An important feature of many real world facility location problems are capacity limits on the facilities. We show here how capacity constraints make it harder to design strategy proof mechanisms for facility location, but counter-intuitively can improve the guarantees on how well we can approximate the optimal solution.

Social gravity law widely exists in human travel, population migration, commodity trade, information communication, scientific collaboration and so on. Why is there such a simple law in many complex social systems is an interesting question. Although scientists from fields of statistical physics, complex systems, economics and transportation science have explained the social gravity law, a theoretical

We study the impact on mechanisms for facility location of moving from one dimension to two (or more) dimensions and Euclidean or Manhattan distances. We consider three fundamental axiomatic properties: anonymity which is a basic fairness property, Pareto optimality which is one of the most important efficiency properties, and strategy proofness which ensures agents do not have an incentive to mis-report

Facility location problems often permit facilities to be located at any position. But what if this is not the case in practice? What if facilities can only be located at particular locations like a highway exit or close to a bus stop? We consider here the impact of such constraints on the location of facilities on the performance of strategy proof mechanisms for locating facilities.We study four different

In mobile Internet ecosystem, Mobile Users (MUs) purchase wireless data services from Internet Service Provider (ISP) to access to Internet and acquire the interested content services (e.g., online game) from Content Provider (CP). The popularity of intelligent functions (e.g., AI and 3D modeling) increases the computation-intensity of the content services, leading to a growing computation pressure

Often---for example in war games, strategy video games, and financial simulations---the game is given to us only as a black-box simulator in which we can play it. In these settings, since the game may have unknown nature action distributions (from which we can only obtain samples) and/or be too large to expand fully, it can be difficult to compute strategies with guarantees on exploitability. Recent

Secure Message Transmission (SMT) is a two-party cryptographic protocol by which the sender can securely and reliably transmit messages to the receiver using multiple channels. An adversary for SMT can corrupt a subset of the channels and make eavesdropping and tampering over the channels. In this work, we introduce a game-theoretic security model for SMT in which adversaries have some preferences

This study investigates the efficiency and effectiveness of area-based tradable credit scheme (TCS) based on the trip-based Macroscopic Fundamental Diagram model for the morning commute problem. In the proposed tradable credit scheme, the regulator distributes initial credits to all travelers and designs a time-varying and trip length specific credit tariff. Credits are traded between travelers and

We address the question of aggregating the preferences of voters in the context of participatory budgeting. We scrutinize the voting method currently used in practice, underline its drawbacks, and introduce a novel scheme tailored to this setting, which we call "Knapsack Voting". We study its strategic properties - we show that it is strategy-proof under a natural model of utility (a dis-utility given

We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category, which can be used to compose probabilistic games in parallel and sequentially. We also consider morphisms between games, and show that intuitive constructions give

Mobility as a Service (MaaS) has recently received a significant attention from researchers, industry stakeholders, and the public sector. The vast majority of existing MaaS paradigms are articulated based on the traditional segmentation of travel modes, e.g. private vehicle, public transportation (bus, metro, light rail) and shared mobility (car/bike/ride-sharing, ride-sourcing). In the context of

Markov Decision Processes (MDPs) are known to be sensitive to parameter specification. Distributionally robust MDPs alleviate this issue by allowing for ambiguity sets which give a set of possible distributions over parameter sets. The goal is to find an optimal policy with respect to the worst-case parameter distribution. We propose a first-order methods framework for solving Distributionally robust

We consider the one-sided matching problem, where n agents have preferences over n items, and these preferences are induced by underlying cardinal valuation functions. The goal is to match every agent to a single item so as to maximize the social welfare. Most of the related literature, however, assumes that the values of the agents are not a priori known, and only access to the ordinal preferences

The connection between games and no-regret algorithms has been widely studied in the literature. A fundamental result is that when all players play no-regret strategies, this produces a sequence of actions whose time-average is a coarse-correlated equilibrium of the game. However, much less is known about equilibrium selection in the case that multiple equilibria exist. In this work, we study the convergence

Recent work on decision making and planning for autonomous driving has made use of game theoretic methods to model interaction between agents. We demonstrate that methods based on the Stackelberg game formulation of this problem are susceptible to an issue that we refer to as conflict. Our results show that when conflict occurs, it causes suboptimal and potentially dangerous behaviour. In response

On-line firms deploy suites of software platforms, where each platform is designed to interact with users during a certain activity, such as browsing, chatting, socializing, emailing, driving, etc. The economic and incentive structure of this exchange, as well as its algorithmic nature, have not been explored to our knowledge; we initiate their study in this paper. We model this interaction as a Stackelberg

Matching algorithms have been classically studied with the goal of finding stable solutions. However, in many important societal problems, the degree of fairness in the matching assumes crucial importance, for instance when we have to match COVID-19 patients to care units. We study the problem of finding a stable many-to-one matching while satisfying fairness among all the agents with cardinal utilities

In this work, we study the interaction of strategic agents in continuous action Cournot games with limited information feedback. Cournot game is the essential market model for many socio-economic systems where agents learn and compete without the full knowledge of the system or each other. We consider the dynamics of the policy gradient algorithm, which is a widely adopted continuous control reinforcement

Counterfactual regret minimization (CFR) is a popular method to deal with decision-making problems of two-player zero-sum games with imperfect information. Unlike existing studies that mostly explore for solving larger scale problems or accelerating solution efficiency, we propose a framework, RLCFR, which aims at improving the generalization ability of the CFR method. In the RLCFR, the game strategy

Reinforcement learning from self-play has recently reported many successes. Self-play, where the agents compete with themselves, is often used to generate training data for iterative policy improvement. In previous work, heuristic rules are designed to choose an opponent for the current learner. Typical rules include choosing the latest agent, the best agent, or a random historical agent. However,

A rich class of mechanism design problems can be understood as incomplete-information games between a principal who commits to a policy and an agent who responds, with payoffs determined by an unknown state of the world. Traditionally, these models require strong and often-impractical assumptions about beliefs (a common prior over the state). In this paper, we dispense with the common prior. Instead

We study the stable marriage problem in two-sided markets with randomly generated preferences. We consider agents on each side divided into a constant number of "soft tiers", which intuitively indicate the quality of the agent. Specifically, every agent within a tier has the same public score, and agents on each side have preferences independently generated proportionally to the public scores of the

A popular formalism for multiagent control applies tools from game theory, casting a multiagent decision problem as a cooperation-style game in which individual agents make local choices to optimize their own local utility functions in response to the observable choices made by other agents. When the system-level objective is submodular maximization, it is known that if every agent can observe the

We consider the Nash equilibrium problem in a partial-decision information scenario. Specifically, each agent can only receive information from some neighbors via a communication network, while its cost function depends on the strategies of possibly all agents. In particular, while the existing methods assume undirected or balanced communication, in this paper we allow for non-balanced, directed graphs

We consider 2-players, 2-values minimization games where the players' costs take on two values, $a,b$, $a b$, then there exists a normal 2-players, 2-values, 3-strategies game without $\mathsf{F}$-equilibrium. To the best of our knowledge, this work is the first to provide an (almost complete) answer on whether there is, for a given concave function $\mathsf{F}$, a counterexample game without $\ma

Unlike normal-form games, where correlated equilibria have been studied for more than 45 years, extensive-form correlation is still generally not well understood. Part of the reason for this gap is that the sequential nature of extensive-form games allows for a richness of behaviors and incentives that are not possible in normal-form settings. This richness translates to a significantly different complexity

In this paper, we study large population multi-agent reinforcement learning (RL) in the context of discrete-time linear-quadratic mean-field games (LQ-MFGs). Our setting differs from most existing work on RL for MFGs, in that we consider a non-stationary MFG over an infinite horizon. We propose an actor-critic algorithm to iteratively compute the mean-field equilibrium (MFE) of the LQ-MFG. There are

Three decades ago, Karp, Vazirani, and Vazirani (STOC 1990) defined the online matching problem and gave an optimal $1-\frac{1}{e} \approx 0.632$-competitive algorithm. %introduced the Ranking algorithm with the optimal $1-\frac{1}{e}$ competitive ratio. Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first generalization called \emph{AdWords} driven by online

Despite the emphases on computability issues in research of algorithmic game theory, the limited computational capacity of players have received far less attention. This work examines how different levels of players' computational ability (or "rationality") impact the outcomes of sequential scheduling games. Surprisingly, our results show that a lower level of rationality of players may lead to better

We study the computation of equilibria in prediction markets in perhaps the most fundamental special case with two players and three trading opportunities. To do so, we show equivalence of prediction market equilibria with those of a simpler signaling game with commitment introduced by Kong and Schoenebeck (2018). We then extend their results by giving computationally efficient algorithms for additional

We study the implications of selling through a voice-based virtual assistant (VA). The seller has a set of products available and the VA decides which product to offer and at what price, seeking to maximize its revenue, consumer- or total-surplus. The consumer is impatient and rational, seeking to maximize her expected utility given the information available to her. The VA selects products based on

Priced timed games are two-player zero-sum games played on priced timed automata (whose locations and transitions are labeled by weights modelling the price of spending time in a state and executing an action, respectively). The goals of the players are to minimise and maximise the price to reach a target location, respectively. We consider priced timed games with one clock and arbitrary integer weights

This paper presents a theoretical framework for probably approximately correct (PAC) multi-agent reinforcement learning (MARL) algorithms for Markov games. The paper offers an extension to the well-known Nash Q-learning algorithm, using the idea of delayed Q-learning, in order to build a new PAC MARL algorithm for general-sum Markov games. In addition to guiding the design of a provably PAC MARL algorithm

We present an algorithm that correctly updates the Forsyth-Edwards Notation (FEN) chessboard character string after any move is made without the need for an intermediary array representation of the board. In particular, this relates to software that have to do with chess, certain chess variants and possibly even similar board games with comparable position representation. Even when performance may

In participatory budgeting we are given a set of projects---each with a cost, an available budget, and a set of voters who in some form express their preferences over the projects. The goal is to select---based on voter preferences---a subset of projects whose total cost does not exceed the budget. We propose several aggregation methods based on the idea of cumulative votes, e.g., for the setting when

In this paper, zero-sum mean-field type games (ZSMFTG) with linear dynamics and quadratic utility are studied under infinite-horizon discounted utility function. ZSMFTG are a class of games in which two decision makers whose utilities sum to zero, compete to influence a large population of agents. In particular, the case in which the transition and utility functions depend on the state, the action

This study establishes a novel framework of Markovian traffic equilibrium assignment based on the network generalized extreme value (NGEV) model, which we call NGEV equilibrium assignment. The use of the NGEV model in traffic assignment has recently been proposed and enables capturing the path correlation without explicit path enumeration. However, the NGEV equilibrium assignment has never been investigated

The mechanism behind the emergence of cooperation in both biological and social systems is currently not understood. In particular, human behavior in the Ultimatum game is almost always irrational, preferring mutualistic sharing strategies, while chimpanzees act rationally and selfishly. However, human behavior varies with geographic and cultural differences leading to distinct behaviors. In this letter

The iterated prisoner's dilemma is a game that produces many counter-intuitive and complex behaviors in a social environment, based on very simple basic rules. It illustrates that cooperation can be a good thing even in a competitive world, that individual fitness need not be the most import criteria of success, and that some strategies are very strong in a direct confrontation but could still perform

This paper compares mathematical models for automated market makers including logarithmic market scoring rule (LMSR), liquidity sensitive LMSR (LS-LMSR), constant product/mean/sum, and others. It is shown that though LMSR may not be a good model for Decentralized Finance (DeFi) applications, LS-LMSR has several advantages over constant product/mean based automated market makers. However, LS-LMSR requires

Cyclic dominance offers not just a way to maintain biodiversity, but also serves as a sort of defensive alliance against an external invader. Interestingly, a new level of competition can be observed when two cyclic loops are present. Here the inner invasion speed plays a decisive role on the evolutionary outcome, because faster invasion rate provides an evolutionary advantage to an alliance. In this

Online auctions play a central role in online advertising, and are one of the main reasons for the industry's scalability and growth. With great changes in how auctions are being organized, such as changing the second- to first-price auction type, advertisers and demand platforms are compelled to adapt to a new volatile environment. Bid shading is a known technique for preventing overpaying in auction

Consider an online facility assignment problem where a set of facilities $F = \{ f_1, f_2, f_3, \cdots, f_{|F|} \}$ of equal capacity $l$ is situated on a metric space and customers arrive one by one in an online manner on that space. We assign a customer $c_i$ to a facility $f_j$ before a new customer $c_{i+1}$ arrives. The cost of this assignment is the distance between $c_i$ and $f_j$. The objective

In this paper, zero-sum mean-field type games (ZSMFTG) with linear dynamics and quadratic cost are studied under infinite-horizon discounted utility function. ZSMFTG are a class of games in which two decision makers whose utilities sum to zero, compete to influence a large population of indistinguishable agents. In particular, the case in which the transition and utility functions depend on the state

In this paper, we present a game-theoretic model describing the voluntary social distancing during the spread of an epidemic. The payoffs of the agents depend on the social distancing they practice and on the probability of getting infected. We consider two types of agents, the vulnerable agents who have a small cost if they get infected, and the non-vulnerable agents who have a higher cost. For the

In this paper, we give a new completion for quasi-uniform spaces which generalizes the completion theories of Doitchinov [8] and Stoltenberg [20]. The presented completion theory is very well-behaved and extends the completion theory of uniform spaces in a natural way. That is, the definition of Cauchy net and the constructed completion coincide with the classical in the case of uniform spaces. The

When selfish users share a road network and minimize their individual travel costs, the equilibrium they reach can be worse than the socially optimal routing. Tolls are often used to mitigate this effect in traditional congestion games, where all vehicle contribute identically to congestion. However, with the proliferation of autonomous vehicles and driver-assistance technology, vehicles become heterogeneous

We explore the use of policy approximation for reducing the computational cost of learning Nash equilibria in multi-agent reinforcement learning scenarios. We propose a new algorithm for zero-sum stochastic games in which each agent simultaneously learns a Nash policy and an entropy-regularized policy. The two policies help each other towards convergence: the former guides the latter to the desired

We study voting rules for participatory budgeting, where a group of voters collectively decides which projects should be funded using a common budget. We allow the projects to have arbitrary costs, and the voters to have arbitrary additive valuations over the projects. We formulate two axioms that guarantee proportional representation to groups of voters with common interests. To the best of our knowledge

We establish sharp asymptotically optimal strategies for the problem of online prediction with history dependent experts. The prediction problem is played (in part) over a discrete graph called the $d$ dimensional de Bruijn graph, where $d$ is the number of days of history used by the experts. Previous work [11] established $O(\varepsilon)$ optimal strategies for $n=2$ experts and $d\leq 4$ days of

We consider a game of persuasion with evidence between a sender and a receiver. The sender has private information. By presenting evidence on the information, the sender wishes to persuade the receiver to take a single action (e.g., hire a job candidate, or convict a defendant). The sender's utility depends solely on whether or not the receiver takes the action. The receiver's utility depends on both

We study a coordination game motivated by the formation of Internet Exchange Points (IXPs), in which agents choose which facilities to join. Joining the same facility as other agents you communicate with has benefits, but different facilities have different costs for each agent. Thus, the players wish to join the same facilities as their "friends", but this is balanced by them not wanting to pay the

We introduce a discrete-time search game, in which two players compete to find an object first. The object moves according to a time-varying Markov chain on finitely many states. The players know the Markov chain and the initial probability distribution of the object, but do not observe the current state of the object. The players are active in turns. The active player chooses a state, and this choice

Augmented reality (AR), virtual reality (VR) and mixed reality (MR) are technologies of great potential due to the engaging and enriching experiences they are capable of providing. Their use is rapidly increasing in diverse fields such as medicine, manufacturing or entertainment. However, the possibilities that AR, VR and MR offer in the area of environmental applications are not yet widely explored

For prediction of interacting agents' trajectories, we propose an end-to-end trainable architecture that hybridizes neural nets with game-theoretic principles, has interpretable intermediate representations, and transfers to robust downstream decisions. It combines a differentiable implicit layer, that maps preferences to local Nash equilibria, with a learned equilibrium refinement concept and preference

We prove the existence and computability of optimal strategies in weighted limit games, zero-sum infinite-duration games with a B\"uchi-style winning condition requiring to produce infinitely many play prefixes that satisfy a given regular specification. Quality of plays is measured in the maximal weight of infixes between successive play prefixes that satisfy the specification.

We consider a two-player search game on a tree $T$. One vertex (unknown to the players) is randomly selected as the target. The players alternately guess vertices. If a guess $v$ is not the target, then both players are informed in which subtree of $T \smallsetminus v$ the target lies. The winner is the player who guesses the target. When both players play optimally, we show that each wins with probability

We study qualitative multi-objective reachability problems for Ordered Branching Markov Decision Processes (OBMDPs), or equivalently context-free MDPs, building on prior results for single-target reachability on Branching Markov Decision Processes (BMDPs). We provide two separate algorithms for "almost-sure" and "limit-sure" multi-target reachability for OBMDPs. Specifically, given an OBMDP, $\mathcal{A}$

We propose a smart contract that allows two mutually distrusting parties to transact any non-digital good or service by deploying a smart contract on a blockchain to act as escrow. The contract settles disputes by letting parties wager that they can convince an arbiter that they were the honest party. We analyse the contract as an extensive-form game and prove that the honest strategy is secure in

This paper studies two-player zero-sum stochastic Bayesian games where each player has its own dynamic state that is unknown to the other player. Using typical techniques, we provide the recursive formulas and the sufficient statistics in both the primal game and its dual games. It's also shown that with a specific initial parameter, the optimal strategy of one player in a dual game is also the optimal