We introduce a new class of games where each player's aim is to randomise her strategic choices in order to affect the other players' expectations aside from her own. The way each player intends to exert this influence is expressed through a Boolean combination of polynomial equalities and inequalities with rational coefficients. We offer a logical representation of these games as well as a computational study of the existence of equilibria.
{"title":"Games for the Strategic Influence of Expectations","authors":"L. Godo, Enrico Marchioni","doi":"10.4204/EPTCS.146.2","DOIUrl":"https://doi.org/10.4204/EPTCS.146.2","url":null,"abstract":"We introduce a new class of games where each player's aim is to randomise her strategic choices in order to affect the other players' expectations aside from her own. The way each player intends to exert this influence is expressed through a Boolean combination of polynomial equalities and inequalities with rational coefficients. We offer a logical representation of these games as well as a computational study of the existence of equilibria.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"65 1","pages":"9-15"},"PeriodicalIF":0.0,"publicationDate":"2014-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81381604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players become uncertain about the current state of the game, and this uncertainty lasts forever. Here we consider games where the players attain certainty about the current state over and over again along any play. For finite-state games, we note that this kind of recurring certainty implies a stronger condition of periodic certainty, that is, the events of state certainty ultimately occur at uniform, regular intervals. We show that it is decidable whether a given game presents recurring certainty, and that, if so, the problem of synthesising coordination strategies under w-regular winning conditions is solvable.
{"title":"Games with recurring certainty","authors":"Dietmar Berwanger, A. Mathew","doi":"10.4204/EPTCS.146.12","DOIUrl":"https://doi.org/10.4204/EPTCS.146.12","url":null,"abstract":"Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players become uncertain about the current state of the game, and this uncertainty lasts forever. Here we consider games where the players attain certainty about the current state over and over again along any play. For finite-state games, we note that this kind of recurring certainty implies a stronger condition of periodic certainty, that is, the events of state certainty ultimately occur at uniform, regular intervals. We show that it is decidable whether a given game presents recurring certainty, and that, if so, the problem of synthesising coordination strategies under w-regular winning conditions is solvable.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"1 1","pages":"91-96"},"PeriodicalIF":0.0,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82098591","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We propose extending Alternating-time Temporal Logic (ATL) by an operator F to express that agent i can distribute its powers to a set of sub-agents G in a way which satisfies ATL condition f on the strategic ability of the coalitions they may form, possibly together with others agents. We prove the decidability of model-checking of formulas whose subformulas with this operator as the main connective have the form ... f, with no further occurrences of this operator in f.
{"title":"Refining and Delegating Strategic Ability in ATL","authors":"Dimitar P. Guelev","doi":"10.4204/EPTCS.146.8","DOIUrl":"https://doi.org/10.4204/EPTCS.146.8","url":null,"abstract":"We propose extending Alternating-time Temporal Logic (ATL) by an operator F to express that agent i can distribute its powers to a set of sub-agents G in a way which satisfies ATL condition f on the strategic ability of the coalitions they may form, possibly together with others agents. We prove the decidability of model-checking of formulas whose subformulas with this operator as the main connective have the form ... f, with no further occurrences of this operator in f.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"38 1","pages":"57-63"},"PeriodicalIF":0.0,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80883810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the security of interaction protocols when incentives of participants are taken into account. We begin by formally defining correctness of a protocol, given a notion of rationality and utilities of participating agents. Based on that, we propose how to assess security when the precise incentives are unknown. Then, the security level can be defined in terms of defender sets, i.e., sets of participants who can effectively "defend" the security property as long as they are in favor of the property. We present some theoretical characterizations of defendable protocols under Nash equilibrium, first for bijective games (a standard assumption in game theory), and then for games with non-injective outcomes that better correspond to interaction protocols. Finally, we apply our concepts to analyze fairness in the ASW contract-signing protocol.
{"title":"On Defendability of Security Properties","authors":"W. Jamroga, Matthijs Melissen, Henning Schnoor","doi":"10.4204/EPTCS.146.3","DOIUrl":"https://doi.org/10.4204/EPTCS.146.3","url":null,"abstract":"We study the security of interaction protocols when incentives of participants are taken into account. We begin by formally defining correctness of a protocol, given a notion of rationality and utilities of participating agents. Based on that, we propose how to assess security when the precise incentives are unknown. Then, the security level can be defined in terms of defender sets, i.e., sets of participants who can effectively \"defend\" the security property as long as they are in favor of the property. \u0000We present some theoretical characterizations of defendable protocols under Nash equilibrium, first for bijective games (a standard assumption in game theory), and then for games with non-injective outcomes that better correspond to interaction protocols. Finally, we apply our concepts to analyze fairness in the ASW contract-signing protocol.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"6 1","pages":"17-25"},"PeriodicalIF":0.0,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79060468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a prototype tool for automated reasoning for Coalition Logic, a non-normal modal logic that can be used for reasoning about cooperative agency. The theorem prover CLProver is based on recent work on a resolution-based calculus for Coalition Logic that operates on coalition problems, a normal form for Coalition Logic. We provide an overview of coalition problems and of the resolution-based calculus for Coalition Logic. We then give details of the implementation of CLProver and present the results for a comparison with an existing tableau-based solver.
{"title":"A Resolution Prover for Coalition Logic","authors":"C. Nalon, Lan Zhang, C. Dixon, U. Hustadt","doi":"10.4204/EPTCS.146.9","DOIUrl":"https://doi.org/10.4204/EPTCS.146.9","url":null,"abstract":"We present a prototype tool for automated reasoning for Coalition Logic, a non-normal modal logic that can be used for reasoning about cooperative agency. The theorem prover CLProver is based on recent work on a resolution-based calculus for Coalition Logic that operates on coalition problems, a normal form for Coalition Logic. We provide an overview of coalition problems and of the resolution-based calculus for Coalition Logic. We then give details of the implementation of CLProver and present the results for a comparison with an existing tableau-based solver.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"38 1","pages":"65-73"},"PeriodicalIF":0.0,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76363427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Exploiting the algebraic structure of the set of bimatrix games, a divide-and-conquer algorithm for finding Nash equilibria is proposed. The algorithm is fixed-parameter tractable with the size of the largest irreducible component of a game as parameter. An implementation of the algorithm is shown to yield a significant performance increase on inputs with small parameters.
{"title":"Efficient Decomposition of Bimatrix Games (Extended Abstract)","authors":"Xiang Jiang, A. Pauly","doi":"10.4204/EPTCS.146.10","DOIUrl":"https://doi.org/10.4204/EPTCS.146.10","url":null,"abstract":"Exploiting the algebraic structure of the set of bimatrix games, a divide-and-conquer algorithm for finding Nash equilibria is proposed. The algorithm is fixed-parameter tractable with the size of the largest irreducible component of a game as parameter. An implementation of the algorithm is shown to yield a significant performance increase on inputs with small parameters.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"39 1","pages":"75-81"},"PeriodicalIF":0.0,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76164883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article is about temporal multi-agent logics. Several of these formalisms have been already presented (ATL-ATL*, ATLsc, SL). They enable to express the capacities of agents in a system to ensure the satisfaction of temporal properties. Particularly, SL and ATLsc enable several agents to interact in a context mixing the different strategies they play in a semantical game. We generalize this possibility by proposing a new formalism, Updating Strategy Logic (USL). In USL, an agent can also refine its own strategy. The gain in expressive power rises the notion of "sustainable capacities" for agents. USL is built from SL. It mainly brings to SL the two following modifications: semantically, the successor of a given state is not uniquely determined by the data of one choice from each agent. Syntactically, we introduce in the language an operator, called an "unbinder", which explicitely deletes the binding of a strategy to an agent. We show that USL is strictly more expressive than SL.
{"title":"Towards an Updatable Strategy Logic","authors":"Christophe Chareton, Julien Brunel, D. Chemouil","doi":"10.4204/EPTCS.112.14","DOIUrl":"https://doi.org/10.4204/EPTCS.112.14","url":null,"abstract":"This article is about temporal multi-agent logics. Several of these formalisms have been already presented (ATL-ATL*, ATLsc, SL). They enable to express the capacities of agents in a system to ensure the satisfaction of temporal properties. Particularly, SL and ATLsc enable several agents to interact in a context mixing the different strategies they play in a semantical game. We generalize this possibility by proposing a new formalism, Updating Strategy Logic (USL). In USL, an agent can also refine its own strategy. The gain in expressive power rises the notion of \"sustainable capacities\" for agents. USL is built from SL. It mainly brings to SL the two following modifications: semantically, the successor of a given state is not uniquely determined by the data of one choice from each agent. Syntactically, we introduce in the language an operator, called an \"unbinder\", which explicitely deletes the binding of a strategy to an agent. We show that USL is strictly more expressive than SL.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"82 1","pages":"91-98"},"PeriodicalIF":0.0,"publicationDate":"2013-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86545916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study infinite two-player games where one of the players is unsure about the set of moves available to the other player. In particular, the set of moves of the other player is a strict superset of what she assumes it to be. We explore what happens to sets in various levels of the Borel hierarchy under such a situation. We show that the sets at every alternate level of the hierarchy jump to the next higher level.
{"title":"Infinite games with uncertain moves","authors":"Nicholas Asher, Soumya Paul","doi":"10.4204/EPTCS.112.7","DOIUrl":"https://doi.org/10.4204/EPTCS.112.7","url":null,"abstract":"We study infinite two-player games where one of the players is unsure about the set of moves available to the other player. In particular, the set of moves of the other player is a strict superset of what she assumes it to be. We explore what happens to sets in various levels of the Borel hierarchy under such a situation. We show that the sets at every alternate level of the hierarchy jump to the next higher level.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"12 15","pages":"25-32"},"PeriodicalIF":0.0,"publicationDate":"2013-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72388099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate uniformity properties of strategies. These properties involve sets of plays in ord er to express useful constraints on strategies that are not μ-calculus definable. Typically, we can state that a strategy is observation-based. We propose a formal language to specify uniformity properties, interpreted over two-player turn-based arenas equip ped with a binary relation between plays. This way, we capture e.g. games with winning conditions expressible in epistemic temporal logic, whose underlying equivalence relation between plays reflec ts the observational capabilities of agents (for example, synchronous perfect recall). Our framework naturally generalizes many other situations from the literature. We establish that the problem of s ynthesizing strategies under uniformity constraints based on regular binary relations between plays is non-elementary complete.
{"title":"The Complexity of Synthesizing Uniform Strategies","authors":"Bastien Maubert, S. Pinchinat, L. Bozzelli","doi":"10.4204/EPTCS.112.17","DOIUrl":"https://doi.org/10.4204/EPTCS.112.17","url":null,"abstract":"We investigate uniformity properties of strategies. These properties involve sets of plays in ord er to express useful constraints on strategies that are not μ-calculus definable. Typically, we can state that a strategy is observation-based. We propose a formal language to specify uniformity properties, interpreted over two-player turn-based arenas equip ped with a binary relation between plays. This way, we capture e.g. games with winning conditions expressible in epistemic temporal logic, whose underlying equivalence relation between plays reflec ts the observational capabilities of agents (for example, synchronous perfect recall). Our framework naturally generalizes many other situations from the literature. We establish that the problem of s ynthesizing strategies under uniformity constraints based on regular binary relations between plays is non-elementary complete.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"159 1","pages":"115-122"},"PeriodicalIF":0.0,"publicationDate":"2013-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86989305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Truls Pedersen, Sjur K. Dyrkolbotn, Piotr Kazmierczak, Erik Parmann
In the following paper we present a new semantics for the well-known strategic logic ATL. It is based on adding roles to concurrent game structures, that is at every state, each agent belongs to exactly one role, and the role specifies what actions are available to him at that state. We show advantages of the new semantics, provide motivating examples based on sensor networks, and analyze model checking complexity.
{"title":"Concurrent Game Structures with Roles","authors":"Truls Pedersen, Sjur K. Dyrkolbotn, Piotr Kazmierczak, Erik Parmann","doi":"10.4204/EPTCS.112.11","DOIUrl":"https://doi.org/10.4204/EPTCS.112.11","url":null,"abstract":"In the following paper we present a new semantics for the well-known strategic logic ATL. It is based on adding roles to concurrent game structures, that is at every state, each agent belongs to exactly one role, and the role specifies what actions are available to him at that state. We show advantages of the new semantics, provide motivating examples based on sensor networks, and analyze model checking complexity.","PeriodicalId":53035,"journal":{"name":"Hkhmt m`Sr","volume":"96 1","pages":"61-69"},"PeriodicalIF":0.0,"publicationDate":"2013-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90385829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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