Extensive form games

A leading solution concept in the evolutionary study of extensive-form games is Selten's (1983) [16] notion of limit ESS. This note demonstrates that a limit ESS does not imply neutral stability, and that it may be dynamically unstable (almost any small perturbation takes the population away). These problems arise due to an implicit assumption that "mutants" are arbitrarily rare relative to "trembling" incumbents. Finally, I present a novel definition that solves this issue and has appealing properties.

Negotiations in which participants exchange offers based on their chosen positions can be extended to include dialogue about their interests. Revelation of negotiators' interests allows them to make more acceptable offers and perhaps propose possible alternative approaches toward each other's interests, both of which may result in mutually and individually beneficial outcomes. However, it can also expose their strategies, and possibly their dependencies on other negotiators toward the achievement of their goals. Revealing this information can leave them vulnerable to extortion or retribution, but it can also be used to gain sympathy or build a relationship of trust and reciprocity.

There were eight invited talks: Andrea Asperti (Bologna), Formalizing Turing Machines. Hans van Ditmarsch (Sevilla), Quantifying over information change. Laura Kallmeyer (Düsseldorf), Syntax-driven semantic frame composition in lexicalized tree adjoining grammars. George Metcalfe (Bern), Admissible rules: From characterizations to applications. Anca Muscholl (Bordeaux), On distributed control and monitoring. Andre Nies (Auckland), Interactions of computability and randomness. Nicole Schweikardt (Frankfurt), On the expressive power of logics with invariant uses of arithmetic predicates. Peter Selinger (Halifax), Logical methods in quantum information theory.

Motivated by the organization of online service systems, we study models for throughput scheduling in a decentralized setting. In throughput scheduling, we have a set of jobs j with values wj, processing times pj, and release dates rj and deadlines and dj, to be processed nonpreemptively on a set of unrelated machines. The goal is to maximize the total value of jobs scheduled within their time window [rj, dj]. While several approximation algorithms with different performance guarantees exist for this and related models, we are interested in the situation where subsets of servers are governed by selfish players. We give a universal result that bounds the price of decentralization, in the sense that any local α-approximation algorithms, α ≥ 1, yield equilibria that are at most a factor (α + 1) away from the global optimum, and this bound is tight. For models with identical machines, we improve this bound to α √ e/(α √ e − 1) ≈ (α + 1/2), which is shown to be tight, too. We also address some variations of the problem.

This paper introduces a new Negotiating Agent for automated negotiation on continuous domains and without considering a specified deadline. The agent bidding strategy relies on Monte Carlo Tree Search, which is a trendy method since it has been used with success on games with high branching factor such as Go. It uses two opponent modeling techniques for its bidding strategy and its utility: Gaussian process regression and Bayesian learning. Evaluation is done by confronting the existing agents that are able to negotiate in such context: Random Walker, Tit-fortat and Nice Tit-for-Tat. None of those agents succeeds in beating our agent; moreover the modular and adaptive nature of our approach is a huge advantage when it comes to optimize it in specific applicative contexts.

The success of human civilization is rooted in our ability to cooperate by communicating and making joint plans. We study how artificial agents may use communication to better cooperate in Diplomacy, a long-standing AI challenge. We propose negotiation algorithms allowing agents to agree on contracts regarding joint plans, and show they outperform agents lacking this ability. For humans, misleading others about our intentions forms a barrier to cooperation. Diplomacy requires reasoning about our opponents' future plans, enabling us to study broken commitments between agents and the conditions for honest cooperation. We find that artificial agents face a similar problem as humans: communities of communicating agents are susceptible to peers who deviate from agreements. To defend against this, we show that the inclination to sanction peers who break contracts dramatically reduces the advantage of such deviators. Hence, sanctioning helps foster mostly truthful communication, despite conditions that initially favor deviations from agreements. Coordination, cooperation and negotiation play a key role in our everyday lives, from small-scale problems such as safely driving on roads and scheduling meetings to large-scale efforts such as international trade or mediating peace. A key driver to the success of humans as a species is our ability to cooperate with others 1,2. Systems based on artificial intelligence (AI) control a growing part of our lives, from personal assistants to high-stake decisions such as authorizing loans or automated job market screening 3,4. Cooperation and negotiation are central to AI 5-11 , and AI systems already affect human trade and negotiation through algorithmic trading and bidding 10,12-16. It is thus imperative that we endow our AI systems with the tools to coordinate and negotiate with others 3,7,11,17,18. Game playing has been a focus area of AI since its inception. Progress on search, reinforcement learning, and game theory 9,19-21 led to successes in Chess 22 , Go 23 , Poker 24 , control 25 , and video games 26,27. However, the majority of such work deals with two-player games that are fully competitive (zero-sum), which are mathematically easier to analyze 18,28 , but cannot capture alliance formation and negotiation. Similarly, work on games where agent goals are fully aligned 29,30 , or two teams of agents engaged in a competition 27,31,32 , lacks the need to negotiate. In contrast, many real-life domains require negotiation as the goals of participants only partially align. These domains exhibit tensions between cooperation and competition 7,33-35 , making them harder to tackle using AI agents 21,36,37. Communication has a key role in such settings as it enables us to share beliefs, goals and intents with others, allowing us to negotiate, form alliances and find mutually beneficial agreements 10. Diplomacy 38 is a prominent 7-player board game that focuses on communication, cooperation and negotiation. An introduction to the rules of Diplomacy is given in Supplementary Note 1. Diplomacy is played on a map of Europe partitioned into provinces, some of which are special and marked as Supply Centers. Each player attempts to own the majority of the supply centers, and controls multiple units (armies or fleets). A unit may support another unit (owned by the same or another player), allowing it to overcome resistance by other units. Due to the inter-dependencies between units, players stand to gain by

Logic and the foundations of the theory of games and decisions: introduction This special issue of Research in Economics contains a selection of papers presented at the fifth conference on "Logic and the Foundations of the Theory of Games and Decisions" (LOFT5), which took place in Torino at the International Center for Economics Research (ICER) in June 2002. 1 The LOFT conferences have been a regular biannual event since 1994. With the exception of the first conference, which was hosted by the Centre International de Recherches Mathematiques in Marseille, the LOFT events have taken place at ICER and would not have been possible without ICER's generous support and hospitality. The LOFT conferences are interdisciplinary events that bring together researchers from a variety of fields: computer science, economics, game theory, logic, mathematical psychology, philosophy and statistics. There is substantial overlap between the LOFT community and the community of researchers who are active in another regular, biannual event, namely the conferences on Theoretical Aspects of Rationality and Knowledge (TARK), which have a longer history than the LOFT conferences. 2 In its original conception, LOFT had as its central theme the application of logic, in particular modal epistemic logic, to foundational issues in the theory of games and individual decision-making. Epistemic considerations have been central to game theory for a long time. For example, work has been done on the role of beliefs in refinements of Nash equilibrium since the 1970s and much has been written on common knowledge and common belief since Aumann's seminal paper during that time. The expression interactive epistemology has been used in the game-theory literature to refer to the analysis of what individuals involved in a strategic interaction know about facts concerning the external world as well as facts concerning each other's knowledge and beliefs. What is relatively new is the realization that the tools and methodology that were used in game theory are

WoLLIC (http://wollic.org) is a series of workshops which started in 1994 with the aim of fostering interdisciplinary research in pure and applied logic. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation, and yet is small enough to allow for concrete and useful interaction among participants. Previous versions were held at:

This paper introduces a new negotiating agent model for automated negotiation. We focus on applications without time pressure with multidimensional negotiation on both continuous and discrete domains. The agent bidding strategy relies on Monte Carlo Tree Search, which is a trendy method since it has been used with success on games with high branching factor such as Go. It also exploits opponent modeling techniques thanks to Gaussian process regression and Bayesian learning. Evaluation is done by confronting the existing agents that are able to negotiate in such context: Random Walker, Tit-for-tat and Nice Titfor-Tat. None of those agents succeeds in beating our agent. Also, the modular and adaptive nature of our approach is a huge advantage when it comes to optimize it in specific applicative contexts.

In epistemic logic, Kripke structures are used to model the distribution of information in a multi-agent system. In this paper, we present an approach to quantifying how much information each particular agent in a system has, or how important the agent is, with respect to some fact represented as a goal formula. It is typically the case that the goal formula is distributed knowledge in the system, but that no individual agent alone knows it. It might be that several different groups of agents can get to know the goal formula together by combining their individual knowledge. By using power indices developed in voting theory, such as the Banzhaf index, we get a measure of how important an agent is in such groups. We analyse the properties of this notion of information-based power in detail, and characterise the corresponding class of voting games. Although we mainly focus on distributed knowledge, we also look at variants of this analysis using other notions of group knowledge. An adv...

We first discuss two caveats to the identification of higher-order rationality presented in Kneeland [9, Econometrica, 83, (2015), 2065‐2079]. We then propose an alternative identification approach, which not only does not require an assumption but also delivers the same identification outcome as in Kneeland [9]. Finally, our identification approach can be implemented using the chain game, which is considerably simpler than Kneeland’s ring game [9].

When contracts are incomplete or unenforceable, inefficient levels of investment may occur because of holdup. If individuals care for negative reciprocity, these problems may be reduced, as revenge becomes a credible threat. However, negative reciprocity has this effect only when the investor holds the rights of control of the investment proceeds. We explore this issue analytically, deriving predictions for holdup games which differ as regards assignment of rights of control. We also test and support these predictions in an experiment.

This paper presents the Deniz agent, that has been specifically designed to support human negotiators in their bidding. The design of Deniz is done with the criteria of robustness and the availability of small data, due to a small number of negotiation rounds in mind. Deniz's bidding strategy is based on an existing optimal concession strategy that concedes in relation to the expected duration of the negotiation. This accounts for the small data and small number of rounds. Deniz deploys an adaptive behaviour-based mechanism to make it robust against exploitation. We tested Deniz against typical bidding strategies and against human negotiators. Our evaluation shows that Deniz is robust against exploitation and gains statistically significantly higher utilities than human test subjects, even though it is not designed specifically to get the highest utility against humans.

We consider an oligopolistic market game, in which the players are competing ®rms in the same market of a homogeneous consumption good. The consumer side is represented by a ®xed demand function. The ®rms decide how much to produce of a perishable consumption good, and they decide upon a number of information signals to be sent into the population in order to attract customers. Due to the minimal information provided, the players do not have a well-speci®ed model of their environment. Our main objective is to characterize the adaptive behavior of the players in such a situation.

Preface Johan van Benthem Research lines are like those enticing hiking trails that lure us far and wide into Nature, always across the next ridge into the next valley. Often they do not run in the direction that we had planned, and often also, they present us with surprising encounters. Every year, the Dynamics Yearbook shows where the trails in our community have taken us, and whom we met on the way. In this volume, you will find a variety of fresh perspectives when walking along major map lines in logical information dynamics for rational agents. Topics including the nature of explicit non-omniscient beliefs, the creation of strategies in parallel games, general patterns in interactive rationality, agents' attention horizons in games, information-based coalitional influence in epistemic models, and richer views of choice, preference, obligation in social scenarios all the way up to the cathartic finale of voting. But you also get to read about new developments of a more fundamental nature. Logical tools do not get blunt in the course of applications, they often get shinier and even sharper with new edges. Examples of such new gloss and cutting edge show in this Yearbook with papers on new substitution-closed versions of public announcement logic, frame correspondence analysis of update postulates, generalized algebraic views of logical dynamics, and new interfaces with categorial and linear logics as a resourceconscious paradigm of information. So much for the trails. Which strangers did we meet on the way? This Yearbook contains several interesting encounters with colleagues in the empirical domain of natural language, with papers Johan van Benthem

Negotiation is an essential skill for agents in a multiagent system. Much work has been published on this subject, but traditional approaches assume negotiators are able to evaluate all possible deals and pick the one that is best according to some negotiation strategy. Such an approach fails when the set of possible deals is too large to analyze exhaustively. For this reason the Annual Negotiating Agents Competition of 2014 has focused on negotiations over very large agreement spaces. In this paper we present a negotiating agent that explores the search space by means of a Genetic Algorithm. It has participated in the competition successfully and finished in 2nd and 3rd place in the two categories of the competition respectively.

Existing work on automated negotiations has mainly focused on bilateral negotiations with linear utility functions. It is often assumed that all possible agreements and their utility values are given beforehand. Most real-world negotiations however are much more complex. We introduce a new family of negotiation algorithms that is applicable to domains with many agents, an intractably large space of possible agreements, non-linear utility functions and limited time so an exhaustive search for the best proposals is not feasible. We assume that agents are selfish and cannot be blindly trusted, so the algorithm does not rely on any mediator. This family of algorithms is called NB 3 and applies heuristic Branch & Bound search to find good proposals. Search and negotiation happen simultaneously and therefore strongly influence each other. It applies a new time-based negotiation strategy that considers two utility aspiration levels: one for the agent itself and one for its opponents. Also, we introduce a negotiation protocol that imposes almost no restrictions and is therefore better applicable to negotiations with humans. We present the Negotiating Salesmen Problem (NSP): a variant of the Traveling Salesman Problem with multiple negotiating agents, as a test case. We describe an implementation of NB 3 designed for the NSP and present the results of experiments with this implementation. We conclude that the algorithm is able to decrease the costs of the agents significantly, that the heuristic search is efficient and that the algorithm scales well with increasing complexity of the problem.

We define a cautious version of extensive-form rationalizability for generalized extensiveform games with unawareness that we call prudent rationalizability. It is an extensive-form analogue of iterated admissibility. In each round of the procedure, for each tree and each information set of a player a surviving strategy of hers is required to be rational visa -vis a belief system with a full-support belief on the opponents' previously surviving strategies that reach that information set. We demonstrate the applicability of prudent rationalizability. In games of disclosure of verifiable information, we show that prudent rationalizability yields unraveling under full awareness but unraveling might fail under unawareness. We compare prudent rationalizability to extensive-form rationalizability. We show that prudent rationalizability may not refine extensive-form rationalizability strategies but conjecture that the paths induced by prudent rationalizable strategy profiles (weakly) refine the set of paths induced by extensive-form rationalizable strategies.

We define generalized extensive-form games which allow for mutual unawareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties and prove existence. We define also a new variant of this solution concept, prudent rationalizability, which refines the set of outcomes induced by extensive-form rationalizable strategies. Finally, we define the normal form of a generalized extensive-form game, and characterize in it extensive-form rationalizability by iterative conditional dominance.

Orientadores: Flávio Keidi Miyazawa, Rafael Crivellari Saliba SchoueryDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Problemas relacionados com meios de transporte são comumente encontrados na área de Otimização Combinatória, como, por exemplo, o Problema do Caixeiro Viajante e o Problema de Roteamento de Veículos. Nesta dissertação, consideramos um problema de transporte sob a perspectiva da teoria de jogos algorítmica onde todos os jogadores querem ser transportados a um destino em comum o mais rápido possível, e para isso eles devem escolher um dentre os ônibus disponíveis. Revisamos alguns resultados quanto à existência e à ineficiência de equilíbrios puros de Nash em relação a duas funções sociais. Então, apresentamos limitantes para o Preço de Anarquia para uma nova função social, chamada de função utilitária. Consideramos também o jogo na forma extensiva, o qual chamamos de jogos de transporte sequenciais e apresentamos limitantes p...

Coalition logic (CL) is one of the most influential logical formalisms for strategic abilities of multi-agent systems. CL can specify what a group of agents can achieve through choices of their actions, denoted by [C]φ to state that a group of agents C can have a strategy to bring about φ by collective actions, no matter what the other agents do. However, CL lacks the temporal dimension and thus can not capture the dynamic aspects of a system. Therefore, CL can not formalize the evolvement of rational mental attitudes of the agents such as knowledge, which has been shown to be very useful in specifications and verifications of distributed systems, and has received substantial amount of studies. In this paper, we introduce coalition logic of temporal knowledge (CLTK), by incorporating a temporal logic of knowledge (Halpern and Vardi's logic of CKL n) into CL to equip CL with the power to formalize how agents' knowledge (individual or group knowledge) evolves over the time by coalitional forces and the temporal properties of strategic abilities as well. Furthermore, we provide an axiomatic system for CLTK and prove that it is sound and complete, along with the complexity of the satisfiability problem which is shown to be EXPTIME-complete.

When studying extensive-form games it is commonly assumed that players make their decisions individually. One usually does not allow the possibility for the players to negotiate their respective strategies and formally commit themselves to future moves. As a consequence, many non-zero-sum games have been shown to have equilibrium outcomes that are suboptimal and arguably counter-intuitive. For this reason we feel there is a need to explore a new line of research in which game-playing agents are allowed to negotiate binding agreements before they make their moves. We analyze what happens under such assumptions and define a new equilibrium solution concept to capture this. We show that this new solution concept indeed yields solutions that are more efficient and, in a sense, closer to what one would expect in the real world. Furthermore, we demonstrate that our ideas are not only theoretical in nature, but can also be implemented on bounded rational agents, with a number of experiments conducted with a new algorithm that combines techniques from Automated Negotiations, (Algorithmic) Game Theory, and General Game Playing. Our algorithm, which we call Monte Carlo Negotiation Search, is an adaptation of Monte Carlo Tree Search that equips the agent with the ability to negotiate. It is completely domain-independent in the sense that it is not tailored to any specific game. It can be applied to any non-zero-sum game, provided that its rules are described in Game Description Language. We show with several experiments that it strongly outperforms non-negotiating players, and that it closely approximates the theoretically optimal outcomes, as defined by our new solution concept. Keywords Automated negotiations • Non-zero-sum games • Extensive-form games • General game playing • Monte Carlo tree search

We consider the solution concept of stochastic stability, and propose the price of stochastic anarchy as an alternative to the price of (Nash) anarchy for quantifying the cost of selfishness and lack of coordination in games. As a solution concept, the Nash equilibrium has disadvantages that the set of stochastically stable states of a game avoid: unlike Nash equilibria, stochastically stable states are the result of natural dynamics of computationally bounded and decentralized agents, and are resilient to small perturbations from ideal play. The price of stochastic anarchy can be viewed as a smoothed analysis of the price of anarchy, distinguishing equilibria that are resilient to noise from those that are not. To illustrate the utility of stochastic stability, we study the load balancing game on unrelated machines. This game has an unboundedly large price of Nash anarchy even when restricted to two players and two machines. We show that in the two player case, the price of stochastic anarchy is 2, and that even in the general case, the price of stochastic anarchy is bounded. We conjecture that the price of stochastic anarchy is O(m), matching the price of strong Nash anarchy without requiring player coordination. We expect that stochastic stability will be useful in understanding the relative stability of Nash equilibria in other games where the worst equilibria seem to be inherently brittle.

Multi-agent environments comprise decision makers whose deliberations involve reasoning about the expected behavior of other agents. Apposite concepts of rational choice have been studied and formalized in game theory and our particular interest is with their integration in a logical specification language for multiagent systems. This paper concerns the logical analysis of the gametheoretical notions of a (subgame perfect) Nash equilibrium and that of a (subgame perfect) best response strategy. Extensive forms of games are conceived of as Kripke frames and a version of Propositional Dynamic Logic is employed to describe them. We show how formula schemes of our language characterize those classes of frames in which the strategic choices of the agents can be said to be Nashoptimal. Our analysis focuses on extensive games of perfect information without repetition. 2 Game Theoretical Notions The investigations of this paper concern finite games in extensive form with perfect information. A (pure) strategy for a game consists of a complete plan for a player © how to play that game. Strategy profiles, denoted by , combine strategies, one for each player. A strategy profile determines for each node a unique outcome, though not necessarily for each node the same one.

In the past few years, there is a growing interest in automated negotiation in which software agents facilitate negotiation on behalf of their users and try to reach joint agreements. The potential value of developing such mechanisms becomes enormous when negotiation domain is too complex for humans to find agreements (e.g. e-commerce) and when software components need to reach agreements to work together (e.g. web-service composition). Here, one of the major challenges is to design agents that are able to deal with incomplete information about their opponents in negotiation as well as to effectively negotiate on their users' behalves. To facilitate the research in this field, an automated negotiating agent competition has been organized yearly. This paper introduces the research challenges in ANAC 2014 and explains the competition set up and competition results. Furthermore, a detailed analysis of the best performing five agent has been examined.

In a scheduling game, each player owns a job and chooses a machine to execute it. While the social cost is the maximal load over all machines (makespan), the cost (disutility) of each player is the completion time of its own job. In the game, players may follow selfish strategies to optimize their cost and therefore their behaviors do not necessarily lead the game to an equilibrium. Even in the case there is an equilibrium, its makespan might be much larger than the social optimum, and this inefficiency is measured by the price of anarchy-the worst ratio between the makespan of an equilibrium and the optimum. Coordination mechanisms aim to reduce the price of anarchy by designing scheduling policies that specify how jobs assigned to a same machine are to be scheduled. Typically these policies define the schedule according to the processing times as announced by the jobs. One could wonder if there are policies that do not require this knowledge, and still provide a good price of anarchy. This would make the processing times be private information and avoid the problem of truthfulness. In this paper we study these so-called non-clairvoyant policies. In particular, we study the RANDOM policy that schedules the jobs in a random order without preemption, and the EQUI policy that schedules the jobs in parallel using time-multiplexing, assigning each job an equal fraction of CPU time. For these models we study two important questions, the existence of Nash equilibria and the price of anarchy. We show that the game under RANDOM policy is a potential game for uniform machines or for two unrelated machines. However, it is not a potential game for three or more unrelated machines. Moreover, we prove that the game under the EQUI policy is a potential game. Next, we analyze the inefficiency of EQUI policy. Interestingly, the (strong) price of anarchy of EQUI, a non-clairvoyant policy, is asymptotically the same as that of the best strongly local policy-policies in which a machine may look at the processing time of jobs assigned to it. The result also indicates that knowledge of jobs' characteristics is not necessarily needed.

Multi-agent systems comprise entities whose individual decision making behavior may depend on one another's. Game-theory provides apposite concepts to reason in a mathematically precise fashion about such interactive and interdependent situations. This paper concerns a logical analysis of the game-theoretical notions of Nash equilibrium and its subgame perfect variety as they apply to a particular class of extensive games of perfect information. Extensive games are defined as a special type of labelled graph and we argue that modal languages can be employed in their description. We propose a logic for a multi-modal language and prove its completeness with respect to a class of frames that correspond with a particular class of extensive games. In this multimodal language (subgame perfect) Nash equilibria can be characterized. Finally, we show how this approach can formally be refined by using Propositional Dynamic Logic ( ¡¢£ ), though we leave completeness as an open question.

Plants have different leaf morphological characteristics starting from the leaf surface, leaf bone, leaf tips, leaf edges, leaf base, and even leaf color. The study of plants has been progressing rapidly. One of them is the branch of science in plant morphology. Morphological characteristics of leaves are one of the properties possessed by leaves and can be seen clearly. This morphological study learns about the structure of the plant body, especially about the edge leaf shape. This study will be done based on leaf shape. Leaf shape can be used as a reference in the classification process. The classification process requires a good data extraction feature, so it is necessary to improve the feature process at the pre-processing level. Combining the median filter and image erosion is used to improve the feature process. As for feature extraction, the seven moment invariant method is used. The classification method used for grouping is the Hierarchical Clustering. This method consists ...

The cognitive hierarchy (CH) approach posits that players in a game are heterogeneous with respect to levels of strategic sophistication. A level-k player believes all other players in the game have lower levels of sophistication distributed from 0 to k 1, and these beliefs correspond to the truncated distribution of a “true” distribution of levels. We extend the CH framework to extensive form games, where these initial beliefs over lower levels are updated as the history of play in the game unfolds, providing information to players about other players’ levels of sophistication. For a class of centipede games with a linearly increasing pie, we fully characterize the dynamic CH solution and show that it leads to the game terminating earlier than in the static CH solution for the centipede game in reduced normal form. JEL Classification Numbers: C72

We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect recall and can be solved efficiently by standard methods. We are interested in the properties of the subgame perfect equilibria of this game. We first show that uniformly random strategy is a subgame perfect equilibrium strategy for both teams when there are no redundant players (i.e., the number of players in each team equals to the number of rounds of the competition). Secondly, a team can safely abandon its weak players if it has redundant players and the strength of players is transitive. We then focus on the more interesting case where there are redundant players and the strength of players is not transitive. In this case, we obtain several counterintuitive results. First of all, a player might help improve the payoff of its team, even if it is dominated by the entire other team. We give a necessary condition for a dominated player to be useful. We also study the extent to which the dominated players can increase the payoff. These results bring insights into playing and designing general team competitions.

This paper presents research proposals on the interdisciplinary research infrastructure for understanding human reasoning in game-theoretic terms. Strategic reasoning impacts human decision making in social, economical and competitive interactions. The provided introduction summarizes concepts from AI, game theory and psychology. First result is a concept of interdisciplinary game description language as a part of the focused interdisciplinary research infrastructure. The need of this domain-specific language is motivated and is aimed to accelerate the current developments. As second result, the paper provides a summary of ongoing research and its significance.

We study the number of steps required to reach a pure Nash Equilibrium in a load balancing scenario where each job behaves selfishly and attempts to migrate to a machine which will minimize its cost. We consider a variety of load balancing models, including identical, restricted, related and unrelated machines. Our results have a crucial dependence on the weights assigned to jobs. We consider arbitrary weights, integer weights, K distinct weights and identical (unit) weights. We look both at an arbitrary schedule (where the only restriction is that a job migrates to a machine which lowers its cost) and specific efficient schedulers (such as allowing the largest weight job to move first).

Many natural games can have a dramatic difference between the quality of their best and worst Nash equilibria, even in pure strategies. Yet, nearly all work to date on dynamics shows only convergence to some equilibrium, especially within a polynomial number of steps. In this work we study how agents with some knowledge of the game might be able to quickly (within a polynomial number of steps) find their way to states of quality close to the best equilibrium. We consider two natural learning models in which players choose between greedy behavior and following a proposed good but untrusted strategy and analyze two important classes of games in this context, fair cost-sharing and consensus games. Both games have extremely high Price of Anarchy and yet we show that behavior in these models can efficiently reach low-cost states.

We study the number of steps required to reach a pure Nash equilibrium in a load balancing scenario where each job behaves selfishly and attempts to migrate to a machine which will minimize its cost. We consider a variety of load balancing models, including identical, restricted, related, and unrelated machines. Our results have a crucial dependence on the weights assigned to jobs. We consider arbitrary weights, integer weights, k distinct weights, and identical (unit) weights. We look both at an arbitrary schedule (where the only restriction is that a job migrates to a machine which lowers its cost) and specific efficient schedulers (e.g., allowing the largest weight job to move first). A by-product of our results is establishing a connection between various scheduling models and the game-theoretic notion of potential games. We show that load balancing in unrelated machines is a generalized ordinal potential game, load balancing in related machines is a weighted potential game, and...

Aumann has proved that common knowledge of substantive rationality implies the backwards induction solution in games of perfect information. Stalnaker has proved that it does not. Roughly speaking, a player is substantively rational if, for all vertices v, if the player were to reach vertex v, then the player would be rational at vertex v". It is shown here that the key di erence between Aumann and Stalnaker lies in how they interpret this counterfactual. A formal model is presented that lets us capture this di erence, in which both Aumann's result and Stalnaker's result are true (under appropriate assumptions). Starting with the work of Bicchieri 1988, 1989], Binmore 1987], and Reny 1992], there has been intense scrutiny of the assumption of common knowledge of rationality, the use of counterfactual reasoning in games, and the role of common knowledge and counterfactuals in the arguments for backward

for non-mathematicians Explaining the subject of my Bachelor thesis to those who do not study either Mathematics or Computer Science isn’t an easy task, but I can give an idea of the problem studied by giving an example. Imagine, for example, that there are only two roads from Paris to Brussels: road A & road B. If you take road A you’ll always drive 5 hours, independent from the usage of road A by other drivers (agents is the more game theoretical word). If you take road B, the time you need depends of the number of other agents using road B: you’ll drive 5 x 100 hours, with x the number of agents, but also on this road the maximum time spend is 5 hours, so mathematically that becomes min(5, 5 x 100 ) hours. Because every agent acts selfish and rational, the result under this circumstances and with only this information will be that every agent will take at any time road B: with road A they drive always 5 hours, with road B there is a chance to get to Brussels in less time. But con...

We present a logic which supports reasoning about an agent’s belief formation and belief change due to evidence provided by other agents in the society. We call this logic DEL-ES which stands for “Dynamic Epistemic Logic of Evidence Sources”. The term "evidence source" refers to an agent in the society who provides evidence to believe something to another agent. According to DEL-ES, if an agent has gathered a sufficient amount of evidence in support a given fact φ then, as a consequence, she should start to believe that φ is true. A sound and complete axiomatization for DEL-ES is given. We discuss some of its interesting properties and illustrate it in a concrete example from legal contexts.

Game theory has gained popularity as an approach to analysing and understanding distributed systems with selfinterested agents. Central to game theory is the concept of Nash equilibrium as a stable state (solution) of the system, which comes with a price − the loss in efficiency. The quantification of the efficiency loss is one of the main research concerns. In this paper, we study the quality and computational characteristic of the best Nash equilibrium in two selfish scheduling models: the congestion model and the sequencing model. In particular, we present the following results: (1) In the congestion model: first, the best Nash equilibrium is socially optimum and consequently, computing the best Nash is NP-hard. And second, any-approximation algorithm for finding the optimum can be transformed into an-approximation algorithm for the best Nash. (2) In sequencing model for identical machines, we show that the best Nash is no better than the worst Nash and it is easy to compute. For related machines, we show that there is a gap between the worst and the best Nash equilibrium. We left the bounding of this gap for future work.

Nash equilibrium (NE) assumes that players always make a best response. However, this is not always true; sometimes people cooperate even it is not a best response to do so. For example, in the Prisoner's Dilemma, people often cooperate. Are there rules underlying cooperative behavior? In an effort to answer this question, we propose a new equilibrium concept: perfect cooperative equilibrium (PCE), and two related variants: max-PCE and cooperative equilibrium. PCE may help explain players' behavior in games where cooperation is observed in practice. A player's payoff in a PCE is at least as high as in any NE. However, a PCE does not always exist. We thus consider α-PCE, where α takes into account the degree of cooperation; a PCE is a 0-PCE. Every game has a Pareto-optimal max-PCE (M-PCE); that is, an α-PCE for a maximum α. We show that M-PCE does well at predicting behavior in quite a few games of interest. We also consider cooperative equilibrium (CE), another generalization of PCE that takes punishment into account. Interestingly, all Pareto-optimal M-PCE are CE. We prove that, in 2-player games, both a PCE (if it exists) and a M-PCE can be found in polynomial time, using bilinear programming. This is a contrast to Nash equilibrium, which is PPAD complete even in 2-player games [Chen, Deng, and Teng 2009]. We compare M-PCE to the coco value [Kalai and Kalai 2009], another solution concept that tries to capture cooperation, both axiomatically and in terms of an algebraic characterization, and show that the two are closely related, despite their very different definitions.

We investigate pure Nash equilibria in generalized graph k-coloring games where we are given an edge-weighted undirected graph together with a set of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player consists of k colors. The utility of a player v in a given state or coloring is given by the sum of the weights of edges \(\{v,u\}\) incident to v such that the color chosen by v is different than the one chosen by u, plus the profit gained by using the chosen color. Such games form some of the basic payoff structures in game theory, model lots of real-world scenarios with selfish players and extend or are related to several fundamental class of games.

Dufwenberg and Kirchsteiger�s (2004) extends Rabin�s (1993) theory of reciprocity in a dynamic sense, introducing a rule of revision for player�s beliefs. The Sequential Reciprocity Equilibrium [SRE] they define can be dynamically inconsistent. In this article it is argued that such dynamic inconsistency is not intrinsically related to issues of reciprocity, but rather to the particular way the beliefs�updating process is modeled. A refinement of the SRE, which is both dynamically consistent and, it is argued, more sound to assumptions usually made in the literature of information economics and philosophy, is proposed.

This paper introduces a new Negotiating Agent for automated negotiation on continuous domains and without considering a specified deadline. The agent bidding strategy relies on Monte Carlo Tree Search, which is a trendy method since it has been used with success on games with high branching factor such as Go. It uses two opponent modeling techniques for its bidding strategy and its utility: Gaussian process regression and Bayesian learning. Evaluation is done by confronting the existing agents that are able to negotiate in such context: Random Walker, Tit-for-tat and Nice Tit-for-Tat. None of those agents succeeds in beating our agent; moreover the modular and adaptive nature of our approach is a huge advantage when it comes to optimize it in specific applicative contexts.

This paper introduces a new negotiating agent model for automated negotiation. We focus on applications without time pressure with multidimensional negotiation on both continuous and discrete domains. The agent bidding strategy relies on Monte Carlo Tree Search, which is a trendy method since it has been used with success on games with high branching factor such as Go. It also exploits opponent modeling techniques thanks to Gaussian process regression and Bayesian learning. Evaluation is done by confronting the existing agents that are able to negotiate in such context: Random Walker, Tit-for-tat and Nice Titfor-Tat. None of those agents succeeds in beating our agent. Also, the modular and adaptive nature of our approach is a huge advantage when it comes to optimize it in specific applicative contexts.

The current state of the art in playing many important perfect information games, including Chess and Go, combines planning and deep reinforcement learning with self-play. We extend this approach to imperfect information games and present ExIt-OOS, a novel approach to playing imperfect information games within the Expert Iteration framework and inspired by AlphaZero. We use Online Outcome Sampling, an online search algorithm for imperfect information games in place of MCTS. While training online, our neural strategy is used to improve the accuracy of playouts in OOS, allowing a learning and planning feedback loop for imperfect information games.

We consider strategic-form games with ordinal payoffs and provide a syntactic analysis of common belief/knowledge of rationality, which we define axiomatically. Two axioms are considered. The first says that a player is irrational if she chooses a particular strategy while believing that another strategy is better. We show that common belief of this weak notion of rationality characterizes the iterated deletion of pure strategies that are strictly dominated by pure strategies. The second axiom says that a player is irrational if she chooses a particular strategy while believing that a different strategy is at least as good and she considers it possible that this alternative strategy is actually better than the chosen one. We show that common knowledge of this stronger notion of rationality characterizes the restriction to pure strategies of the iterated deletion procedure introduced by Stalnaker (1994).

In epistemic logic, Kripke structures are used to model the distribution of information in a multi-agent system. In this paper, we present an approach to quantifying how much information each particular agent in a system has, or how important the agent is, with respect to some fact represented as a goal formula. It is typically the case that the goal formula is distributed knowledge in the system, but that no individual agent alone knows it. It might be that several different groups of agents can get to know the goal formula together by combining their individual knowledge. By using power indices developed in voting theory, such as the Banzhaf index, we get a measure of how important an agent is in such groups. We analyse the properties of this notion of information-based power in detail, and characterise the corresponding class of voting games. Although we mainly focus on distributed knowledge, we also look at variants of this analysis using other notions of group knowledge. An adv...

General Game Playing aims to create AI systems that can understand the rules of new games and learn to play them effectively without human intervention. The recent proposal for general game-playing robots extends this to AI systems that play games in the real world. Execution monitoring becomes a necessity when moving from a virtual to a physical environment, because in reality actions may not be executed properly and (human) opponents may make illegal game moves. We develop a formal framework for execution monitoring by which an action theory that provides an axiomatic description of a game is automatically embedded in a meta-game for a robotic player--called the arbiter -- whose role is to monitor and correct failed actions. This allows for the seamless encoding of recovery behaviours within a meta-game, enabling a robot to recover from these unexpected events.

We revisit the discussion on reasoning about games in dynamic-epistemic logic and present a language for describing reasoning in possibly infinite games from the perspective of the players. We argue that even though a plethora of sophisticated logics of strategic reasoning in games are available, it is still worthwhile to consider the game structures themselves from the perspective of logic. In the process, we provide complete axiom systems for these games satisfying characteristic properties from the gametheoretic literature. Decidability of the satisfiability problem is also taken up to consider the existence of games following certain rules that can be expressed in the logical language.

Despite abundant negotiation strategies in literature, the complexity of automated negotiation forbids a single strategy from being dominant against all others in different negotiation scenarios. To overcome this, one approach is to use mixture of experts, but at the same time one problem of this method is the selection of experts, as this approach is limited by the competency of the experts selected. Another problem with most negotiation strategies is their incapability of adapting to dynamic variation of the opponent’s behaviour within a single negotiation session resulting in poor performance. This work focuses on both, solving the problem of expert selection and adapting to the opponent’s behaviour with our Autonomous Negotiating Agent Framework. This framework allows real-time classification of opponent’s behaviour and provides a mechanism to select, switch or combine strategies within a single negotiation session. Additionally, our framework has a reviewer component which enab...