共查询到20条相似文献,搜索用时 905 毫秒
1.
Geir B. Asheim 《International Journal of Game Theory》2002,30(4):453-478
Proper consistency is defined by the property that each player takes all opponent strategies into account (is cautious) and deems one opponent strategy to be infinitely more likely than another if the opponent prefers the one to the other (respects preferences). When there is common certain belief of proper consistency, a most preferred strategy is properly rationalizable. Any strategy used with positive probability in a proper equilibrium is properly rationalizable. Only strategies that lead
to the backward induction outcome are properly rationalizable in the strategic form of a generic perfect information game.
Proper rationalizability can test the robustness of inductive procedures.
Final version: December 2001 相似文献
2.
Proper rationalizability and backward induction 总被引:1,自引:0,他引:1
Frank Schuhmacher 《International Journal of Game Theory》1999,28(4):599-615
This paper introduces a new normal form rationalizability concept, which in reduced normal form games corresponding to generic
finite extensive games of perfect information yields the unique backward induction outcome. The basic assumption is that every
player trembles “more or less rationally” as in the definition of a ε-proper equilibrium by Myerson (1978). In the same way
that proper equilibrium refines Nash and perfect equilibrium, our model strengthens the normal form rationalizability concepts
by Bernheim (1984), B?rgers (1994) and Pearce (1984). Common knowledge of trembling implies the iterated elimination of strategies
that are strictly dominated at an information set. The elimination process starts at the end of the game tree and goes backwards
to the beginning.
Received: October 1996/Final version: May 1999 相似文献
3.
Yaron Azrieli 《International Journal of Game Theory》2009,38(2):209-219
An information structure in a non-cooperative game determines the signal that each player observes as a function of the strategy profile. Such information
structure is called non-manipulable if no player can gain new information by changing his strategy. A Conjectural Equilibrium (CE) (Battigalli in Unpublished undergraduate dissertation, 1987; Battigalli and Guaitoli 1988; Decisions, games and markets,
1997) with respect to a given information structure is a strategy profile in which each player plays a best response to his
conjecture about his opponents’ play and his conjecture is not contradicted by the signal he observes. We provide a sufficient
condition for the existence of pure CE in games with a non-manipulable information structure. We then apply this condition
to prove existence of pure CE in two classes of games when the information that players have is the distribution of strategies
in the population.
This work is based on a chapter from my Ph.D. dissertation written at the School of Mathematical Sciences of Tel-Aviv University
under the supervision of Prof. Ehud Lehrer. I am grateful to Ehud Lehrer as well as to Pierpaolo Battigalli, Yuval Heller,
two anonymous referees, an Associate Editor and the Editor for very helpful comments and references. 相似文献
4.
Ryoichi Nishimura Shunsuke Hayashi Masao Fukushima 《Journal of Global Optimization》2012,53(1):107-120
Consider the N-person non-cooperative game in which each player’s cost function and the opponents’ strategies are uncertain. For such an
incomplete information game, the new solution concept called a robust Nash equilibrium has attracted much attention over the
past several years. The robust Nash equilibrium results from each player’s decision-making based on the robust optimization
policy. In this paper, we focus on the robust Nash equilibrium problem in which each player’s cost function is quadratic,
and the uncertainty sets for the opponents’ strategies and the cost matrices are represented by means of Euclidean and Frobenius
norms, respectively. Then, we show that the robust Nash equilibrium problem can be reformulated as a semidefinite complementarity
problem (SDCP), by utilizing the semidefinite programming (SDP) reformulation technique in robust optimization. We also give
some numerical example to illustrate the behavior of robust Nash equilibria. 相似文献
5.
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
6.
Roman Kozhan 《International Journal of Game Theory》2011,40(2):215-230
This paper introduces a class of non-additive anonymous games where agents are assumed to be uncertain (in the sense of Knight)
about opponents’ strategies and about the initial distribution over players’ characteristics in the game. We model uncertainty
by non-additive measures or capacities and prove the Cournot–Nash equilibrium existence theorem for this class of games. Equilibrium
distribution can be symmetrized under milder conditions than in the case of additive games. In particular, it is not required
for the space characteristics to be atomless under capacities. The set-valued map of the Cournot–Nash equilibria is upper-semicontinuous
as a function of initial beliefs of the players for non-additive anonymous games. 相似文献
7.
Talat S. Genc 《Computational Management Science》2007,4(2):141-157
This paper studies market outcome equivalence of two dynamic production-capital investment games under uncertainty. One is
played under complete information, while the other, feedback (FB) game, is played under incomplete information about the opponents’
costs and market demand. The FB game structure may be observed in some newly initiated industries, in which a homogeneous
good is exchanged via an auction mechanism. In that case, the FB game setting may predict the complete information equilibrium
market outcomes.
相似文献
8.
Robert Samuel Simon 《Israel Journal of Mathematics》2006,156(1):285-309
A stochastic game isvalued if for every playerk there is a functionr
k:S→R from the state spaceS to the real numbers such that for every ε>0 there is an ε equilibrium such that with probability at least 1−ε no states is reached where the future expected payoff for any playerk differs fromr
k(s) by more than ε. We call a stochastic gamenormal if the state space is at most countable, there are finitely many players, at every state every player has only finitely many
actions, and the payoffs are uniformly bounded and Borel measurable as functions on the histories of play. We demonstrate
an example of a recursive two-person non-zero-sum normal stochastic game with only three non-absorbing states and limit average
payoffs that is not valued (but does have ε equilibria for every positive ε). In this respect two-person non-zero-sum stochastic
games are very different from their zero-sum varieties. N. Vieille proved that all such non-zero-sum games with finitely many
states have an ε equilibrium for every positive ε, and our example shows that any proof of this result must be qualitatively
different from the existence proofs for zero-sum games. To show that our example is not valued we need that the existence
of ε equilibria for all positive ε implies a “perfection” property. Should there exist a normal stochastic game without an
ε equilibrium for some ε>0, this perfection property may be useful for demonstrating this fact. Furthermore, our example sews
some doubt concerning the existence of ε equilibria for two-person non-zero-sum recursive normal stochastic games with countably
many states.
This research was supported financially by the German Science Foundation (Deutsche Forschungsgemeinschaft) and the Center
for High Performance Computing (Technical University, Dresden). The author thanks Ulrich Krengel and Heinrich Hering for their
support of his habilitation at the University of Goettingen, of which this paper is a part. 相似文献
9.
Michael Trost 《International Journal of Game Theory》2013,42(3):755-776
Bonanno (Logics and the foundations of game and decision theory, Amsterdam University Press, Amsterdam, 2008) provides an epistemic characterization for the solution concept of iterated deletion of inferior strategy profiles (IDIP) by embedding strategic-form games with ordinal payoffs in non-probabilistic epistemic models which are built on Kripke frames. In this paper, we will follow the event-based approach to epistemic game theory and supplement strategic games with type space models, where each type is associated with a preference relation on the state space. In such a framework, IDIP can be characterized by the conditions that at least one player has correct beliefs about the state of the world and that there is common belief that every player is rational, has correct beliefs about the state of the world and has strictly monotone preferences. Moreover, we shall compare the epistemic motivations for IDIP and its mixed strategy variant known as strong rationalizability (SR). Presuppose the above conditions. Whenever there is also common belief that players’ preferences are representable by some expected utility function IDIP still applies. But if there is common belief that players’ preferences are representable by some expected payoff function, then SR results. 相似文献
10.
G. Schoenmakers J. Flesch F. Thuijsman O. J. Vrieze 《Journal of Optimization Theory and Applications》2008,136(3):459-473
This paper deals with 2-player zero-sum repeated games in which player 1 receives a bonus at stage t if he repeats the action he played at stage t−1. We investigate the optimality of simple strategies for player 1. A simple strategy for player 1 consists of playing the
same mixed action at every stage, irrespective of past play. Furthermore, for games in which player 1 has a simple optimal
strategy, we characterize the set of stationary optimal strategies for player 2. 相似文献
11.
This paper provides an overview of the various shapes the best-reply multifunctions can take in 2×2×2 trimatrix games. It
is shown that, unlike in 2×2 bimatrix games, the best replies to the opponents’ pure strategies do not completely determine
the structure of the Nash equilibrium set.
相似文献
12.
Walter O. Krawec 《International Journal of Game Theory》2012,41(2):345-367
Combinatorial game theory is the study of two player perfect information games. While work has been done in the past on expanding
this field to include n-player games we present a unique method which guarantees a single winner. Specifically our goal is to derive a function which,
given an n-player game, is able to determine the winning player (assuming all n players play optimally). Once this is accomplished we use this function in analyzing a certain family of three player subtraction
games along with a complete analysis of three player, three row Chomp. Furthermore we make use of our new function in producing
alternative proofs to various well known two player Chomp games. Finally the paper presents a possible method of analyzing
a two player game where one of the players plays a completely random game. As it turns out this slight twist to the rules
of combinatorial game theory produces rather interesting results and is certainly worth the time to study further. 相似文献
13.
An absorbing game is a repeated game where some action combinations are absorbing, in the sense that whenever they are played,
there is a positive probability that the game terminates, and the players receive some terminal payoff at every future stage.
We prove that every multi-player absorbing game admits a correlated equilibrium payoff. In other words, for every ε>0 there
exists a probability distribution p
ε over the space of pure strategy profiles that satisfies the following. With probability at least 1−ε, if a pure strategy
profile is chosen according to p
ε and each player is informed of his pure strategy, no player can profit more than ε in any sufficiently long game by deviating
from the recommended strategy.
Received: April 2001/Revised: June 4, 2002 相似文献
14.
Piercesare Secchi 《International Journal of Game Theory》1998,27(1):61-81
This paper discusses the problem regarding the existence of optimal or nearly optimal stationary strategies for a player engaged in a nonleavable stochastic game. It is known that, for these games, player I need not have an -optimal stationary strategy even when the state space of the game is finite. On the contrary, we show that uniformly -optimal stationary strategies are available to player II for nonleavable stochastic games with finite state space. Our methods will also yield sufficient conditions for the existence of optimal and -optimal stationary strategies for player II for games with countably infinite state space. With the purpose of introducing and explaining the main results of the paper, special consideration is given to a particular class of nonleavable games whose utility is equal to the indicator of a subset of the state space of the game. 相似文献
15.
Vianney Perchet 《Journal of Optimization Theory and Applications》2011,149(3):665-677
We provide a necessary and sufficient condition under which a convex set is approachable in a game with partial monitoring,
i.e. where players do not observe their opponents’ moves but receive random signals. This condition is an extension of Blackwell’s
Criterion in the full monitoring framework, where players observe at least their payoffs. When our condition is fulfilled,
we construct explicitly an approachability strategy, derived from a strategy satisfying some internal consistency property in an auxiliary game. 相似文献
16.
Two kinds of vertical cooperative advertising program are considered in a distribution channel constituted by a manufacturer and a retailer, where the manufacturer pays part of
the retailer’s advertising costs. In the first participation scheme, the manufacturer chooses his/her advertising participation
rate in the retailer’s advertising effort and then each player determines the advertising effort that maximizes his/her profit.
In the second scheme, the retailer chooses the manufacturer’s participation rate and then the manufacturer determines the
advertising efforts of both players with the objective of maximizing the manufacturer’s profit. Each participation scheme
corresponds to a special Stackelberg game: the manufacturer is the leader of the first, while the retailer is the leader of
the second. The Stackelberg equilibrium advertising efforts and participation rate in both games are provided. Then the equilibrium
strategies of the two players in the analyzed scenarios are compared with the Nash equilibrium in the competitive framework.
Finally, the conditions which suggest a special kind of agreement to a player are analyzed.
This work was supported by the Italian Ministry of University and Research and the University of Padua. 相似文献
17.
18.
Refinements of rationalizability for normal-form games 总被引:1,自引:0,他引:1
P. Jean-Jacques Herings Vincent J. Vannetelbosch 《International Journal of Game Theory》1999,28(1):53-68
There exist three equivalent definitions of perfect Nash equilibria which differ in the way “best responses against small
perturbations” are defined. It is shown that applying the spirit of these definitions to rationalizability leads to three
different refinements of rationalizable strategies which are termed perfect (Bernheim, 1984), weakly perfect and trembling-hand
perfect rationalizability, respectively. We prove that weakly perfect rationalizability is weaker than both perfect and proper
(Schuhmacher, 1995) rationalizability and in two-player games it is weaker than trembling-hand perfect rationalizability.
By means of examples, it is shown that no other relationships can be found.
Received: January 1997/final version: August 1998 相似文献
19.
We present a unifying framework for transferable utility coalitional games that are derived from a non-negative matrix in which every entry represents the value obtained by combining the corresponding row and column. We assume that every row and every column is associated with a player, and that every player is associated with at most one row and at most one column. The instances arising from this framework are called pairing games, and they encompass assignment games and permutation games as two polar cases. We show that the core of a pairing game is always non-empty by proving that the set of pairing games coincides with the set of permutation games. Then we exploit the wide range of situations comprised in our framework to investigate the relationship between pairing games that have different player sets, but are defined by the same underlying matrix. We show that the core and the set of extreme core allocations are immune to the merging of a row player with a column player. Moreover, the core is also immune to the reverse manipulation, i.e., to the splitting of a player into a row player and a column player. Other common solution concepts fail to be either merging-proof or splitting-proof in general. 相似文献
20.
Repeated zero-sum two-person games of incomplete information on one side are considered. If the one-shot game is played sequentially, the informed player moving first, it is proved that the value of then-shot game is constant inn and is equal to the concavification of the game in which the informed player disregards his extra information. This is a strengthening ofAumann andMaschler's results for simultaneous games. Optimal strategies for both players are constructed explicitly. 相似文献