We thoroughly study a generalized version of the classic Stable Marriage and Stable Roommates problems where agents may share partners. We consider two prominent stability concepts: ordinal stability [Aharoni and Fleiner, Journal of Combinatorial Theory, 2003] and cardinal stability [Caragiannis et al., ACM EC 2019] and two optimality criteria: maximizing social welfare (i.e., the overall satisfaction

We study the complexity of bidding optimally in one-shot combinatorial auction mechanisms. Specifically, we consider the two most-commonly used payment rules: first-price and VCG-nearest. Prior work has largely assumed that bidders only submit bids on their bundles of interest. However, we show the surprising result that a single-minded bidder may lose an exponential amount of utility by playing his

Finding an envy-free allocation of indivisible resources to agents is a central task in many multiagent systems. Often, non-trivial envy-free allocations do not exist, and, when they do, finding them can be computationally hard. Classical envy-freeness requires that every agent likes the resources allocated to it at least as much as the resources allocated to any other agent. In many situations this

With the increasing adoption of blockchain technology, there is a strong need for achieving interoperability between unconnected ledgers. Approaches such as hash time lock contracts (HTLCs) have arisen for cross-chain asset exchange. The solution embraces the likelihood of transaction failure and attempts to "make the best out of worst" by allowing transacting agents to at least keep their original

The application of Internet of Things (IoT) and Machine Learning (ML) to the agricultural industry has enabled the development and creation of smart farms and precision agriculture. The growth in the number of smart farms and potential cooperation between these farms has given rise to the Cooperative Smart Farming (CSF) where different connected farms collaborate with each other and share data for

This paper studies the Two-Person Zero Sum(TPZS) game between a Multiple-Input Multiple-Output(MIMO) radar and an extended target with payoff function being the output Signal-to-Interference-pulse-Noise Ratio(SINR) at the radar receiver. The radar player wants to maximize SINR by adjusting its transmit waveform and receive filter. Conversely, the target player wants to minimize SINR by changing its

Class selectivity is an attribute of a unit in deep neural networks, which characterizes the discriminative ability of units to a specific class. Intuitively, decisions made by several highly selective units are more interpretable since it is easier to be traced back to the origin while that made by complex combinations of lowly selective units are more difficult to interpret. In this work, we develop

Modern financial market dynamics warrant detailed analysis due to their significant impact on the world. This, however, often proves intractable; massive numbers of agents, strategies and their change over time in reaction to each other leads to difficulties in both theoretical and simulational approaches. Notable work has been done on strategy dominance in stock markets with respect to the ratios

In this paper, we provide exponential rates of convergence to the Nash equilibrium of continuous-time game dynamics such as mirror descent (MD) and actor-critic (AC) in $N$-player continuous games that are either potential games or monotone games but possibly potential-free. In the first part of this paper, under the assumption the game admits a relatively strongly concave potential, we show that MD

We introduce a variant of the classic poker game blackjack -- the continuous blackjack. We study the Nash Equilibrium as well as the cases where players deviate from it. We then pivot to the study of a large class of adaptive strategies and obtain a model-free strategy. Finally, we apply reinforcement learning techniques to the game and address several associated engineering challenges.

We consider the problem of selfish agents in discrete-time queuing systems, where competitive queues try to get their packets served. In this model, a queue gets to send a packet each step to one of the servers, which will attempt to serve the oldest arriving packet, and unprocessed packets are returned to each queue. We model this as a repeated game where queues compete for the capacity of the servers

Network games have been instrumental in understanding strategic behaviors over networks for applications such as critical infrastructure networks, social networks, and cyber-physical systems. One critical challenge of network games is that the behaviors of the players are constrained by the underlying physical laws or safety rules, and the players may not have complete knowledge of network-wide constraints

We consider clustering games in which the players are embedded in a network and want to coordinate (or anti-coordinate) their strategy with their neighbors. The goal of a player is to choose a strategy that maximizes her utility given the strategies of her neighbors. Recent studies show that even very basic variants of these games exhibit a large Price of Anarchy: A large inefficiency between the total

Consider the problem of implementing a revenue-optimal, Bayesian Incentive Compatible auction when buyers' values are drawn from distributions $\times_i D_i$ on a particular instance $\vec{v}$. Optimal single-dimensional mechanisms are local: in order to allocate the item correctly on a particular valuation profile $\vec{v}$, only $\tilde{O}(1)$ bits are needed from each player (specifically, their

Auction theory historically focused on the question of designing the best way to sell a single item to potential buyers, with the concurrent objectives of maximizing the revenue generated or the welfare created. Those results relied on some prior Bayesian knowledge agents have on each-other and/or on infinite computational power. All those assumptions are no longer satisfied in new markets such as

We study a cooperative game setting where the grand coalition may change since the initial players are willing to invite their neighbours and also want to incentivize them to invite more players to join. We focus on the monotone games, i.e., adding more players to the grand coalition is not harmful. We model the invitation relationship as a forest since we require that each player can only accept the

We investigate non-adaptive algorithms for matroid prophet inequalities. Matroid prophet inequalities have been considered resolved since 2012 when [KW12] introduced thresholds that guarantee a tight 2-approximation to the prophet; however, this algorithm is adaptive. Other approaches of [CHMS10] and [FSZ16] have used non-adaptive thresholds with a feasibility restriction; however, this translates

In this paper, we consider a network of consumers who are under the combined influence of their neighbors and external influencing entities (the marketers). The consumers' opinion follows a hybrid dynamics whose opinion jumps are due to the marketing campaigns. By using the relevant static game model proposed recently in [1], we prove that although the marketers are in competition and therefore create

The rapid progress in artificial intelligence (AI) and machine learning has opened unprecedented analytics possibilities in various team and individual sports, including baseball, basketball, and tennis. More recently, AI techniques have been applied to football, due to a huge increase in data collection by professional teams, increased computational power, and advances in machine learning, with the

This paper considers downlink of reconfigurable intelligent surface (RIS) assisted cooperative non-orthogonal multiple access (CNOMA) systems. Our objective is to minimize the total transmit power by jointly optimizing the active beamforming vectors, transmit-relaying power, and RIS phase shifts. The formulated problem is a mixed-integer nonlinear programming (MINLP) problem. To tackle this problem

Families are places of affection and cooperation, but also of conflict. In his famous paper Parent-Offspring Conflict, Robert L. Trivers builds upon W. D. Hamilton's concept of inclusive fitness to argue for genetic conflict in parent-offspring relationships, and to derive numerical predictions on the intensity of the conflict. We propose a mathematical model of game theory that depicts how each member

One of the key features of this paper is that the agents' opinion of a social network is assumed to be not only influenced by the other agents but also by two marketers in competition. One of our contributions is to propose a pragmatic game-theoretical formulation of the problem and to conduct the complete corresponding equilibrium analysis (existence, uniqueness, dynamic characterization, and determination)

In mechanism design theory, a designer would like to implement a social choice function which specifies her favorite outcome for each possible profile of agents' private types. The revelation principle asserts that if a social choice function can be implemented by a mechanism in equilibrium, then there exists a direct mechanism that can truthfully implement it. This paper aims to propose a failure

In the secretary problem we are faced with an online sequence of elements with values. Upon seeing an element we have to make an irrevocable take-it-or-leave-it decision. The goal is to maximize the probability of picking the element of maximum value. The most classic version of the problem is that in which the elements arrive in random order and their values are arbitrary. However, by varying the

We provide the first separation in the approximation guarantee achievable by truthful and non-truthful combinatorial auctions with polynomial communication. Specifically, we prove that any truthful mechanism guaranteeing a $(\frac{3}{4}-\frac{1}{240}+\varepsilon)$-approximation for two buyers with XOS valuations over $m$ items requires $\exp(\Omega(\varepsilon^2 \cdot m))$ communication, whereas a

Temporary fork is a fundamental phenomenon in many blockchains with proof of work, and the analysis of temporary fork has recently drawn great attention. Different from existing efforts that focus on the blockchain system factors such as block size, network propagation delay or block generation speed, in this paper we explore a new key dimension of computing power from the miners' perspective. Specifically

Existing game-theoretic planning methods assume that the robot knows the objective functions of the other agents a priori while, in practical scenarios, this is rarely the case. This paper introduces LUCIDGames, an inverse optimal control algorithm that is able to estimate the other agents' objective functions in real time, and incorporate those estimates online into a receding-horizon game-theoretic

Decision makers often need to rely on imperfect probabilistic forecasts. While average performance metrics are typically available, it is difficult to assess the quality of individual forecasts and the corresponding utilities. To convey confidence about individual predictions to decision-makers, we propose a compensation mechanism ensuring that the forecasted utility matches the actually accrued utility

Many real-world multi-agent interactions consider multiple distinct criteria, i.e. the payoffs are multi-objective in nature. However, the same multi-objective payoff vector may lead to different utilities for each participant. Therefore, it is essential for an agent to learn about the behaviour of other agents in the system. In this work, we present the first study of the effects of such opponent

In autonomous Vehicles technology Image segmentation was a major problem in visual perception. This image segmentation process is mainly used in medical applications. Here we adopted an image segmentation process to visual perception tasks for predicting the agents on the surrounding environment, identifying the road boundaries and tracking the line markings. Main objective of the paper is to divide

We extend the concept of zero-determinant strategies to memory-two strategies in repeated games. Memory-two zero-determinant strategies enforce linear relation between correlation functions of payoffs and payoffs at the previous round. An example of memory-two zero-determinant strategy in repeated prisoner's dilemma game is provided.

We prove communication complexity lower bounds for (possibly mixed) Nash equilibrium in potential games. In particular, we show that finding a Nash equilibrium requires $poly(N)$ communication in two-player $N \times N$ potential games, and $2^{poly(n)}$ communication in $n$-player two-action games. To the best of our knowledge, these are the first results to demonstrate hardness in any model of (possibly

We model the behavioral biases of human decision-making in securing interdependent systems and show that such behavioral decision-making leads to a suboptimal pattern of resource allocation compared to non-behavioral (rational) decision-making. We provide empirical evidence for the existence of such behavioral bias model through a controlled subject study with 145 participants. We then propose three

Two fundamental models in online decision making are that of competitive analysis and that of optimal stopping. In the former the input is produced by an adversary, while in the latter the algorithm has full distributional knowledge of the input. In recent years, there has been a lot of interest in bridging these two models by considering data-driven or sample-based versions of optimal stopping problems

Once a viable vaccine for SARS-CoV-2 has been identified, vaccination uptake will determine our success in containing the COVID-19 pandemic. We argue that game theory and social network models should be used to guide decisions pertaining to vaccination programs for the best possible results. In the months following the introduction of vaccines, their availability and the human resources needed to run

We study a market of investments on networks, where each agent (vertex) can invest in any enterprise linked to him, and at the same time, raise capital for his firm own enterprise from other agents he is linked to. Failing to raise sufficient capital results with the firm defaulting, being unable to invest in others. Our main objective is to examine the role of collaterals in handling the strategic

A bipartite graph consists of two disjoint vertex sets, where vertices of one set can only be joined with an edge to vertices in the opposite set. Hall's theorem gives a necessary and sufficient condition for a bipartite graph to have a saturating matching, meaning every vertex in one set is matched to some vertex in the other in a one-to-one correspondence. When we imagine vertices as agents and let

There is increasing interest in using observed individual-level data to formulate personalized policy. Examples of this include heterogeneous pricing, individualized credit offers, and targeted social programs. This paper provides a general model of how personalized policy creates incentives for individuals to modify their behavior to obtain a better treatment. For a given planner objective, we show

We consider for the first time a stochastic generalized Nash equilibrium problem, i.e., with expected-value cost functions and joint feasibility constraints, under partial-decision information, meaning that the agents communicate only with some trusted neighbours. We propose several distributed algorithms for network games and aggregative games that we show being special instances of a preconditioned

Towards characterizing the optimization landscape of games, this paper analyzes the stability and spectrum of gradient-based dynamics near fixed points of two-player continuous games. We introduce the quadratic numerical range as a method to bound the spectrum of game dynamics linearized about local equilibria. We also analyze the stability of differential Nash equilibria and their robustness to variation

It is well understood that the structure of a social network is critical to whether or not agents can aggregate information correctly. In this paper, we study social networks that support information aggregation when rational agents act sequentially and irrevocably. Whether or not information is aggregated depends, inter alia, on the order in which agents decide. Thus, to decouple the order and the

In this paper, the user association and resource allocation problem is investigated for a two-tier HetNet consisting of one macro Base Station (BS) and a number of pico BSs. The effectiveness of user association to BSs is evaluated in terms of fairness and load distribution. In particular, the problem of determining a fair user association is formulated as a bargaining game so that for the Nash Bargaining

Poker is a multiplayer game of imperfect information and has been widely studied in game theory. Many popular variants of poker (e.g., Texas Hold'em and Omaha) at the edge of modern game theory research are large games. However, even toy poker games, such as Kuhn poker, can pose new challenges. Many Kuhn poker variants have been investigated: varying the number of players, initial pot size, and number

Motivated by recent applications of sequential decision making in matching markets, in this paper we attempt at formulating and abstracting market designs in peer lending. In the rest of this paper, what will follow is a paradigm to set the stage for how peer lending can be conceived from a matching market perspective with sequential design making embedded in it. We attempt at laying the stepping stones

Understanding the likelihood for an election to be tied is a classical topic in many disciplines including social choice, game theory, political science, and public choice. The problem is important not only as a fundamental problem in probability theory and statistics, but also because of its critical roles in many other important issues such as indecisiveness of voting, strategic voting, privacy of

We study long-run market stability for repeated price competitions between two firms, where consumer demand depends on firms' posted prices and consumers' price expectations called reference prices. Consumers' reference prices vary over time according to a memory-based dynamic, which is a weighted average of all historical prices. We focus on the setting where firms are not aware of demand functions

Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural notion of a local equilibrium is a differential Nash equilibrium. However, the set of locally exponentially stable equilibria of the learning dynamics do not necessarily

Deployed supervised machine learning models make predictions that interact with and influence the world. This phenomenon is called "performative prediction" by Perdomo et al. (2020), who investigated it in a stateless setting. We generalize their results to the case where the response of the population to the deployed classifier depends both on the classifier and the previous distribution of the population

Prediction markets are powerful tools to elicit and aggregate beliefs from strategic agents. However, in current prediction markets, agents may exhaust the social welfare by competing to be the first to update the market. We initiate the study of the trade-off between how quickly information is aggregated by the market, and how much this information costs. We design markets to aggregate timely information

A Bernoulli factory is an algorithmic procedure for exact sampling of certain random variables having only Bernoulli access to their parameters. Bernoulli access to a parameter $p \in [0,1]$ means the algorithm does not know $p$, but has sample access to independent draws of a Bernoulli random variable with mean equal to $p$. In this paper, we study the problem of Bernoulli factories for polytopes:

Motivated by applications such as college admission and insurance rate determination, we propose an evaluation problem where the inputs are controlled by strategic individuals who can modify their features at a cost. A learner can only partially observe the features, and aims to classify individuals with respect to a quality score. The goal is to design an evaluation mechanism that maximizes the overall

Human-robot interactions (HRI) can be modeled as dynamic or differential games with incomplete information, where each agent holds private reward parameters. Due to the open challenge in finding perfect Bayesian equilibria of such games, existing studies often consider approximated solutions composed of parameter estimation and motion planning steps, in order to decouple the belief and physical dynamics

We study the subclass of singleton congestion games with identical and increasing cost functions, i.e., each agent tries to utilize from the least crowded resource in her accessible subset of resources. Our main contribution is a novel approach for proving the existence of equilibrium outcomes that are resilient to weakly improving deviations: $(i)$ by singletons (Nash equilibria), $(ii)$ by the grand

We consider a team formation setting where agents have varying levels of expertise in a global set of required skills, and teams are ranked with respect to how well the expertise of teammates complement each other. We model this setting as a hedonic game, and we show that this class of games possesses many desirable properties, some of which are as follows: A partition that is Nash stable, core stable

This paper considers a game-theoretic framework for distributed learning problems over networks where communications between nodes are costly. In the proposed game, players decide both the learning parameters and the network structure for communications. The Nash equilibrium characterizes the tradeoff between the local performance and the global agreement of the learned classifiers. We introduce a

We consider the problem of security-aware planning in an unknown stochastic environment, in the presence of attacks on control signals (i.e., actuators) of the robot. We model the attacker as an agent who has the full knowledge of the controller as well as the employed intrusion-detection system and who wants to prevent the controller from performing tasks while staying stealthy. We formulate the problem

We provide online algorithms for secretary matching in general weighted graphs, under the well-studied models of vertex and edge arrivals. In both models, edges are associated with arbitrary weights that are unknown from the outset, and are revealed online. Under vertex arrival, vertices arrive online in a uniformly random order; upon the arrival of a vertex $v$, the weights of edges from $v$ to all

While social networks are widely used as a media for information diffusion, attackers can also strategically employ analytical tools, such as influence maximization, to maximize the spread of adversarial content through the networks. We investigate the problem of limiting the diffusion of negative information by blocking nodes and edges in the network. We formulate the interaction between the defender

We expand the literature on the price of anarchy (PoA) of simultaneous item auctions by considering settings with correlated values; we do this via the fundamental economic model of interdependent values (IDV). It is well-known that in multi-item settings with private values, correlated values can lead to bad PoA, which can be polynomially large in the number of agents $n$. In the more general model

We study two-sided decentralized matching markets in which participants have uncertain preferences. We present a statistical model to learn the preferences. The model incorporates uncertain state and the participants' competition on one side of the market. We derive an optimal strategy that maximizes the agent's expected payoff and calibrate the uncertain state by taking the opportunity costs into