Periodic Reporting for period 1 - SEAL (Strategic reasoning for socially good mechanisms)
Reporting period: 2023-08-01 to 2025-07-31
Summary of the context and overall objectives of the project
The design and evaluation of games (also known as mechanisms) for aggregating preferences is a central problem in Multi-Agent Systems (MAS). In such a setting, we need to be able to aggregate individual preferences, which are conflicting when agents are self-interested. More importantly, the mechanism should choose a socially desirable (or “good”) outcome and reach an equilibrium even though agents can lie about their preferences. For instance, an election is a mechanism that combines agents' votes into the choice of one or several winning candidates. The main issues in designing such a mechanism are to motivate a desirable behavior of strategic voters and to ensure characteristics regarding the quality of the joint decision. In particular, elections could be designed to avoid a dictatorship (a participant that chooses the result all by herself), to incentivize people to participate, to choose a winner that maximizes social welfare, and so on. The real-world applications of designing and verifying mechanisms for social choice are manifold, including the classic problems of auctions, markets, and government policies. Furthermore, new and trending applications include fair division protocols, secure voting, and truth-tracking via approval voting (i.e. unveiling a hidden ground truth given votes). In Automated Mechanism Design (AMD), the design of new mechanisms is treated as a computational optimization problem for specific preference aggregation settings and domains.
Although logic-based languages have been widely used for verification and synthesis of MAS, the use of formal methods for reasoning about auctions under strategic behavior as well as automated mechanism design has not been much explored yet. An advantage of adopting such a perspective lies in the high expressivity and generality of logics for strategic reasoning. Moreover, by relying on precise semantics, formal methods provide tools for rigorously analyzing the correctness of systems, which is important to improve trust in mechanisms (fully or partially) created by machines. The problem of formally reasoning about mechanisms is, however, nontrivial: it requires considering quantitative information (e.g. utilities and payments), non-determinism, incomplete (e.g. Bayesian) and imperfect information about the participant’s preferences, and complex strategic concepts (such as strategy dominance and equilibria).
The use of strategic logics developed for the verification of MAS as formal frameworks to reason about mechanism was advocated by Wooldridge et al.11. They consider the Alternating-time Temporal Logic (ATL), which has limitations to express some solution concepts as well to handle the quantitative aspects of mechanisms.
As these are key features of mechanisms, Maubert et. al (21) recently proposed the use of variants of Strategy Logic (SL) for the verification and synthesis of deterministic mechanisms.
This current approach has several limitations. First, as SL semantics is deterministic, the logic is unable to express probabilistic features, which are essential when considering Bayesian and randomized (or stochastic) mechanisms. Second, in the general setting, logics based on SL face decidability and complexity issues, which may prevent the practical use of such an approach. Finally, the works considered up to now were focused on auction mechanisms, which are usually designed for maximizing revenue. The validation of a logic-based approach for mechanism design requires investigating the feasibility of modeling other social choice problems as well as characterizing results and properties in those settings.
This project aims to design a logical framework based on Strategy Logic for formally verifying and designing mechanisms for social choice. In particular, we aim to extend the existing approach of logic-based mechanism design to take into account the probabilistic setting (with Bayesian information, stochastic transitions, and mixed strategies), and identify fragments of SL that enjoy both good complexity and satisfying expressive power for being applied to classes of mechanisms. Additionally, we aim to model and reason about relevant problems from the state-of-the-art in computational social choice using the proposed logical framework.
Although logic-based languages have been widely used for verification and synthesis of MAS, the use of formal methods for reasoning about auctions under strategic behavior as well as automated mechanism design has not been much explored yet. An advantage of adopting such a perspective lies in the high expressivity and generality of logics for strategic reasoning. Moreover, by relying on precise semantics, formal methods provide tools for rigorously analyzing the correctness of systems, which is important to improve trust in mechanisms (fully or partially) created by machines. The problem of formally reasoning about mechanisms is, however, nontrivial: it requires considering quantitative information (e.g. utilities and payments), non-determinism, incomplete (e.g. Bayesian) and imperfect information about the participant’s preferences, and complex strategic concepts (such as strategy dominance and equilibria).
The use of strategic logics developed for the verification of MAS as formal frameworks to reason about mechanism was advocated by Wooldridge et al.11. They consider the Alternating-time Temporal Logic (ATL), which has limitations to express some solution concepts as well to handle the quantitative aspects of mechanisms.
As these are key features of mechanisms, Maubert et. al (21) recently proposed the use of variants of Strategy Logic (SL) for the verification and synthesis of deterministic mechanisms.
This current approach has several limitations. First, as SL semantics is deterministic, the logic is unable to express probabilistic features, which are essential when considering Bayesian and randomized (or stochastic) mechanisms. Second, in the general setting, logics based on SL face decidability and complexity issues, which may prevent the practical use of such an approach. Finally, the works considered up to now were focused on auction mechanisms, which are usually designed for maximizing revenue. The validation of a logic-based approach for mechanism design requires investigating the feasibility of modeling other social choice problems as well as characterizing results and properties in those settings.
This project aims to design a logical framework based on Strategy Logic for formally verifying and designing mechanisms for social choice. In particular, we aim to extend the existing approach of logic-based mechanism design to take into account the probabilistic setting (with Bayesian information, stochastic transitions, and mixed strategies), and identify fragments of SL that enjoy both good complexity and satisfying expressive power for being applied to classes of mechanisms. Additionally, we aim to model and reason about relevant problems from the state-of-the-art in computational social choice using the proposed logical framework.
Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far
We have proposed an approach for formally verifying mechanisms for social choice and Bayesian mechanisms with variants of Strategy Logic (SL). We have shown how to use it to encode classic notions from Mechanism Design, including Bayesian-Nash equilibrium and incentive compatibility. This approach allows for automatic verification of a wide class of mechanisms, and motivates further research on applications of logic-based approaches for AMD.
We introduced Incentive Design, a new class of problems for equilibrium verification in multi-agent systems. In our model, agents attempt to maximize their utility functions, which are expressed as formulae in temporal logic with quantitative semantics. We assume agents are rational in the sense that they adopt strategies consistent with game-theoretic solution concepts such as Nash equilibrium.
We propose an extension of the ATL that enables reasoning about the dynamics of model change and show how it can express various intuitions and ideas from normative updates and mechanism design. We also investigated the problem of finding minimal repairs for game descriptions that violate formal requirements, and we provide complexity results for various computational problems related to minimal repair.
We have investigated the strategy logics PATL and PATL∗ (fragments of PSL) under imperfect information. Since the model-checking problem is undecidable in general in this setting, we restrict our attention to agents with memoryless (positional) strategies.
We have proposed Behavioral Natural Strategies, a probabilistic extension of Natural Strategies, and variants of the probabilistic temporal logics PATL and PATL* to handle such strategies (the resulting logics are called NatPATL and NatPATL*, resp.).
We have investigated the problem of quantitative module checking in Multi-Agent Systems, which formalizes the verification of (possibly multi-agent) systems that must adapt their behavior to the input they receive from the environment, also viewed as an authority. The quantitative setting enables the verification of different levels of satisfaction.
To enable reasoning about the strategic behavior of agents with partial observability in general game playing, we presented a formal translation from games with imperfect information specified in GDL-II to models of Epistemic Strategy Logic (SLK).
We introduced Incentive Design, a new class of problems for equilibrium verification in multi-agent systems. In our model, agents attempt to maximize their utility functions, which are expressed as formulae in temporal logic with quantitative semantics. We assume agents are rational in the sense that they adopt strategies consistent with game-theoretic solution concepts such as Nash equilibrium.
We propose an extension of the ATL that enables reasoning about the dynamics of model change and show how it can express various intuitions and ideas from normative updates and mechanism design. We also investigated the problem of finding minimal repairs for game descriptions that violate formal requirements, and we provide complexity results for various computational problems related to minimal repair.
We have investigated the strategy logics PATL and PATL∗ (fragments of PSL) under imperfect information. Since the model-checking problem is undecidable in general in this setting, we restrict our attention to agents with memoryless (positional) strategies.
We have proposed Behavioral Natural Strategies, a probabilistic extension of Natural Strategies, and variants of the probabilistic temporal logics PATL and PATL* to handle such strategies (the resulting logics are called NatPATL and NatPATL*, resp.).
We have investigated the problem of quantitative module checking in Multi-Agent Systems, which formalizes the verification of (possibly multi-agent) systems that must adapt their behavior to the input they receive from the environment, also viewed as an authority. The quantitative setting enables the verification of different levels of satisfaction.
To enable reasoning about the strategic behavior of agents with partial observability in general game playing, we presented a formal translation from games with imperfect information specified in GDL-II to models of Epistemic Strategy Logic (SLK).
Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)
We have proposed an approach for formally verifying mechanisms for social choice and Bayesian mechanisms with variants of Strategy Logic (SL). We have shown how to use it to encode classic notions from Mechanism Design, including Bayesian-Nash equilibrium and incentive compatibility. This approach allows for automatic verification of a wide class of mechanisms, and motivates further research on applications of logic-based approaches for AMD. Our approach for automated verification of Bayesian mechanisms can take into account a wide range of settings (e.g. randomized, indirect, and Bayesian mechanisms). Furthermore, thanks to the great expressiveness of the specification language, the verification ex-ante, interim, and ex-post of complex solution concepts and properties is fully automated through model checking of logical formulas.
In many settings, the underlying structure that describes the agents’ interactions with the environment and other agents is already known. While those mechanisms may not comply with the designer’s objective, a complete redesign is not always feasible. To deal with this problem, we investigated the repair of mechanisms that do not comply with their specifications and the effect of model modifications on the agents’ capabilities. We introduced Incentive Design, a new class of problems for equilibrium verification in multi-agent systems. In our model, agents attempt to maximize their utility functions, which are expressed as formulae in temporal logic with quantitative semantics. We assume agents are rational in the sense that they adopt strategies consistent with game-theoretic solution concepts such as Nash equilibrium. For each solution concept we consider, we analyze the problems of verifying whether an incentive scheme achieves a societal objective and finding one that does so, whether it be social welfare or any other aggregate measure of collective well-being. We study both static and dynamic incentive schemes, showing that the latter are more powerful than the former.
We also explored the effects of modifications on the system underlying structure and agents’ strategic abilities. Namely, we investigated the problem of verifying and synthesising modifications (or updates) of Multi-Agent Systems. We propose an extension of the Alternating-time Temporal Logic (ATL) that enables reasoning about the dynamics of model change and show how it can express various intuitions and ideas from normative updates and mechanism design. We then investigated the problem of finding minimal repairs for game descriptions that violate formal requirements, and we provide complexity results for various computational problems related to minimal repair. We present an Answer Set Programming-based encoding for solving the minimal repair problem and demonstrate its application for automatically repairing ill-defined game descriptions.
We have investigated the strategy logics PATL and PATL∗ (fragments of PSL) under imperfect information. Since the model-checking problem is undecidable in general in this setting, we restrict our attention to agents with memoryless (positional) strategies. We present novel decidability and complexity results when the model transitions are stochastic and agents play uniform strategies. As the main result, we show that, in stochastic MAS under II, model-checking PATL is in EXPTIME when agents play probabilistic strategies. We also show that model-checking PATL∗ is PSPACE-complete when the proponent coalition is restricted to deterministic strategies. Under the same assumption, the model checking of PATL is on the second level of the polynomial hierarchy. We illustrate the usefulness of this setting with applications on mechanism design problems (online approval-based elections and probabilistic social choice), and security games.
We have proposed Behavioral Natural Strategies, a probabilistic extension of Natural Strategies, and variants of the probabilistic temporal logics PATL and PATL* to handle such strategies (the resulting logics are called NatPATL and NatPATL*, resp.). As the main result, we show that, in stochastic MAS, NatPATL model-checking is NP-complete when the active coalition is restricted to deterministic strategies. We also give a 2NEXPTIME complexity result for NatPATL* with the same restriction. In the unrestricted case, we give an EXPSPACE complexity for NatPATL and 3EXPSPACE complexity for NatPATLs. We provide examples based on secure voting.
We have investigated the problem of quantitative module checking in Multi-Agent Systems, which formalizes the verification of (possibly multi-agent) systems that must adapt their behavior to the input they receive from the environment, also viewed as an authority. The quantitative setting enables the verification of different levels of satisfaction. We consider specifications given in Quantitative Alternating-time Temporal logics and investigate complexity and expressivity results. We illustrate the approach with an example based on a weighted voting game.
To enable reasoning about the strategic behavior of agents with partial observability in general game playing, we presented a formal translation from games with imperfect information specified in GDL-II to models of Epistemic Strategy Logic (SLK). We prove the correctness of this translation and show how crucial properties of general games, including playability and the existence of Nash equilibria, can be expressed as formulas in SLK. Finally, we demonstrate the application of an existing model-checking system to verify the properties of GDL-II games.
In many settings, the underlying structure that describes the agents’ interactions with the environment and other agents is already known. While those mechanisms may not comply with the designer’s objective, a complete redesign is not always feasible. To deal with this problem, we investigated the repair of mechanisms that do not comply with their specifications and the effect of model modifications on the agents’ capabilities. We introduced Incentive Design, a new class of problems for equilibrium verification in multi-agent systems. In our model, agents attempt to maximize their utility functions, which are expressed as formulae in temporal logic with quantitative semantics. We assume agents are rational in the sense that they adopt strategies consistent with game-theoretic solution concepts such as Nash equilibrium. For each solution concept we consider, we analyze the problems of verifying whether an incentive scheme achieves a societal objective and finding one that does so, whether it be social welfare or any other aggregate measure of collective well-being. We study both static and dynamic incentive schemes, showing that the latter are more powerful than the former.
We also explored the effects of modifications on the system underlying structure and agents’ strategic abilities. Namely, we investigated the problem of verifying and synthesising modifications (or updates) of Multi-Agent Systems. We propose an extension of the Alternating-time Temporal Logic (ATL) that enables reasoning about the dynamics of model change and show how it can express various intuitions and ideas from normative updates and mechanism design. We then investigated the problem of finding minimal repairs for game descriptions that violate formal requirements, and we provide complexity results for various computational problems related to minimal repair. We present an Answer Set Programming-based encoding for solving the minimal repair problem and demonstrate its application for automatically repairing ill-defined game descriptions.
We have investigated the strategy logics PATL and PATL∗ (fragments of PSL) under imperfect information. Since the model-checking problem is undecidable in general in this setting, we restrict our attention to agents with memoryless (positional) strategies. We present novel decidability and complexity results when the model transitions are stochastic and agents play uniform strategies. As the main result, we show that, in stochastic MAS under II, model-checking PATL is in EXPTIME when agents play probabilistic strategies. We also show that model-checking PATL∗ is PSPACE-complete when the proponent coalition is restricted to deterministic strategies. Under the same assumption, the model checking of PATL is on the second level of the polynomial hierarchy. We illustrate the usefulness of this setting with applications on mechanism design problems (online approval-based elections and probabilistic social choice), and security games.
We have proposed Behavioral Natural Strategies, a probabilistic extension of Natural Strategies, and variants of the probabilistic temporal logics PATL and PATL* to handle such strategies (the resulting logics are called NatPATL and NatPATL*, resp.). As the main result, we show that, in stochastic MAS, NatPATL model-checking is NP-complete when the active coalition is restricted to deterministic strategies. We also give a 2NEXPTIME complexity result for NatPATL* with the same restriction. In the unrestricted case, we give an EXPSPACE complexity for NatPATL and 3EXPSPACE complexity for NatPATLs. We provide examples based on secure voting.
We have investigated the problem of quantitative module checking in Multi-Agent Systems, which formalizes the verification of (possibly multi-agent) systems that must adapt their behavior to the input they receive from the environment, also viewed as an authority. The quantitative setting enables the verification of different levels of satisfaction. We consider specifications given in Quantitative Alternating-time Temporal logics and investigate complexity and expressivity results. We illustrate the approach with an example based on a weighted voting game.
To enable reasoning about the strategic behavior of agents with partial observability in general game playing, we presented a formal translation from games with imperfect information specified in GDL-II to models of Epistemic Strategy Logic (SLK). We prove the correctness of this translation and show how crucial properties of general games, including playability and the existence of Nash equilibria, can be expressed as formulas in SLK. Finally, we demonstrate the application of an existing model-checking system to verify the properties of GDL-II games.