1,173 research outputs found
Logics for Non-Cooperative Games with Expectations
International audienceWe introduce the logics E(G) for reasoning about probabilistic expectation over classes G of games with discrete polynomial payoff functions represented by finite-valued Lukasiewicz formulas and provide completeness and complexity results. In addition, we introduce a new class of games where playersâ expected payoff functions are encoded by E(G)-formulas. In these games each playerâs aim is to randomise her strategic choices in order to affect the other playersâ expectations over an outcome as well as their own. We offer a logical and computational characterisation of this new class of games
Logics for Non-Cooperative Games with Expectations
We introduce the logics E(G) for reasoning about probabilistic expectation over classes G of games with discrete polynomial payoff functions represented by finite-valued Lukasiewicz formulas and provide completeness and complexity results. In addition, we introduce a new class of games where players' expected payoff functions are encoded by E(G)-formulas. In these games each player's aim is to randomise her strategic choices in order to affect the other players' expectations over an outcome as well as their own. We offer a logical and computational characterisation of this new class of games.Godo acknowledges support from the Spanish projects EdeTRI (TIN2012-39348-C02-01) and AT (CONSOLIDER CSD 2007-0022). Marchioni acknowledges support from the Marie Curie Project NAAMSI (FP7-PEOPLE-2011-IEF).Peer Reviewe
Discounting in Strategy Logic
Discounting is an important dimension in multi-agent systems as long as we
want to reason about strategies and time. It is a key aspect in economics as it
captures the intuition that the far-away future is not as important as the near
future. Traditional verification techniques allow to check whether there is a
winning strategy for a group of agents but they do not take into account the
fact that satisfying a goal sooner is different from satisfying it after a long
wait. In this paper, we augment Strategy Logic with future discounting over a
set of discounted functions D, denoted SLdisc[D]. We consider "until" operators
with discounting functions: the satisfaction value of a specification in
SLdisc[D] is a value in [0, 1], where the longer it takes to fulfill
requirements, the smaller the satisfaction value is. We motivate our approach
with classical examples from Game Theory and study the complexity of
model-checking SLdisc[D]-formulas.Comment: Extended version of the paper accepted at IJCAI 202
Robust Alternating-Time Temporal Logic
In multi-agent system design, a crucial aspect is to ensure robustness,
meaning that for a coalition of agents A, small violations of adversarial
assumptions only lead to small violations of A's goals. In this paper we
introduce a logical framework for robust strategic reasoning about multi-agent
systems. Specifically, inspired by recent works on robust temporal logics, we
introduce and study rATL and rATL*, logics that extend the well-known
Alternating-time Temporal Logic ATL and ATL* by means of an opportune
multi-valued semantics for the strategy quantifiers and temporal operators. We
study the model-checking and satisfiability problems for rATL and rATL* and
show that dealing with robustness comes at no additional computational cost.
Indeed, we show that these problems are PTime-complete and ExpTime-complete for
rATL, respectively, while both are 2ExpTime-complete for rATL*
Computer-aided verification in mechanism design
In mechanism design, the gold standard solution concepts are dominant
strategy incentive compatibility and Bayesian incentive compatibility. These
solution concepts relieve the (possibly unsophisticated) bidders from the need
to engage in complicated strategizing. While incentive properties are simple to
state, their proofs are specific to the mechanism and can be quite complex.
This raises two concerns. From a practical perspective, checking a complex
proof can be a tedious process, often requiring experts knowledgeable in
mechanism design. Furthermore, from a modeling perspective, if unsophisticated
agents are unconvinced of incentive properties, they may strategize in
unpredictable ways.
To address both concerns, we explore techniques from computer-aided
verification to construct formal proofs of incentive properties. Because formal
proofs can be automatically checked, agents do not need to manually check the
properties, or even understand the proof. To demonstrate, we present the
verification of a sophisticated mechanism: the generic reduction from Bayesian
incentive compatible mechanism design to algorithm design given by Hartline,
Kleinberg, and Malekian. This mechanism presents new challenges for formal
verification, including essential use of randomness from both the execution of
the mechanism and from the prior type distributions. As an immediate
consequence, our work also formalizes Bayesian incentive compatibility for the
entire family of mechanisms derived via this reduction. Finally, as an
intermediate step in our formalization, we provide the first formal
verification of incentive compatibility for the celebrated
Vickrey-Clarke-Groves mechanism
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