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1.
Wojciech Połowczuk Piotr Więcek Tadeusz Radzik 《Mathematical Methods of Operations Research》2007,65(1):141-152
This paper gives wide characterization of n-person non-coalitional games with finite players’ strategy spaces and payoff functions having some concavity or convexity
properties. The characterization is done in terms of the existence of two-point-strategy Nash equilibria, that is equilibria
consisting only of mixed strategies with supports being one or two-point sets of players’ pure strategy spaces. The structure
of such simple equilibria is discussed in different cases. The results obtained in the paper can be seen as a discrete counterpart
of Glicksberg’s theorem and other known results about the existence of pure (or “almost pure”) Nash equilibria in continuous
concave (convex) games with compact convex spaces of players’ pure strategies. 相似文献
2.
The “Nash program” initiated by Nash (Econometrica 21:128–140, 1953) is a research agenda aiming at representing every axiomatically
determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L-Nash solution
first defined by Forgó (Interactive Decisions. Lecture Notes in Economics and Mathematical Systems, vol 229. Springer, Berlin,
pp 1–15, 1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative
infinity in a fixed direction. In Forgó and Szidarovszky (Eur J Oper Res 147:108–116, 2003), the L-Nash solution was related
to the solution of multiciteria decision making and two different axiomatizations of the L-Nash solution were also given in
this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two-person bargaining
problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement
point to obtain the L-Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein’s
alternative offer game (Econometrica 50:97–109, 1982) is shown to asymptotically implement the L-Nash solution. If penalty
is internalized as a decision variable of one of the players, then a modification of Howard’s game (J Econ Theory 56:142–159,
1992) also implements the L-Nash solution. 相似文献
3.
Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account,
don’t have an a-priori opinion on the relative importance of all these criteria. Roemer (Econ. Bull. 3:1–13, 2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining
game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky
bargaining solution (see Kalai and Smorodinsky in Econometrica 43:513–518, 1975). We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered by Roemer (Econ. Bull. 3:1–13, 2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement
concepts based on stability with respect to perturbations; in particular, we consider the extension to multicriteria games
of the Selten’s trembling hand perfect equilibrium concept (see Selten in Int. J. Game Theory 4:25–55, 1975) and prove that perfect Kalai-Smorodinsky bargaining solution equilibria exist and properly refine both the perfect equilibria
and the Kalai-Smorodinsky bargaining solution equilibria. 相似文献
4.
In this note we provide a characterization of a subclass of bargaining problems for which the Nash solution has the property
of disagreement point monotonicity. While the original d-monotonicity axiom and its stronger notion, strong d-monotonicity, were introduced and discussed by Thomson (J Econ Theory, 42: 50–58, 1987), this paper introduces local strong
d-monotonicity and derives a necessary and sufficient condition for the Nash solution to be locally strongly d-monotonic. This characterization is given by using the sensitivity matrix of the Nash bargaining solution w.r.t. the disagreement
point d. Moverover, we present a sufficient condition for the Nash solution to be strong d-monotonic. 相似文献
5.
Shiran Rachmilevitch 《International Journal of Game Theory》2011,40(4):691-696
We provide a new axiomatization of the Kalai–Smorodinsky bargaining solution, which replaces the axiom of individual monotonicity
by disagreement point monotonicity and a restricted version of Nash’s IIA. 相似文献
6.
There exists a Nash equilibrium (ε-Nash equilibrium) for every n-person stochastic game with a finite (countable) state space and finite action sets for the players if the payoff to each
player i is one when the process of states remains in a given set of states G
i and is zero otherwise.
Received: December 2000 相似文献
7.
Prof. P. P. Shenoy 《International Journal of Game Theory》1979,8(3):133-164
This paper deals with the question of coalition formation inn-person cooperative games. Two abstract game models of coalition formation are proposed. We then study the core and the dynamic solution of these abstract games. These models assume that there is a rule governing the allocation of payoffs to each player in each coalition structure called a payoff solution concept. The predictions of these models are characterized for the special case of games with side payments using various payoff solution concepts such as the individually rational payoffs, the core, the Shapley value and the bargaining set M1 (i). Some modifications of these models are also discussed. 相似文献
8.
In this paper, we prove the validity of the Chern conjecture in affine geometry [18], namely that an affine maximal graph
of a smooth, locally uniformly convex function on two dimensional Euclidean space, R
2, must be a paraboloid. More generally, we shall consider the n-dimensional case, R
n
, showing that the corresponding result holds in higher dimensions provided that a uniform, “strict convexity” condition holds.
We also extend the notion of “affine maximal” to non-smooth convex graphs and produce a counterexample showing that the Bernstein
result does not hold in this generality for dimension n≥10.
Oblatum 16-IV-1999 & 4-XI-1999?Published online: 21 February 2000 相似文献
9.
Quitting games are multi-player sequential games in which, at every stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; each player i then receives a payoff r
S
i, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is zero.? We exhibit a four-player
quitting game, where the “simplest” equilibrium is periodic with period two. We argue that this implies that all known methods
to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail in general, and provide
some geometric intuition for this phenomenon.
Received: October 2001 相似文献
10.
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
11.
In this paper we consider n-person games in which each player has a convex strategy set over which his closed strictly quasi-concave payoff function is defined. The interaction of the players' strategies is via linear constraints in the form of a convex cone. An appropriate duality theory is developed and applied to an example with economic significance. The resulting analysis leads naturally to a means for solving such a game that merely involves the solution of a set of linear equations. 相似文献
12.
Maschler, Owen and Peleg (1988) constructed a dynamic system for modelling a possible negotiation process for players facing
a smooth n-person pure bargaining game, and showed that all paths of this system lead to the Nash point. They also considered the non-convex
case, and found in this case that the limiting points of solutions of the dynamic system belong to the Nash set. Here we extend
the model to i) general convex pure bargaining games, and to ii) games generated by “divide the cake” problems. In each of
these cases we construct a dynamic system consisting of a differential inclusion (generalizing the Maschler-Owen-Peleg system
of differential equations), prove existence of solutions, and show that the solutions converge to the Nash point (or Nash
set). The main technical point is proving existence, as the system is neither convex valued nor continuous. The intuition
underlying the dynamics is the same as (in the convex case) or analogous to (in the division game) that of Maschler, Owen,
and Peleg.
Received August 1997/Final version May 1998 相似文献
13.
Dr. V. Bubelis 《International Journal of Game Theory》1979,8(2):65-79
We are concerned with Nash equilibrium points forn-person games. It is proved that, given any real algebraic numberα, there exists a 3-person game with rational data which has a unique equilibrium point andα is the equilibrium payoff for some player. We also present a method which allows us to reduce an arbitraryn-person game to a 3-person one, so that a number of questions about generaln-person games can be reduced to consideration of the special 3-person case. Finally, a completely mixed game, where the equilibrium set is a manifold of dimension one, is constructed. 相似文献
14.
Ori Haimanko 《International Journal of Game Theory》2000,29(3):451-468
We investigate quasi-values of finite games – solution concepts that satisfy the axioms of Shapley (1953) with the possible
exception of symmetry.
Following Owen (1972), we define “random arrival', or path, values: players are assumed to “enter' the game randomly, according to independently distributed arrival times, between
0 and 1; the payoff of a player is his expected marginal contribution to the set of players that have arrived before him.
The main result of the paper characterizes quasi-values, symmetric with respect to some coalition structure with infinite
elements (types), as random path values, with identically distributed random arrival times for all players of the same type.
General quasi-values are shown to be the random order values (as in Weber (1988) for a finite universe of players).
Pseudo-values (non-symmetric generalization of semivalues) are also characterized, under different assumptions of symmetry.
Received: April 1998/Revised version: February 2000 相似文献
15.
A division rule for claims problems, also known as bankruptcy or rationing problems, based on the pseudo-average solution
is studied (for 2-person problems). This solution was introduced in Moulin (Jpn Econ Rev 46:303–332, 1995) for discrete cost allocation problems. Using the asymptotic approach, we obtain a division rule for claims problems. We
characterize the division rule axiomatically and show that it coincides with the rule associated to the equal area bargaining
solution (this is not true for n = 3). Moreover, following Moulin and Shenker (J Econ Theor 64:178–201, 1994), we show that its associated solution for continuous homogeneous goods is precisely the continuous pseudo-average solution. 相似文献
16.
We consider bargaining problems under the assumption that players are loss averse, i.e., experience disutility from obtaining an outcome lower than some reference point. We follow the approach of Shalev (2002) by imposing the self-supporting condition on an outcome: an outcome z in a bargaining problem is self-supporting under a given bargaining solution, whenever transforming the problem using outcome z as a reference point, yields a transformed problem in which the solution is z.We show that n-player bargaining problems have a unique self-supporting outcome under the Kalai-Smorodinsky solution. For all possible loss aversion coefficients we determine the bargaining solutions that give exactly these outcomes, and characterize them by the standard axioms of Scale Invariance, Individual Monotonicity, and Strong Individual Rationality, and a new axiom called Proportional Concession Invariance (PCI). A bargaining solution satisfies PCI if moving the utopia point in the direction of the solution outcome does not change this outcome. 相似文献
17.
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
18.
Gérard Hamiache 《International Journal of Game Theory》2001,30(2):279-289
In this work, a new axiomatization of the Shapley is presented. An associated game is constructed. We define a sequence of
games, when the term of order n, in this sequence, is the associated game of the term of order (n−1). We show that the sequence converges and that the limit game is inessential. The solution is obtained using the inessential
game axiom, the associated consistency axiom and the continuity axiom. As a by-product, we note that neither the additivity
nor the efficiency axioms are needed.
Accepted September 2001 相似文献
19.
Aubrey Blecher Charlotte Brennan Toufik Mansour 《Central European Journal of Mathematics》2012,10(2):788-796
Compositions and partitions of positive integers are often studied in separate frameworks where partitions are given by q-series generating functions and compositions exhibiting specific patterns are designated by generating functions for these
patterns. Here, we view compositions as alternating sequences of weakly increasing and strictly decreasing partitions (i.e.
alternating blocks). We obtain generating functions for the number of such partitions in terms of the size of the composition,
the number of parts and the total number of “valleys” and “peaks”. From this, we find the total number of “peaks” and “valleys”
in the composition of n which have the mentioned pattern. We also obtain the generating function for compositions which split into just two partition
blocks. Finally, we obtain the two generating functions for compositions of n that start either with a weakly increasing partition or a strictly decreasing partition. 相似文献
20.
Trevor D. Wooley 《Monatshefte für Mathematik》2000,130(2):161-170
Estimates are provided for small moments of exponential sums over smooth numbers substantially sharper than available hitherto.
These bounds arise from the author’s recent breaking of “classical convexity” in Waring’s problem. The methods underlying
these new estimates provide guidance on good choices of parameters in the new iterative methods for smaller exponents.
(Received 13 September 1999) 相似文献