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1.
Edward M. Bolger 《International Journal of Game Theory》2000,29(1):93-99
In Bolger [1993], an efficient value was obtained for a class of games called games with n players and r alternatives. In these games, each of the n players must choose one and only one of the r alternatives. This value can be used to determine a player’s “a priori” value in such a game. In this paper, we show that
the value has a consistency property similar to the “consistency” for TU games in Hart/Mas-Colell [1989] and we present a
set of axioms (including consistency) which characterizes this value.
The games considered in this paper differ from the multi-choice games considered by Hsiao and Raghavan [1993]. They consider
games in which the actions of the players are ordered in the sense that, if i >j, then action i carries more “weight” than action j.
These games also differ from partition function games in that the worth of a coalition depends not only on the partitioning
of the players but also on the action chosen by each subset of the partition.
Received: April 1994/final version: June 1999 相似文献
2.
David H. Wolpert 《International Journal of Game Theory》2009,38(4):539-551
The quantal response equilibrium (QRE) is a powerful alternative to full rationality equilibrium concepts. At a QRE, all joint
moves have non-zero probability. However in “mixed scenarios”, where some players use quantal response and some use best response,
equilibrium strategy profiles can have joint moves with zero probability. This raises the question of applying the trembling
hand refinement to such mixed scenarios. To address this I first show how to reformulate the QRE as a “best response” equilibrium
where expected utilities are replaced by more general objective functions. I then show that under this reformulation the two
popular types of trembling hand perfection can differ when some players use quantal response and some use best response. I
end by showing that one of those types of trembling hand perfection cannot be used to remove certain troubling kinds of equilibrium
in such mixed scenarios, while the other type can. The conclusion is that only the one type of trembling hand perfection should
be applied when we allow some players to be quantal response and some to be best response. 相似文献
3.
Licun Xue 《International Journal of Game Theory》2000,29(3):339-357
This paper defines “negotiation-proof Nash equilibrium', a notion that applies to environments where players can negotiate
openly and directly prior to the play of a noncooperative game. It recognizes the possibility that a group of self-interested
players may choose, voluntarily and without binding agreement, to coordinate their choice of strategies and make joint objections;
moreover, it takes the perfect foresight of rational players fully into account. The merit of the notion of negotiation-proof
Nash equilibrium is twofold: (1) It offers a way to rectify the nestedness assumption and myopia embedded in the notion of
coalition-proof Nash equilibrium. (2) The negotiation process is formalized by a “graph”, which serves as a natural extension to the approach that models
preplay communication by an extensive game.
Received: October 1998/Final version: May 2000 相似文献
4.
Alessio Moretti 《Logica Universalis》2009,3(1):19-57
Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic
(both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”,
“permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s
“logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic
oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical
representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie
73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter,
Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic
internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic
has appeared, that is “n-opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m” (m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper,
by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s
unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”,
“deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities
is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra),
whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional
very regular solid).
相似文献
5.
Aviad Heifetz 《International Journal of Game Theory》1999,28(3):435-442
Aumann (1989) argued that the natural partitions on the space of all maximally consistent sets of formulas in multi-player
S5 logic are necessarily “commonly known” by the players. We show, however, that there are many other sets of partitions on
this space that conform with the formulas that build the states – as many as there are subsets of the continuum! Thus, assuming
a set of partitions on this space is “common knowledge” is an informal but meaningful meta-assumption. 相似文献
6.
We demonstrate that, if there are sufficiently many players, any Bayesian equilibrium of an incomplete information game can
be “ε-purified” . That is, close to any Bayesian equilibrium there is an approximate Bayesian equilibrium in pure strategies. Our
main contribution is obtaining this result for games with a countable set of pure strategies. In order to do so we derive
a mathematical result, in the spirit of the Shapley–Folkman Theorem, permitting countable strategy sets. Our main assumption
is a “large game property,” dictating that the actions of relatively small subsets of players cannot have large affects on
the payoffs of other players.
E. Cartwright and M. Wooders are indebted to Phillip Reny, Frank Page and two anonymous referees for helpful comments. 相似文献
7.
Rade T. Živaljević 《Discrete and Computational Geometry》2009,41(1):135-161
This paper lays the foundation for a theory of combinatorial groupoids that allows us to use concepts like “holonomy”, “parallel transport”, “bundles”, “combinatorial curvature”, etc. in the context
of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. We introduce a new, holonomy-type
invariant for cubical complexes, leading to a combinatorial “Theorema Egregium” for cubical complexes that are non-embeddable
into cubical lattices. Parallel transport of Hom-complexes and maps is used as a tool to extend Babson–Kozlov–Lovász graph coloring results to more general statements about
nondegenerate maps (colorings) of simplicial complexes and graphs.
The author was supported by grants 144014 and 144026 of the Serbian Ministry of Science and Technology. 相似文献
8.
9.
G. J. Olsder 《Journal of Optimization Theory and Applications》2009,143(3):601-618
Games are considered in which the role of the players is a hierarchical one. Some players behave as leaders, others as followers.
Such games are named after Stackelberg. In the current paper, a special type of these games is considered, known in the literature
as inverse Stackelberg games. In such games, the leader (or: leaders) announces his strategy as a mapping from the follower
(or: followers) decision space into his own decision space. Arguments for studying such problems are given. The routine way
of analysis, leading to a study of composed functions, is not very fruitful. Other approaches are given, mainly by studying
specific examples. Phenomena in problems with more than one leader and/or follower are studied within the context of the inverse
Stackelberg concept. As a side issue, expressions like “two captains on a ship” and “divide and conquer” are given a mathematical
foundation. 相似文献
10.
We prove a preservation theorem for limit steps of countable support iterations of proper forcing notions whose particular
cases are preservations of the following properties on limit steps: “no random reals are added”, “μ(Random(V))≠1”, “no dominating reals are added”, “Cohen(V) is not comeager”. Consequently, countable support iterations of σ-centered forcing notions do not add random reals.
The work was supported by BRF of Israel Academy of Sciences and by grant GA SAV 365 of Slovak Academy of Sciences. 相似文献
11.
V. S. Levchenkov 《Computational Mathematics and Modeling》2008,19(1):102-115
A new approach to the solution of one-step games is constructed, without using the concept of mixed strategy. The notion of
a “set” solution of a bimatrix game is defined. It is shown that this solution always exists and may be found by a finite
procedure. Examples are given illustrating the form of the “set” solution and the structure of the set of best responses for
various levels of information availability to the players regarding the opponent’s behavior.
__________
Translated from Nelineinaya Dinamika i Upravlenie, No. 4, pp. 341–356, 2004. 相似文献
12.
We consider the following “silent duel” of m players with a possible economic interpretation. Each player has one “bullet”, which she can shoot at any time during the time interval [0,1]. The probability that the i-th player hits the “target” at moment t is given by an increasing accuracy function f
i
(t). The winner is the player who hits the target first. Under natural assumptions on the functions f
i
(t) we prove the existence and uniqueness of a Nash equilibrium point in this game, and we provide an explicit construction of this equilibrium. This construction allows us to obtain exact solutions for many specific examples. Some of them are presented.This work was partly supported by RBRF grants 03-01-00479. 相似文献
13.
T. V. Panchapagesan 《Rendiconti del Circolo Matematico di Palermo》1995,44(3):417-440
The concept of an orthogonal spectral representation (OTSR) of a Hilbert spaceH relative to a spectral measureE(.) is introduced and it is shown that every Hilbert space admits an OTSR relative to a given spectral measure. Apart from
the various results obtained about OTSRs, the principal result of Allan Brown (1974) is deduced as an easy consequence of
this study. A new complete system of unitary invariants called the “equivalence of OTSRs”, is given for spectral measures.
Two special types of OTSRs called “BOTSR” and “COBOTSR” are introduced and characterized respectively in terms of the “GCGS-property”
and “CGS-property” of the associated spectral measure. Various complete systems of unitary invariants are given for spectral
measures with the GCGS-property. Finally, the Wecken-Plesner-Rohlin theorem on hermitian operators with simple spectra is
generalized to arbitrary spectral measures. 相似文献
14.
Manuel Abellanas Ma Dolores López Javier Rodrigo Isabel Lillo 《International Journal of Game Theory》2011,40(3):449-459
Spatial models of two-player competition in spaces with more than one dimension almost never have pure-strategy Nash equilibria,
and the study of the equilibrium positions, if they exist, yields a disappointing result: the two players must choose the
same position to achieve equilibrium. In this work, a discrete game is proposed in which the existence of Nash equilibria
is studied using a geometric argument. This includes a definition of equilibrium which is weaker than the classical one to
avoid the uniqueness of the equilibrium position. As a result, a “region of equilibrium” appears, which can be located by
geometric methods. In this area, the players can move around in an “almost-equilibrium” situation and do not necessarily have
to adopt the same position. 相似文献
15.
We consider the “and” communication device that receives inputs from two players and outputs the public signal yes if both messages are yes, and outputs no otherwise. We prove that no correlation can securely be implemented using this device, even when infinitely many stages of
communication are allowed.
Received December 1998/Final version November 2000 相似文献
16.
Rémi Peyre 《Potential Analysis》2008,29(1):17-36
Carne’s bound is a sharp inequality controlling the transition probabilities for a discrete reversible Markov chain (Section 1).
Its ordinary proof uses spectral techniques which look as efficient as miraculous. Here we present a new proof, comparing
a “drift” for ways “out” and “back”, to get the gaussian part of the bound (Section 2), and using a conditioning technique
to get the flight factor (Section 4). Moreover we show how our proof is more “supple” than Carne’s one and may generalize
(Section 3.2).
相似文献
17.
Various statistics on wreath products are defined via canonical words, “colored” right to left minima and “colored” descents.
It is shown that refined counts with respect to these statistics have nice recurrence formulas of binomial-Stirling type.
These extended Stirling numbers determine (via matrix inversion) dual systems, which are also shown to have combinatorial
realizations within the wreath product. The above setting also gives rise to a MacMahon-type equi-distribution theorem over
subsets with prescribed statistics.
Partially supported by Minerva Grant No. 8441 and by EC's IHRP Programme, within the Research Training Network “Algebraic
Combinatorics in Europe”, grant HPRN-CT-2001-00272.
Partially supported by EC's IHRP Programme, within the Research Training Network “Algebraic Combinatorics in Europe”, grant
HPRN-CT-2001-00272. 相似文献
18.
Gábor Czédli 《Mathematica Slovaca》2011,61(6):859-870
For each of the relations “less than or equal to”, “less than”, “covered by”, and “covered by or equal to”, we characterize
finite orders (also called posets) with the property that the pair of Galois closure operators induced by the relation in
question coincides with the pair of closure operators introduced and applied in our previous paper in 2007. We also consider
the “less than or equal to” relation between the set of join-irreducible elements and the set of meet-irreducible elements,
and we show that the above-mentioned pairs of closure operators coincide for finite modular lattices. 相似文献
19.
We consider a duopolistic industry where the current sales of each firm is proportional to its goodwill stock. The evolution
of the latter depends positively on own advertising effort and negatively on competitor’s advertising. A standard assumption
in the literature in differential games of advertising is that the players remain active throughout the whole (infinite) duration
of the game. We relax this assumption and characterize the circumstances under which a firm finds it optimal to remain or
exit the industry. Among other things, it is shown that, if both players are “strong”, then the unique Nash equilibrium is
the same that one would obtain in the absence of interference from competitor’s advertising.
Research supported by Ministry of University and Research of Italy, University of Padua and NSERC, Canada. 相似文献
20.
The ancient record, “During the first year of King Yi, the day dawned twice at Zheng”, has provided important clues to early
Chinese chronicles. The astronomical conditions and visible area distributions related to such a “double dawn” event are discussed,
and the precision and current problems in the calculations of ancient astronomical phenomena are shown. On such a basis, all
the solar eclipses from 1000 BC to 840 BC are calculated and their associated “double dawn” features investigated. The conclusion
that the “double dawn” was a solar eclipse occurring on April 21st, 899 BC is corfirmed to be the most reasonable.
Project supported by the Xia-Shang-Zhou Chronology Project and Director Foundation of the Chinese Academy of Sciences. 相似文献