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We present and discuss a novel language restriction for modal logics for multiagent systems, called modal context restriction, that reduces the complexity of the satisfiability problem from EXPTIME complete to NPTIME complete. We focus on BDI multimodal logics that contain fix-point modalities like common beliefs and mutual intentions together with realism and introspection axioms. We show how this combination of modalities and axioms affects complexity of the satisfiability problem and how it can be reduced by restricting the modal context of formulas.

Consider the practical goal of making a desired action profile played, when the planner can only change the payoffs, bound by stringent constraints. Applications include motivating people to choose the closest school, the closest subway station, or to coordinate on a communication protocol or an investment strategy. Employing subsidies and tolls, we adjust the game so that choosing this predefined action profile becomes strictly dominant. Inspired mainly by the work of Monderer and Tennenholtz, where the promised subsidies do not materialise in the not played profiles, we provide a fair and individually rational game adjustment, such that the total outside investments sum up to zero at any profile, thereby facilitating easy and frequent usage of our adjustment without bearing costs, even if some players behave unexpectedly. The resultant action profile itself needs no adjustment. Importantly, we also prove that our adjustment minimises the general transfer among all such adjustments, counting the total subsidising and taxation.

The History of the Depot Buildings at 8 Łazienkowska Street (Warsaw) in the Years 1920–1975 As a result of World War I, the Polish lands were severely destroyed, and the population was poor. The widespread poverty, supply problems, and high prices led to the establishment of the Warsaw Municipal Supply Facilities (Miejskie Zakłady Zaopatrzenia Warszawy/MZZW). The task of the MZZW fleet was to ensure the supply of food and essential goods to the poorest social groups. Thus, the municipality bypassed intermediaries and their high margins. The articles were distributed through a network of municipal stores. The article describes the history of the buildings at 8 Łazienkowska Street, erected over a hundred years ago, now no longer extant. It was one of the first facilities built by the Capital City of Warsaw shortly after regaining independence. The described complex of buildings was designed from scratch, as the first such facility in Warsaw, meant only for trucks and not for horse traction vehicles. The second owner of the described development was the Municipal Tram and Bus Company, which took over the depot along with the rolling stock. The change of ownership was caused by the seemingly unrelated crash of the New York Stock Exchange. Before the war, Warsaw buses were parked there, the fleet of which was growing rapidly. The defensive war in September 1939 and the occupation removed buses from the streets of Warsaw. After the war, the depot – destroyed in 45% during the Warsaw Uprising – was rebuilt, becoming a symbol of the new socialist Poland. Following the example of the cities of Soviet Russia, with the help of their specialists and trolleybuses, the same service was launched in Warsaw. The depot became the first public transport base to be rebuilt after the war. A trolleybus network plan for the city of Lublin was created within its walls. Before the buildings were demolished, it was once again briefly a bus depot, and, in the end, it played a somewhat important role in the construction of the Łazienkowska Route, becoming the construction base No. 5 for the aforementioned investment.

We propose and study a strategic model of hiding in a network, where the network designer chooses the links and his position in the network facing the seeker who inspects and disrupts the network. We characterize optimal networks for the hider, as well as equilibrium hiding and seeking strategies on these networks. We show that optimal networks are either equivalent to cycles or variants of a core-periphery networks where every node in the periphery is connected to a single node in the core., 27 pages

Both authors thank the European Research Area Complexity Net for financial support. Marcin Dziubi nskiwas supported by the Strategic Resilience of Networks project realized within the Homing Plus program ofthe Foundation for Polish Science and was co-financed by the European Union from the Regional Devel-opment Fund within Operational Programme Innovative Economy (grants for innovation). Sanjeev Goyalacknowledges financial support from a Keynes Fellowship and the Cambridge INET Institute.

This paper develops a theoretical framework for the study of war and conquest. The analysis highlights the role of three factors – the technology of war, resources, and contiguity network – in shaping the dynamics of appropriation and the formation of empires.

We study a generalization of hide and seek game of von Neumann [14], where each player has one or more resources. We characterize the value and Nash equilibria of such games in terms of their unidimensional marginal distributions. We propose a \(\mathcal {O}(n \log (n))\) time algorithm for computing unidimensional marginal distributions of equilibrium strategies and a quadratic time algorithm for computing mixed strategies given the margins. The characterization allows us to establish a number of interesting qualitative features of equilibria.

Building on our diverse research traditions in the study of reasoning, language and communication, the Polish School of Argumentation integrates various disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Our primary goal is to craft a methodological programme and establish organisational infrastructure: this is the first key step in facilitating and fostering our research movement, which joins people with a common research focus, complementary skills and an enthusiasm to work together. This statement—the Manifesto—lays the foundations for the research programme of the Polish School of Argumentation.

Infrastructure networks are a key feature of an economy. Their functionality depends on the connectivity and sizes of different components and they face a variety of threats, from natural disasters to intelligent attacks. How should networks be defended and designed to ensure the best functionality? We develop a model to study this question. There are two players, the Designer and the Adversary. The Designer forms costly links among n given nodes and chooses to protect some of them at a cost. The Adversary then allocates resources to attack nodes. Successful attack on a node leads to its elimination. We study sub-game perfect equilibria of this game. Our main finding is that if defence is affordable and reliable, then the network is sparse and heterogeneous, and either centrally or fully protected. On the other hand, if defence is relatively costly compared to linking, then dense and homogeneous networks arise in equilibrium.

Osborne shows that for almost all distributions of voters' preferences, a pure strategy Nash equilibrium does not exist in the classical Hotelling-Downs model of electoral competition with free entry. We show that equilibrium is generically possible if in addition one allows voters an option to announce their candidacy to compete side-by-side with office-seeking players. The model studied in this paper renders Osborne and the celebrated citizen-candidate model a la Osborne and Slivinski as two extreme cases. We characterize the equilibrium set with two central questions: (i) can there be equilibria where only voters contest? and (ii) are equilibria with contesting office-seeking players possible? We also show that in our general setting, extremists are typically voter-candidates so that in every two-party contest, office-seeking politicians stay out of competition.

We study Nash equilibria of a symmetric Colonel Blotto and Colonel Lotto games. In these game two players, with \(N \ge 1\) units of resources each, distribute their resources simultaneously across \(K \ge 2\) battlefields. We introduce a characteristic of equilibria in this game called spectrum which stands for the fraction of battlefields receiving given numbers of units. We provide complete characterization of spectra of Nash equilibria in Colonel Lotto game as well as necessary conditions on spectra of Nash equilibria in Colonel Blotto game for the case of \({K}\! \mid \!{N}\).

Players are endowed with resources. A player can engage in conflict with others to enlarge his resources. The set of potential conflicts is defined by a contiguity network. Players are farsighted and aim to maximize their resources. They decide on whether to wage war or remain peaceful. The winner of a war takes control of the loser's node and resources; he then decides on whether to wage war against other neighbours, or to stay peaceful. The game ends when either all players choose to be peaceful or when only one player is left. We study the influence of the technology of conflict and the structure of the network on war and peace. Our first result identifies a threshold property in the technology of conflict: above this threshold, every ruler wishes to wage war and, eventually, there is a hegemon. Below the threshold, resources and networks determine the prospects for peace and the number of kingdoms. We develop sufficient conditions for war and provide examples with lasting peace.

Conflict remains a central element in human interaction. Networks - social, economic and infrastructure - are a defining feature of society. The two intersect in a wide range of empirical contexts. This motivates the recent interest in con flict and networks. The aim of the survey is to present the general themes, provide a survey of the nascent research and point to a number of interesting open questions.

We consider the Hotelling-Downs model with n 2 oce seeking candidates and runo voting. We show that Nash equilibria in pure strategies always exist and that there are typically multiple equilibria, both convergent (all candidates are located at the median) and divergent (candidates locate at distinct positions), though only divergent equilibria are robust to free entry. Moreover, two-policy equilibria exist under any distribution of voters’ ideal policies, while equilibria with more than two policies exist generically but under restrictive conditions that we characterize.

In an evolutionary model, players from a given population meet randomly in pairs each instant to play a coordination game. At each instant, the learning model used is determined via some replicator dynamics that respects payoff fitness. We allow for two such models: a belief-based best-response model that uses a costly predictor, and a costless reinforcement-based one. This generates dynamics over the choice of learning models and the consequent choices of endogenous variables. We report conditions under which the long run outcomes are efficient (or inefficient) and they support the exclusive use of either of the models (or their co-existence).

In this paper we continue our research in computational complexity of fragments of a particular belief-desire-intention (BDI) logic for cooperative problem solving (CPS) called TeamLog. The logic in question combines propositional multi-modal logic to express static aspects of CPS with propositional dynamic logic used for dynamic aspects of CPS. We concentrate here on the static fragment of the logic. The complexity of the satisfiability problem for the static fragment of TeamLog is known to be EXPTIME-complete, even if modal depth is bounded by a constant ≥ 2. We show a restriction on modal context of formulas that makes the problem PSPACE-complete without setting boundary on modal depth. Bounding modal depth, additionally, leads to NPTIME-completeness.

Two players are endowed with resources for setting up N locations on K line segments of identical length, with N > K ≥ 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival’s. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that, if an analogous game is played on disjoint circles, the second mover advantage is in place only if K = 1, while for K > 1 both players have a tying strategy. It was also shown that these results hold for line segments of identical length when rules of the game additionally require players to take exactly one location in the first round. In this paper we show that the second mover advantage is still in place for K ≥ 1 and 2K − 1 ≤ N, even if the additional restriction is dropped, while K ≤ N < 2K − 1 results in the first mover advantage. Our results allow us to draw conclusions about a natural variant of the game, where the resource mobility constraint is more stringent so that in each round each player chooses a single location and we show that the second mover advantage re-appears for K ≤ N < 2K − 1 if K is an even number. In all the cases the losing player has a strategy guaranteeing him arbitrarily small loss.

Two players are endowed with resources for setting up N locations on K identical circles, with N greater than K which is greater or equal 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. They face a resource mobility constraint such that not all N locations can be placed in the first round. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that for K = 1, the second mover always has a winning strategy in this game. In this paper we show that with K > 1, the second mover advantage disappears as in this case both players have a tying strategy. We also study a natural variant of this game where the resource mobility constraint is more stringent so that in each round each player chooses a single location where we show that the second mover advantage re-appears. We suggest some Nash equilibrium configurations of locations in both versions of the game.

We study a problem of a defender who wants to protect a network against contagious attack by an intelligent adversary. The defender could only protect a fixed number of nodes and does not know the network. Each of the nodes in the network does not know the network either, but knows his/her neighbours only. We propose an incentive compatible mechanism allowing the defender to elicit information about the whole network. The mechanism is efficient in the sense that under truthful reports it assigns the protection optimally.

Individuals derive benefits from being connected to others: computer users benefit from sharing content, criminals benefit from cooperating. Connections, however, may transmit external threats. A virus may spread through a computer network. An investigation may dismantle entire criminal organization. Given agents’ individual incentives to protect, which network(s) should be chosen to maximize agents’ welfare? We consider the tension between the value of being connected and the exposure to contagion when a protection technology is available. There are (n + 2) ‘players’. The designer first chooses the network over the n nodes. Given this network, the nodes (simultaneously) choose whether to protect or not; protection is costly. Finally, the adversary chooses a node to attack. If the attacked node is not protected, then this node and all nodes with a path to the attacked node through unprotected nodes are eliminated. Nodes derive benefits from their connectivity: a surviving node gets, as a gross payoff, an equal share of the value of its surviving component. Component value is a convex and increasing function of its size. Node’s net payoffs are equal to its connectivity payoffs less the cost of protection. The designer seeks to maximize the sum of nodes’ payoffs. The adversary aims to minimize connectivity-related payoffs. The first best design and defence profile that a central planner would choose is as follows. For low costs, all nodes is protected and the network is connected. For intermediate costs, a centrally protected star is chosen. The adversary eliminates a spoke. If costs are high, protection is dropped and network is split into several components. The adversary removes a largest one. A number of problems arise for the designer when he cannot control defence decisions. First, a node does not internalize the benefits accruing to others from its own protection. Thus, it is possible that the center

We consider the Hotelling-Downs model with n ≥ 2 office seeking candidates and runoff voting. We show that Nash equilibria in pure strategies always exist and that there are typically multiple equilibria, both convergent (all candidates are located at the median) and divergent (candidates locate at distinct positions), though only divergent equilibria are robust to free entry. Moreover, two-policy equilibria exist under any distribution of voters' ideal policies, while equilibria with more than two policies exist generically but under restrictive conditions that we characterize. In this sense, our analysis suggests that two-policy equilibria are the most prominent outcomes.

In this paper we study a model of political competition where citizens vote sincerely and candidates may be either citizens or Downsian politicians. The model extends the citizen-candidate model proposed by Osborne and Slivinski [1996] by including Downsian politicians similar to those studied by Osborne [1993]. We give necessary and sufficient conditions for existence, together with complete characterisation, of one party and two party Nash equilibria in our model. An important feature, in view of the Duverger's Law, of the two-party equilibrium is that these equilibria cannot have any Downsian contestant. Moreover, we compare our model with that studied by Osborne and Slivinski [1996], showing that in both cases there exist po- litical configurations that can appear in one of the models only. We show also that in our settings it is possible to have Nash equilibria with Downsian candidates, without requiring to have very restrictive constraints on the dis- tribution function. We also argue that as the number of parties in equilibrium increases, the `likelihood' of an ideology driven citizen-candidate winning the elections and running the government falls. Finally we argue that in any equilibrium extremist parties proposing their policies uniquely are typically ideology-driven as well.

Two players are endowed with resources for setting up N locations on K open curves of identical lengths, with N > K greater than or equal to 1. The players alternately choose these locations (possibly in batches of more than one in each round) in order to secure the area closer to their locations than that of their rival's. The player with the highest secured area wins the game and otherwise the game ends in a tie. Earlier research has shown that, if an analogical game is played on disjoint closed curves, the second mover advantage is in place only if K = 1, while for K > 1 both players have a tying strategy. It was also shown that this results hold for open curves of identical lengths when rules of the game additionally require players to take exactly one location in the rst round. In this paper we show that the second mover advantage is still in place for K greater than or equal to 1 and 2K -1 less than or equal to N, even if the additional restriction is dropped, while K is less than or euqal to N

Theories of multiagent systems (MAS), in particular those based on modal logics, often suffer from a high computational complexity. This is due in part to the combination of agents' individual attitudes (beliefs, goals and intentions), and even more importantly to the presence of group attitudes, such as common belief and collective intention.

Our previous research presents a methodology of cooperative problem solving for belief-desire-intention (BDI) systems, based on a complete formal theory called TEAMLOG. This covers both a static part, defining individual, bilateral and collective agent attitudes, and a dynamic part, describing system reconfiguration in a dynamic, unpredictable environment. In this paper, we investigate the complexity of the satisfiability problem of the static part of TEAMLOG, focusing on individual and collective attitudes up to collective intention. Our logics for teamwork are squarely multi-modal, in the sense that different operators are combined and may interfere. One might expect that such a combination is much more complex than the basic multi-agent logic with one operator, but in fact we show that it is not the case: the individual part of TEAMLOG is PSPACE-complete, just like the single modality case. The full system, modelling a subtle interplay between individual and group attitudes, turns out to be EXPTIME-complete, and remains so even when propositional dynamic logic is added to it.

The paper studies an evolutionary model where players from a given population are randomly matched in pairs each period to play a coordination game. At each instant, a player can choose to adopt one of the two possible behavior rules, called the rational rule and the aspiring rule, and then take actions prescribed by the chosen rule. The choice between the two rules depends upon their relative performance in the immediate past. We show that there are two stable long run outcomes where either the rational rule becomes extinct and all players in the population achieve full efficiency, or that both the behavior rules co-exist and there is only a partial use of efficient strategies in the population. These findings support the use of the aspiration driven behavior in several existing studies and also help us take a comparative evolutionary look at the two rules in retrospect.

Our previous research presents a methodology of cooperative problem solving for BDI systems, based on a complete formal theory. This covers both a static part, defining individual, bilateral and collective agent attitudes, and a dynamic part, describing system reconfiguration in a dynamic, unpredictable environment. In this paper, we investigate the complexity of the satisfiability problem of the static part of our theory, focusing on individual and collective attitudes up to collective intention. Our logics for teamwork are squarely multi-modal, in the sense that different operators are combined and may interfere. One might expect that such a combination is much more complex than the basic multi-agent logic with one operator, but in fact we show that the individual part of our theory of teamwork is PSPACE-complete. The full system, modeling a subtle interplay between individual and group attitudes, turns out to be EXPTlME-complete, and remains so even if propositional dynamic logic is added to it.

We study a non-symmetric variant of General Lotto games introduced in Hart (Int J Game Theory 36:441–460, 2008). We provide a complete characterization of optimal strategies for both players in non-symmetric discrete General Lotto games, where one of the players has an advantage over the other. By this we complete the characterization given in Hart (Int J Game Theory 36:441–460, 2008), where the strategies for symmetric case were fully characterized and some of the optimal strategies for the non-symmetric case were obtained. We find a group of completely new atomic strategies, which are used as building components for the optimal strategies. Our results are applicable to discrete variants of all-pay auctions.