Total: 65
The Team-maxmin equilibrium prescribes the optimal strategies for a team of rational players sharing the same goal and without the capability of correlating their strategies in strategic games against an adversary. This solution concept can capture situations in which an agent controls multiple resources - corresponding to the team members - that cannot communicate. It is known that such equilibrium always exists and it is unique (except degenerate cases) and these properties make it a credible solution concept to be used in real-world applications, especially in security scenarios. Nevertheless, to the best of our knowledge, the Team-maxmin equilibrium is almost completely unexplored in the literature. In this paper, we investigate bounds of (in)efficiency of the Team-maxmin equilibrium w.r.t. the Nash equilibria and w.r.t. the Maxmin equilibrium when the team members can play correlated strategies. Furthermore, we study a number of algorithms to find and/or approximate an equilibrium, discussing their theoretical guarantees and evaluating their performance by using a standard testbed of game instances.
Motivated by the fact that in several cases a matching in a graph is stable if and only if it is produced by a greedy algorithm, we study the problem of computing a maximum weight greedy matching on weighted graphs, termed GREEDYMATCHING. In wide contrast to the maximum weight matching problem, for which many efficient algorithms are known, we prove that GREEDYMATCHING is strongly NP-hard and APX-complete, and thus it does not admit a PTAS unless P=NP, even on graphs with maximum degree at most 3 and with at most three different integer edge weights. Furthermore we prove that GREEDYMATCHING is strongly NP-hard if the input graph is in addition bipartite. Moreover we consider three natural parameters of the problem, for which we establish a sharp threshold behavior between NP-hardness and computational tractability. On the positive side, we present a randomized approximation algorithm (RGMA) for GREEDYMATCHING on a special class of weighted graphs, called bushgraphs. We highlight an unexpected connection between RGMA and the approximation of maximum cardinality matching in unweighted graphs via randomized greedy algorithms. We show that, if the approximation ratio of RGMA is ρ, then for every ε > 0 the randomized MRG algorithm of (Aronson et al. 1995) gives a (ρ − ε)-approximation for the maximum cardinality matching. We conjecture that a tightbound for ρ is 2/3; we prove our conjecture true for four subclasses of bush graphs. Proving a tight bound for the approximation ratio of MRG on unweighted graphs (and thus also proving a tight value for ρ) is a long-standing open problem (Poloczek and Szegedy 2012). This unexpected relation of our RGMA algorithm with the MRG algorithm may provide new insights for solving this problem.
We study the Stable Invitations Problem (SIP) in which an event organizer is to invite a subset of agents (from a group of agents) to an event, subject to certain rationality criteria. In SIP, the agents have friends, enemies, and preferences on the number of attendees at the event; an agent is willing to attend the event if all friends of the agent attend, no enemy of the agent attends, and the number of attendees is acceptable to the agent. We consider two solution concepts: (1) individual rationality (everyone who is invited is willing to attend) and (2) (Nash) stability (no agent wants to deviate from the given invitation).It is known that finding an invitation of given size for either concept is NP-complete. In this work, we study the complexity of SIP on a finer scale, through the lense of parameterized complexity.For the two solution concepts and the special cases where the number of friends and/or enemies is bounded above by a constant, we show that the problems belong to different complexity classes when parameterized by the size of solutions.For instance finding an individually rational invitation of size k is W[1]-complete, yet finding a stable invitation is W[2]-complete.Moreover, when all friend and enemy relations are symmetric, finding a solution of either of the concepts becomes fixed-parameter tractable unless agents have unbounded number(s) of enemies.
Participatory budgeting enables the allocation of public funds by collecting and aggregating individual preferences; it has already had a sizable real-world impact. But making the most of this new paradigm requires a rethinking of some of the basics of computational social choice, including the very way in which individuals express their preferences. We analytically compare four preference elicitation methods -- knapsack votes, rankings by value or value for money, and threshold approval votes -- through the lens of implicit utilitarian voting, and find that threshold approval votes are qualitatively superior. This conclusion is supported by experiments using data from real participatory budgeting elections.
Bounded rationality aims to understand the effects of how limited rationality affects decision-making. The traditional models in game theory and multiagent system research, such as finite automata or unrestricted Turing machine, fall short of capturing how intelligent agents make decision in realistic applications. To address this problem, we model bounded rational agents as restricted Turing machines: restrictions on running time and on storage space. We study our model under the context of two-person repeated games. In the case where the running time of Turing machines is restricted, we show that computing the best response of a given strategy is much harder than the strategy itself. In the case where the storage space of the Turing machines is restricted, we show the best response of a space restricted strategy can not be implemented by machines within the same size (up to a constant factor). Finally, we study how these restrictions affect the set of Nash equilibria in infinitely repeated games.We show restricting the agent’s computational resources will give rise to new Nash equilibria.
The Man-In-The-Middle (MITM) attack is one of the most common attacks employed in the network hacking. MITM attackers can successfully invoke attacks such as denial of service (DoS) and port stealing, and lead to surprisingly harmful consequences for users in terms of both financial loss and security issues. The conventional defense approaches mainly consider how to detect and eliminate those attacks or how to prevent those attacks from being launched in the first place. This paper proposes a game-theoretic defense strategy from a different perspective, which aims at minimizing the loss that the whole system sustains given that the MITM attacks are inevitable. We model the interaction between the attacker and the defender as a Stackelberg security game and adopt the Strong Stackelberg Equilibrium (SSE) as the defender's strategy. Since the defender's strategy space is infinite in our model, we employ a novel method to reduce the searching space of computing the optimal defense strategy. Finally, we empirically evaluate our optimal defense strategy by comparing it with non-strategic defense strategies. The results indicate that our game-theoretic defense strategy significantly outperforms other non-strategic defense strategies in terms of decreasing the total losses against MITM attacks.
We present a new game-theoretic framework in which Bayesian players with bounded rationality engage in a Markov game and each has private but incomplete information regarding other players' types. Instead of utilizing Harsanyi's abstract types and a common prior, we construct intentional player types whose structure is explicit and induces a {\em finite-level} belief hierarchy. We characterize an equilibrium in this game and establish the conditions for existence of the equilibrium. The computation of finding such equilibria is formalized as a constraint satisfaction problem and its effectiveness is demonstrated on two cooperative domains.
Security agencies have found security games to be useful models to understand how to better protect their assets. The key practical elements in this work are: (i) the attacker can simultaneously attack multiple targets, and (ii) different targets exhibit different types of dependencies based on the assets being protected (e.g., protection of critical infrastructure, network security, etc.). However, little is known about the computational complexity of these problems, especially when there exist dependencies among the targets. Moreover, previous security game models do not in general scale well. In this paper, we investigate a general security game where the utility function is defined on a collection of subsets of all targets, and provide a novel theoretical framework to show how to compactly represent such a game, efficiently compute the optimal (minimax) strategies, and characterize the complexity of this problem. We apply our theoretical framework to the network security game. We characterize settings under which we find a polynomial time algorithm for computing optimal strategies. In other settings we prove the problem is NP-hard and provide an approximation algorithm.
In studies of social dynamics, cohesion refers to a group's tendency to stay in unity, which -- as argued in sociometry — arises from the network topology of interpersonal ties. We follow this idea and propose a game-based model of cohesion that not only relies on the social network, but also reflects individuals' social needs. In particular, our model is a type of cooperative games where players may gain popularity by strategically forming groups. A group is socially cohesive if the grand coalition is core stable. We study social cohesion in some special types of graphs and draw a link between social cohesion and a classical notion of structural cohesion by White and Harary. We then focus on the problem of deciding whether a given social network is socially cohesive and show that this problem is CoNP-complete. Nevertheless, we give two efficient heuristics for coalition structures where players enjoy high popularity and experimentally evaluate their performances.
In real life, decisions are often made under ambiguity, where it is difficult to estimate accurately the probability of each single possible consequence of a choice. However, this problem has not been solved well in existing work for the following two reasons. (i) Some of them cannot cover the Ellsberg paradox and the Machina Paradox. Thus, the choices that they predict could be inconsistent with empirical observations. (ii) Some of them rely on parameter tuning without offering explanations for the reasonability of setting such bounds of parameters. Thus, the prediction of such a model in new decision making problems is doubtful. To the end, this paper proposes a new decision making model based on D-S theory and the emotion of ambiguity aversion. Some insightful properties of our model and the validating on two famous paradoxes show that our model indeed is a better alternative for decision making under ambiguity.
The dollar auction is an auction model used to analyse the dynamics of conflict escalation. In this paper, we analyse the course of an auction when participating players are spiteful, i.e., they are motivated not only by their own profit, but also by the desire to hurt the opponent. We investigate this model for the complete information setting, both for the standard scenario and for the situation where auction starts with non-zero bids. Our results give us insight into the possible effects of meanness onto conflict escalation.
We study the problem of computing an Extensive-Form Perfect Equilibrium (EFPE) in 2-player games. This equilibrium concept refines the Nash equilibrium requiring resilience with respect to a specific vanishing perturbation, representing mistakes of the players at each decision node. The scientific challenge is intrinsic to the EFPE definition: it requires a perturbation over the agent form, but the agent form is computationally inefficient due to the presence of highly nonlinear constraints. We show that the sequence form can be exploited in a non-trivial way and that, for general-sum games, finding an EFPE is equivalent to solving a suitably perturbed linear complementarity problem. We prove that Lemke's algorithm can be applied, showing that computing an EFPE is PPAD-complete. In the notable case of zero-sum games, the problem is in FP and can be solved by linear programming. Our algorithms also allow one to find a Nash equilibrium when players cannot perfectly control their moves, being subject to a given execution uncertainty, as is the case in most realistic physical settings.
Consider a situation with n agents or players, where some of the players form a coalition with a certain collective objective. Simple games are used to model systems that can decide whether coalitions are successful (winning) or not (losing). A simple game can be viewed as a monotone boolean function. The dimension of a simple game is the smallest positive integer d such that the simple game can be expressed as the intersection of d threshold functions, where each threshold function uses a threshold and n weights. Taylor and Zwicker have shown that d is bounded from above by the number of maximal losing coalitions. We present two new upper bounds both containing the Taylor-Zwicker bound as a special case. The Taylor-Zwicker bound implies an upper bound of (n choose n/2). We improve this upper bound significantly by showing constructively that d is bounded from above by the cardinality of any binary covering code with length n and covering radius 1. This result supplements a recent result where Olsen et al. showed how to construct simple games with dimension |C| for any binary constant weight SECDED code C with length n. Our result represents a major step in the attempt to close the dimensionality gap for simple games.
Much recent work in the AI community concerns algorithms for computing optimal mixed strategies to commit to, as well as the deployment of such algorithms in real security applications. Another possibility is to commit not to play certain actions. If only one player makes such a commitment, then this is generally less powerful than completely committing to a single mixed strategy. However, if players can alternatingly commit not to play certain actions and thereby iteratively reduce their strategy spaces, then desirable outcomes can be obtained that would not have been possible with just a single player committing to a mixed strategy. We refer to such a setting as a disarmament game. In this paper, we study disarmament for two-player normal-form games. We show that deciding whether an outcome can be obtained with disarmament is NP-complete (even for a fixed number of rounds), if only pure strategies can be removed. On the other hand, for the case where mixed strategies can be removed, we provide a folk theorem that shows that all desirable utility profiles can be obtained, and give an efficient algorithm for (approximately) obtaining them.
We introduce a new class of mechanisms, robust mechanisms, that is an intermediary between ex-post mechanisms and Bayesian mechanisms. This new class of mechanisms allows the mechanism designer to incorporate imprecise estimates of the distribution over bidder valuations in a way that provides strong guarantees that the mechanism will perform at least as well as ex-post mechanisms, while in many cases performing better. We further extend this class to mechanisms that are with high probability incentive compatible and individually rational, ε-robust mechanisms. Using techniques from automated mechanism design and robust optimization, we provide an algorithm polynomial in the number of bidder types to design robust and ε-robust mechanisms. We show experimentally that this new class of mechanisms can significantly outperform traditional mechanism design techniques when the mechanism designer has an estimate of the distribution and the bidder’s valuation is correlated with an externally verifiable signal.
We present three results on the complexity of MINIMAX APPROVAL VOTING. First, we study MINIMAX APPROVAL VOTING parameterized by the Hamming distance d from the solution to the votes. We show MINIMAX APPROVAL VOTING admits no algorithm running in time O⋆(2o(d log d), unless the Exponential Time Hypothesis (ETH) fails. This means that the O⋆(d2d) algorithm of Misra et al. (AAMAS 2015) is essentially optimal. Motivated by this, we then show a parameterized approximation scheme, running in time O⋆((3/ε)2d), which is essentially tight assuming ETH. Finally, we get a new polynomial-time randomized approximation scheme for MINIMAX APPROVAL VOTING, which runs in time nO(1/ε2·log(1/ε))· poly(m), almost matching the running time of the fastest known PTAS for CLOSEST STRING due to Ma and Sun (SIAM J. Comp. 2009).
The optimal pricing problem is a fundamental problem that arises in combinatorial auctions. Suppose that there is one seller who has indivisible items and multiple buyers who want to purchase a combination of the items. The seller wants to sell his items for the highest possible prices, and each buyer wants to maximize his utility (i.e., valuation minus payment) as long as his payment does not exceed his budget. The optimal pricing problem seeks a price of each item and an assignment of items to buyers such that every buyer achieves the maximum utility under the prices. The goal of the problem is to maximize the total payment from buyers. In this paper, we consider the case that the valuations are submodular. We show that the problem is computationally hard even if there exists only one buyer. Then we propose approximation algorithms for the unlimited budget case. We also extend the algorithm for the limited budget case when there exists one buyer and multiple buyers collaborate with each other.
A repeated game is a formal model for analyzing cooperation in long-term relationships, e.g., in the prisoner's dilemma. Although the case where each player observes her opponent's action with some observation errors (imperfect private monitoring) is difficult to analyze, a special type of an equilibrium called belief-free equilibrium is identified to make the analysis in private monitoring tractable. However, existing works using a belief-free equilibrium show that cooperative relations can be sustainable only in ideal situations. We deal with a generic problem that can model both the prisoner's dilemma and the team production problem. We examine a situation with an additional action that is dominated by another action. To our surprise, by adding this seemingly irrelevant action, players can achieve sustainable cooperative relations far beyond the ideal situations. More specifically, we identify a class of strategies called one-shot punishment strategy that can constitute a belief-free equilibrium in a wide range of parameters. Moreover, for a two-player case, the obtained welfare matches a theoretical upper bound.
In this paper, we analyze an emerging economic form, called fans economy, in which a fan donates money to the host and gets allocated proportional to the amount of his donation (normalized by the overall amount of donation). Fans economy is the major way live streaming apps monetize and includes a number of popular economic forms ranging from crowdfunding to mutual fund. We propose an auction game, coined all-pay auctions with proportional allocation (APAPA), to model the fans economy and analyze the auction from the perspective of revenue. Comparing to the standard all-pay auction, which normally has no pure Nash-Equilibrium in the complete information setting, we solve the pure Nash-Equilibrium of the APAPA in closed form and prove its uniqueness. Motivated by practical concerns, we then analyze the case where APAPA is equipped with a reserve and show that there might be multiple equilibria in this case. We give an efficient algorithm to compute all equilibria in this case. For either case, with or without reserve, we show that APAPA always extracts revenue that 2-approximates the second-highest valuation. Furthermore, we conduct experiments to show how revenue changes with respect to different reserves.
We consider a strategic variant of the knapsack problem: the items are owned by agents, and agents can misrepresent their sets of items---either by hiding items (understating), or by reporting fake ones (overstating). Each agent's utility equals the total value of her items included in the knapsack. We wish to maximize social welfare, and attempt to design mechanisms that lead to small worst-case approximation ratios at equilibrium. We provide a randomized mechanism with attractive strategic properties: it has a price of anarchy of 2 for Bayes-Nash and coarse correlated equilibria. For overstating-only agents, it becomes strategyproof, and has a matching lower bound. For the case of two understating-only agents, we provide a specialized randomized strategyproof 1.522-approximate mechanism, and a lower bound of 1.09. When all agents but one are honest, we provide a deterministic strategyproof 1.618-approximate mechanism with a matching lower bound. The latter two mechanisms are also useful in problems beyond the one in consideration.
One of the fundamental research challenges in network science is the centrality analysis, i.e., identifying the nodes that play the most important roles in the network. In this paper, we focus on the game-theoretic approach to centrality analysis. While various centrality indices have been proposed based on this approach, it is still unknown what distinguishes this family of indices from the more classical ones. In this paper, we answer this question by providing the first axiomatic characterization of game-theoretic centralities. Specifically, we show that every centrality can be obtained following the game-theoretic approach, and show that two natural classes of game-theoretic centrality can be characterized by two intuitive properties pertaining to Myerson's notion of Fairness.
We present a complete algorithm for finding an epsilon-Nash equilibrium, for arbitrarily small epsilon, in games with more than two players. The method improves the best-known upper bound with respect to the number of players n, and it is the first implemented algorithm, to our knowledge, that manages to solve all instances. The main components of our tree-search-based method are a node-selection strategy, an exclusion oracle, and a subdivision scheme. The node-selection strategy determines the next region (of the strategy profile probability vector space) to be explored — based on the region's size and an estimate of whether the region contains an equilibrium. The exclusion oracle provides a provably correct sufficient condition for there not to exist an equilibrium in the region. The subdivision scheme determines how the region is split if it cannot be excluded. Unlike the well-known incomplete methods, our method does not need to proceed locally, which avoids it getting stuck in a local minimum---in the space of players' regrets — that may be far from any actual equilibrium. The run time grows rapidly with the game size; this reflects the dimensionality of this difficult problem. That suggests a hybrid scheme where one of the relatively fast prior incomplete algorithms is run, and if it fails to find an equilibrium, then our method is used.
We consider Max-min Share (MmS) fair allocations of indivisible chores (items with negative utilities). We show that allocation of chores and classical allocation of goods (items with positive utilities) have some fundamental connections but also differences which prevent a straightforward application of algorithms for goods in the chores setting and vice-versa. We prove that an MmS allocation does not need to exist for chores and computing an MmS allocation - if it exists - is strongly NP-hard. In view of these non-existence and complexity results, we present a polynomial-time 2-approximation algorithm for MmS fairness for chores. We then introduce a new fairness concept called optimal MmS that represents the best possible allocation in terms of MmS that is guaranteed to exist. We use connections to parallel machine scheduling to give (1) a polynomial-time approximation scheme for computing an optimal MmS allocation when the number of agents is fixed and (2) an effective and efficient heuristic with an ex-post worst-case analysis.
One of the goals of a cooperative game is to compute a valuedivision to the players from which they have no incentive todeviate. This concept is formalized as the notion of the core.To obtain a value division that motivates players to cooperate to a greater extent or that is more robust under noise, the notions of the strong least core and the weak least core have been considered. In this paper, we characterize the strong and the weak least cores of supermodular cooperative games using the theory of minimizing crossing submodular functions. We then apply our characterizations to two representative supermodular cooperative games, namely, the induced subgraph game generalized to hypergraphs and the airport game. For these games, we derive explicit forms of the strong and weak least core values, and provide polynomial-time algorithms that compute value divisions in the strong and weak least cores.
We study the problem of fair division of a heterogeneous resource among strategic players. Given a divisible heterogeneous cake, we wish to divide the cake among n players in a way that meets the following criteria: (I) every player(weakly) prefers his allocated cake to any other player’s share (such notion is known as envy-freeness), (II) the mechanism is strategy-proof (truthful), and (III) the number of cuts made on the cake is minimal. We provide methods, namely expansion process and expansion process with unlocking, for dividing the cake under different assumptions on the valuation functions of the players.