown constraints functions. Such games arise in applications where each agent's action needs to belong to a feasible set, but the feasible set is a priori unknown. For example, in constrained multi-agent reinforcement learning, the constraints on the agents' policies are a function of the unknown dynamics and hence, are themselves unknown. Under kernel-based regularity assumptions on the unknown functions, we develop a no-regret, no-violation approach which exploits similarities among different reward and constraint outcomes. The no-violation property ensures that the time-averaged sum of constraint violations converges to zero as the game is repeated. We show that our algorithm, referred to as c.z.AdaNormalGP, obtains kernel-dependent regret bounds and that the cumulative constraint violations have sublinear kernel-dependent upper bounds. In addition we introduce the notion of constrained contextual coarse correlated equilibria (c.z.CCE) and show that $\epsilon$-c.z.CCEs can be approached whenever players' follow a no-regret no-violation strategy. Finally, we experimentally demonstrate the effectiveness of c.z.AdaNormalGP on an instance of multi-agent reinforcement learning. less

By: Javier Cembrano, Svenja M. Griesbach, Maximilian J. Stahlberg

In the impartial selection problem, a subset of agents up to a fixed size $k$ among a group of $n$ is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of being selected by changing its vote. It is $\alpha$-optimal if, for every instance, the ratio between the votes received by the selected subset is at least a fraction of $\alpha$ of the votes received by ... more

In the impartial selection problem, a subset of agents up to a fixed size $k$ among a group of $n$ is to be chosen based on votes cast by the agents themselves. A selection mechanism is impartial if no agent can influence its own chance of being selected by changing its vote. It is $\alpha$-optimal if, for every instance, the ratio between the votes received by the selected subset is at least a fraction of $\alpha$ of the votes received by the subset of size $k$ with the highest number of votes. We study deterministic impartial mechanisms in a more general setting with arbitrarily weighted votes and provide the first approximation guarantee, roughly $1/\lceil 2n/k\rceil$. When the number of agents to select is large enough compared to the total number of agents, this yields an improvement on the previously best known approximation ratio of $1/k$ for the unweighted setting. We further show that our mechanism can be adapted to the impartial assignment problem, in which multiple sets of up to $k$ agents are to be selected, with a loss in the approximation ratio of $1/2$. less

By: Yu Kato, Jiquan Xie, Tutomu Murase, Sumiko Miyata

For multi-transmission rate environments, access point (AP) connection methods have been proposed for maximizing system throughput, which is the throughput of an entire system, on the basis of the cooperative behavior of users. These methods derive optimal positions for the cooperative behavior of users, which means that new users move to improve the system throughput when connecting to an AP. However, the conventional method only considers... more

For multi-transmission rate environments, access point (AP) connection methods have been proposed for maximizing system throughput, which is the throughput of an entire system, on the basis of the cooperative behavior of users. These methods derive optimal positions for the cooperative behavior of users, which means that new users move to improve the system throughput when connecting to an AP. However, the conventional method only considers the transmission rate of new users and does not consider existing users, even though it is necessary to consider the transmission rate of all users to improve system throughput. In addition, these method do not take into account the frequency of interference between users. In this paper, we propose an AP connection method which maximizes system throughput by considering the interference between users and the initial position of all users. In addition, our proposed method can improve system throughput by about 6% at most compared to conventional methods. less

# Fair $ω$-Regular Games

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By: Daniel Hausmann, Nir Piterman, Irmak Sağlam, Anne-Kathrin Schmuck

We consider two-player games over finite graphs in which both players are restricted by fairness constraints on their moves. Given a two player game graph $G=(V,E)$ and a set of fair moves $E_f\subseteq E$ a player is said to play "fair" in $G$ if they choose an edge $e \in E_f$ infinitely often whenever the source vertex of $e$ is visited infinitely often. Otherwise, they play "unfair". We equip such games with two $\omega$-regular winning... more

We consider two-player games over finite graphs in which both players are restricted by fairness constraints on their moves. Given a two player game graph $G=(V,E)$ and a set of fair moves $E_f\subseteq E$ a player is said to play "fair" in $G$ if they choose an edge $e \in E_f$ infinitely often whenever the source vertex of $e$ is visited infinitely often. Otherwise, they play "unfair". We equip such games with two $\omega$-regular winning conditions $\alpha$ and $\beta$ deciding the winner of mutually fair and mutually unfair plays, respectively. Whenever one player plays fair and the other plays unfair, the fairly playing player wins the game. The resulting games are called "fair $\alpha/\beta$ games". We formalize fair $\alpha/\beta$ games and show that they are determined. For fair parity/parity games, i.e., fair $\alpha/\beta$ games where $\alpha$ and $\beta$ are given each by a parity condition over $G$, we provide a polynomial reduction to (normal) parity games via a gadget construction inspired by the reduction of stochastic parity games to parity games. We further give a direct symbolic fixpoint algorithm to solve fair parity/parity games. On a conceptual level, we illustrate the translation between the gadget-based reduction and the direct symbolic algorithm which uncovers the underlying similarities of solution algorithms for fair and stochastic parity games, as well as for the recently considered class of fair games where only one player is restricted by fair moves. less

By: Marco Bornstein, Amrit Singh Bedi, Anit Kumar Sahu, Furqan Khan, Furong Huang

Edge device participation in federating learning (FL) has been typically studied under the lens of device-server communication (e.g., device dropout) and assumes an undying desire from edge devices to participate in FL. As a result, current FL frameworks are flawed when implemented in real-world settings, with many encountering the free-rider problem. In a step to push FL towards realistic settings, we propose RealFM: the first truly federa... more

Edge device participation in federating learning (FL) has been typically studied under the lens of device-server communication (e.g., device dropout) and assumes an undying desire from edge devices to participate in FL. As a result, current FL frameworks are flawed when implemented in real-world settings, with many encountering the free-rider problem. In a step to push FL towards realistic settings, we propose RealFM: the first truly federated mechanism which (1) realistically models device utility, (2) incentivizes data contribution and device participation, and (3) provably removes the free-rider phenomena. RealFM does not require data sharing and allows for a non-linear relationship between model accuracy and utility, which improves the utility gained by the server and participating devices compared to non-participating devices as well as devices participating in other FL mechanisms. On real-world data, RealFM improves device and server utility, as well as data contribution, by up to 3 magnitudes and 7x respectively compared to baseline mechanisms. less

By: Segev Wasserkrug, Takayuki Osogami

In enterprise cloud computing, there is a big and increasing investment to move to multi-cloud computing, which allows enterprises to seamlessly utilize IT resources from multiple cloud providers, so as to take advantage of different cloud providers' capabilities and costs. This investment raises several key questions: Will multi-cloud always be more beneficial to the cloud users? How will this impact the cloud providers? Is it possible to ... more

In enterprise cloud computing, there is a big and increasing investment to move to multi-cloud computing, which allows enterprises to seamlessly utilize IT resources from multiple cloud providers, so as to take advantage of different cloud providers' capabilities and costs. This investment raises several key questions: Will multi-cloud always be more beneficial to the cloud users? How will this impact the cloud providers? Is it possible to create a multi-cloud market that is beneficial to all participants? In this work, we begin addressing these questions by using the game theoretic model of trading networks and formally compare between the single and multi-cloud markets. This comparson a) provides a sufficient condition under which the multi-cloud network can be considered more efficient than the single cloud one in the sense that a centralized coordinator having full information can impose an outcome that is strongly Pareto-dominant for all players and b) shows a surprising result that without centralized coordination, settings are possible in which even the cloud buyers' utilities may decrease when moving from a single cloud to a multi-cloud network. As these two results emphasize the need for centralized coordination to ensure a Pareto-dominant outcome and as the aforementioned Pareto-dominant result requires truthful revelation of participant's private information, we provide an automated mechanism design (AMD) approach, which, in the Bayesian setting, finds mechanisms which result in expectation in such Pareto-dominant outcomes, and in which truthful revelation of the parties' private information is the dominant strategy. We also provide empirical analysis to show the validity of our AMD approach. less

By: Anne-Kathrin Schmuck, K. S. Thejaswini, Irmak Sağlam, Satya Prakash Nayak

This paper considers the problem of solving infinite two-player games over finite graphs under various classes of progress assumptions motivated by applications in cyber-physical system (CPS) design. Formally, we consider a game graph G, a temporal specification $\Phi$ and a temporal assumption $\psi$, where both are given as linear temporal logic (LTL) formulas over the vertex set of G. We call the tuple $(G,\Phi,\psi)$ an 'augmented gam... more

This paper considers the problem of solving infinite two-player games over finite graphs under various classes of progress assumptions motivated by applications in cyber-physical system (CPS) design. Formally, we consider a game graph G, a temporal specification $\Phi$ and a temporal assumption $\psi$, where both are given as linear temporal logic (LTL) formulas over the vertex set of G. We call the tuple $(G,\Phi,\psi)$ an 'augmented game' and interpret it in the classical way, i.e., winning the augmented game $(G,\Phi,\psi)$ is equivalent to winning the (standard) game $(G,\psi \implies \Phi)$. Given a reachability or parity game $(G,\Phi)$ and some progress assumption $\psi$, this paper establishes whether solving the augmented game $(G,\Phi,\psi)$ lies in the same complexity class as solving $(G,\Phi)$. While the answer to this question is negative for arbitrary combinations of $\Phi$ and $\psi$, a positive answer results in more efficient algorithms, in particular for large game graphs. We therefore restrict our attention to particular classes of CPS-motivated progress assumptions and establish the worst-case time complexity of the resulting augmented games. Thereby, we pave the way towards a better understanding of assumption classes that can enable the development of efficient solution algorithms in augmented two-player games. less