8,300 research outputs found
Non-Zero Sum Games for Reactive Synthesis
In this invited contribution, we summarize new solution concepts useful for
the synthesis of reactive systems that we have introduced in several recent
publications. These solution concepts are developed in the context of non-zero
sum games played on graphs. They are part of the contributions obtained in the
inVEST project funded by the European Research Council.Comment: LATA'16 invited pape
Equilibria, Fixed Points, and Complexity Classes
Many models from a variety of areas involve the computation of an equilibrium
or fixed point of some kind. Examples include Nash equilibria in games; market
equilibria; computing optimal strategies and the values of competitive games
(stochastic and other games); stable configurations of neural networks;
analysing basic stochastic models for evolution like branching processes and
for language like stochastic context-free grammars; and models that incorporate
the basic primitives of probability and recursion like recursive Markov chains.
It is not known whether these problems can be solved in polynomial time. There
are certain common computational principles underlying different types of
equilibria, which are captured by the complexity classes PLS, PPAD, and FIXP.
Representative complete problems for these classes are respectively, pure Nash
equilibria in games where they are guaranteed to exist, (mixed) Nash equilibria
in 2-player normal form games, and (mixed) Nash equilibria in normal form games
with 3 (or more) players. This paper reviews the underlying computational
principles and the corresponding classes
Formation of coalition structures as a non-cooperative game
Traditionally social sciences are interested in structuring people in
multiple groups based on their individual preferences. This pa- per suggests an
approach to this problem in the framework of a non- cooperative game theory.
Definition of a suggested finite game includes a family of nested simultaneous
non-cooperative finite games with intra- and inter-coalition externalities. In
this family, games differ by the size of maximum coalition, partitions and by
coalition structure formation rules. A result of every game consists of
partition of players into coalitions and a payoff? profiles for every player.
Every game in the family has an equilibrium in mixed strategies with possibly
more than one coalition. The results of the game differ from those
conventionally discussed in cooperative game theory, e.g. the Shapley value,
strong Nash, coalition-proof equilibrium, core, kernel, nucleolus. We discuss
the following applications of the new game: cooperation as an allocation in one
coalition, Bayesian games, stochastic games and construction of a
non-cooperative criterion of coalition structure stability for studying focal
points.Comment: arXiv admin note: text overlap with arXiv:1612.02344,
arXiv:1612.0374
Solving Large Extensive-Form Games with Strategy Constraints
Extensive-form games are a common model for multiagent interactions with
imperfect information. In two-player zero-sum games, the typical solution
concept is a Nash equilibrium over the unconstrained strategy set for each
player. In many situations, however, we would like to constrain the set of
possible strategies. For example, constraints are a natural way to model
limited resources, risk mitigation, safety, consistency with past observations
of behavior, or other secondary objectives for an agent. In small games,
optimal strategies under linear constraints can be found by solving a linear
program; however, state-of-the-art algorithms for solving large games cannot
handle general constraints. In this work we introduce a generalized form of
Counterfactual Regret Minimization that provably finds optimal strategies under
any feasible set of convex constraints. We demonstrate the effectiveness of our
algorithm for finding strategies that mitigate risk in security games, and for
opponent modeling in poker games when given only partial observations of
private information.Comment: Appeared in AAAI 201
Expectations or Guarantees? I Want It All! A crossroad between games and MDPs
When reasoning about the strategic capabilities of an agent, it is important
to consider the nature of its adversaries. In the particular context of
controller synthesis for quantitative specifications, the usual problem is to
devise a strategy for a reactive system which yields some desired performance,
taking into account the possible impact of the environment of the system. There
are at least two ways to look at this environment. In the classical analysis of
two-player quantitative games, the environment is purely antagonistic and the
problem is to provide strict performance guarantees. In Markov decision
processes, the environment is seen as purely stochastic: the aim is then to
optimize the expected payoff, with no guarantee on individual outcomes.
In this expository work, we report on recent results introducing the beyond
worst-case synthesis problem, which is to construct strategies that guarantee
some quantitative requirement in the worst-case while providing an higher
expected value against a particular stochastic model of the environment given
as input. This problem is relevant to produce system controllers that provide
nice expected performance in the everyday situation while ensuring a strict
(but relaxed) performance threshold even in the event of very bad (while
unlikely) circumstances. It has been studied for both the mean-payoff and the
shortest path quantitative measures.Comment: In Proceedings SR 2014, arXiv:1404.041
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