4,173 research outputs found
The Complexity of angel-daemons and game isomorphism
The analysis of the computational aspects of strategic situations is a basic field in Computer
Sciences. Two main topics related to strategic games have been developed. First,
introduction and analysis of a class of games (so called angel/daemon games) designed
to asses web applications, have been considered. Second, the problem of isomorphism
between strategic games has been analysed. Both parts have been separately considered.
Angel-Daemon Games
A service is a computational method that is made available for general use through a
wide area network. The performance of web-services may fluctuate; at times of stress the
performance of some services may be degraded (in extreme cases, to the point of failure).
In this thesis uncertainty profiles and Angel-Daemon games are used to analyse servicebased
behaviours in situations where probabilistic reasoning may not be appropriate.
In such a game, an angel player acts on a bounded number of ¿angelic¿ services
in a beneficial way while a daemon player acts on a bounded number of ¿daemonic¿
services in a negative way. Examples are used to illustrate how game theory can be used
to analyse service-based scenarios in a realistic way that lies between over-optimism and
over-pessimism.
The resilience of an orchestration to service failure has been analysed - here angels and
daemons are used to model services which can fail when placed under stress. The Nash
equilibria of a corresponding Angel-Daemon game may be used to assign a ¿robustness¿
value to an orchestration.
Finally, the complexity of equilibria problems for Angel-Daemon games has been
analysed. It turns out that Angel-Daemon games are, at the best of our knowledge, the
first natural example of zero-sum succinct games.
The fact that deciding the existence of a pure Nash equilibrium or a dominant strategy
for a given player is Sp
2-complete has been proven. Furthermore, computing the value of
an Angel-Daemon game is EXP-complete. Thus, matching the already known complexity
results of the corresponding problems for the generic families of succinctly represented
games with exponential number of actions.
Game Isomorphism
The question of whether two multi-player strategic games are equivalent and the computational
complexity of deciding such a property has been addressed. Three notions
of isomorphisms, strong, weak and local have been considered. Each one of these isomorphisms
preserves a different structure of the game. Strong isomorphism is defined to
preserve the utility functions and Nash equilibria. Weak isomorphism preserves only the
player preference relations and thus pure Nash equilibria. Local isomorphism preserves
preferences defined only on ¿close¿ neighbourhood of strategy profiles.
The problem of the computational complexity of game isomorphism, which depends
on the level of succinctness of the description of the input games but it is independent
of the isomorphism to consider, has been shown. Utilities in games can be given succinctly
by Turing machines, boolean circuits or boolean formulas, or explicitly by tables.
Actions can be given also explicitly or succinctly. When the games are given in general
form, an explicit description of actions and a succinct description of utilities have been
assumed. It is has been established that the game isomorphism problem for general form
games is equivalent to the circuit isomorphism when utilities are described by Turing Machines;
and to the boolean formula isomorphism problem when utilities are described by
formulas. When the game is given in explicit form, it is has been proven that the game
isomorphism problem is equivalent to the graph isomorphism problem.
Finally, an equivalence classes of small games and their graphical representation have
been also examined.Postprint (published version
Finding Any Nontrivial Coarse Correlated Equilibrium Is Hard
One of the most appealing aspects of the (coarse) correlated equilibrium
concept is that natural dynamics quickly arrive at approximations of such
equilibria, even in games with many players. In addition, there exist
polynomial-time algorithms that compute exact (coarse) correlated equilibria.
In light of these results, a natural question is how good are the (coarse)
correlated equilibria that can arise from any efficient algorithm or dynamics.
In this paper we address this question, and establish strong negative
results. In particular, we show that in multiplayer games that have a succinct
representation, it is NP-hard to compute any coarse correlated equilibrium (or
approximate coarse correlated equilibrium) with welfare strictly better than
the worst possible. The focus on succinct games ensures that the underlying
complexity question is interesting; many multiplayer games of interest are in
fact succinct. Our results imply that, while one can efficiently compute a
coarse correlated equilibrium, one cannot provide any nontrivial welfare
guarantee for the resulting equilibrium, unless P=NP. We show that analogous
hardness results hold for correlated equilibria, and persist under the
egalitarian objective or Pareto optimality.
To complement the hardness results, we develop an algorithmic framework that
identifies settings in which we can efficiently compute an approximate
correlated equilibrium with near-optimal welfare. We use this framework to
develop an efficient algorithm for computing an approximate correlated
equilibrium with near-optimal welfare in aggregative games.Comment: 21 page
NEEXP is Contained in MIP*
We study multiprover interactive proof systems. The power of classical multiprover interactive proof systems, in which the provers do not share entanglement, was characterized in a famous work by Babai, Fortnow, and Lund (Computational Complexity 1991), whose main result was the equality MIP = NEXP. The power of quantum multiprover interactive proof systems, in which the provers are allowed to share entanglement, has proven to be much more difficult to characterize. The best known lower-bound on MIP* is NEXP ⊆ MIP*, due to Ito and Vidick (FOCS 2012). As for upper bounds, MIP* could be as large as RE, the class of recursively enumerable languages.
The main result of this work is the inclusion of NEEXP = NTIME[2^(2poly(n))] ⊆ MIP*. This is an exponential improvement over the prior lower bound and shows that proof systems with entangled provers are at least exponentially more powerful than classical provers. In our protocol the verifier delegates a classical, exponentially large MIP protocol for NEEXP to two entangled provers: the provers obtain their exponentially large questions by measuring their shared state, and use a classical PCP to certify the correctness of their exponentially-long answers. For the soundness of our protocol, it is crucial that each player should not only sample its own question correctly but also avoid performing measurements that would reveal the other player's sampled question. We ensure this by commanding the players to perform a complementary measurement, relying on the Heisenberg uncertainty principle to prevent the forbidden measurements from being performed
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