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1.
Summary In this paper we consider Anonymous Sequential Games with Aggregate Uncertainty. We prove existence of equilibrium when there is a general state space representing aggregate uncertainty. When the economy is stationary and the underlying process governing aggregate uncertainty Markov, we provide Markov representations of the equilibria.Table of notation
Agents' characteristics space ( )
- A
Action space of each agent (aA)
-
Y
Y = x A
-
Aggregate distribution on agents' characteristics
-
(X)
Space of probability measures onX
-
C(X)
Space of continuous functions onX
-
X
Family of Borel sets ofX
-
State space of aggregate uncertainty ( )
-
x
t=1
aggregate uncertainty for the infinite game
-
= (1,2,...,t,...)
-
t
t (1, 2,..., t)
- L1(t,C ×A),v
t
Normed space of measurable functions from
t
toC( x A)
-
8o(t,( x A))
Space of measurable functions from
tto( x A)
- Xt
Xt= x
s=1
t
X
-
X
t
Borel field onX
t
-
v
Distribution on
- vt
Marginal distribution of v on
t
- v(t)((¦t))
Conditional distribution on
given
t
- vt(s)(vt(¦s))
Conditional distribution on
t
given
s
(wheres)
-
t
Periodt distributional strategy
-
Distributional strategy for all periods =(1,2,...,t,...)
-
t
Transition process for agents' types
- (
t,t,y)(P
t+1(,
t
,
t
,y))
Transition function associated with
t
-
u
t
Utility function
-
V
t
(, a, , t)
Value function for each collection (, a, ,
t
)
-
W
t
(, ,
t
)
Value function given optimal action a
-
C()
Consistency correspondence. Distributions consistent with and characteristics transition functions
-
B()
Best response correspondence (which also satisfy consistency)
-
E
Set of equilibrium distributional strategies
-
x
t=1
(
t
, (x A))
- S
Expanded state space for Markov construction
- (, a, )
Value function for Markov construction
-
P(
t
*
,
t
y)(P(,
t
*
,
t
,
y
))
Invariant characteristics transition function for Markov game
We wish to acknowledge very helpful conversations with C. d'Aspremont, B. Lipman, A. McLennan and J-F. Mertens. The financial support of the SSHRCC and the ARC at Queen's University is gratefully acknowledged. This paper was begun while the first author visited CORE. The financial support of CORE and the excellent research environment is gratefully acknowledged. The usual disclaimer applies. 相似文献
2.
Guilherme Carmona 《Economic Theory》2011,48(1):1-4
This paper introduces the symposium on existence of Nash equilibria in discontinuous games. 相似文献
3.
Tadashi Sekiguchi 《Games and Economic Behavior》2002,40(2):382
We consider finitely repeated games with imperfect private monitoring, and provide several sufficient conditions for such a game to have an equilibrium whose outcome is different from repetition of Nash equilibria of the stage game. Surprisingly, the conditions are consistent with uniqueness of the stage game equilibrium. A class of repeated chicken is shown to satisfy the condition. 相似文献
4.
This paper provides an example showing that for finite extensive form games without perfect recall existence of Nash equilibria in behaviour strategies is not guaranteed in general. 相似文献
5.
Oriol Carbonell-Nicolau 《Journal of Economic Theory》2010,145(1):421-431
A Nash equilibrium x of a normal-form game G is essential if any perturbation of G has an equilibrium close to x. Using payoff perturbations, we show that for games that are generic in the set of compact, quasiconcave, and generalized payoff secure games with upper semicontinuous sum of payoffs, all equilibria are essential. Some variants of this result are also established. 相似文献
6.
We report experiments studying mixed strategy Nash equilibria that are theoretically stable or unstable under learning. The Time Average Shapley Polygon (TASP) predicts behavior in the unstable case. We study two versions of Rock-Paper-Scissors that include a fourth strategy, Dumb. The unique Nash equilibrium is identical in the two games, but the predicted frequency of Dumb is much higher in the game where the NE is stable. Consistent with TASP, the observed frequency of Dumb is lower and play is further from Nash in the high payoff unstable treatment. However, Dumb is played too frequently in all treatments. 相似文献
7.
Vincenzo Scalzo 《Economic Theory》2013,54(1):27-44
We introduce spaces of discontinuous games in which games having essential Nash equilibria are the generic case. In order to prove the existence of essential Nash equilibria in such spaces, we provide new results on the Ky Fan minimax inequality. In the setting of potential games, we show that games with essential Nash equilibria are the generic case when their potentials satisfy a condition called weak upper pseudocontinuity that is weaker than upper semicontinuity. 相似文献
8.
9.
We propose a new concept for the analysis of games, the TASP, which gives a precise prediction about non-equilibrium play in games whose Nash equilibria are mixed and are unstable under fictitious play-like learning. We show that, when players learn using weighted stochastic fictitious play and so place greater weight on recent experience, the time average of play often converges in these “unstable” games, even while mixed strategies and beliefs continue to cycle. This time average, the TASP, is related to the cycle identified by Shapley [L.S. Shapley, Some topics in two person games, in: M. Dresher, et al. (Eds.), Advances in Game Theory, Princeton University Press, Princeton, 1964]. The TASP can be close to or quite distinct from Nash equilibrium. 相似文献
10.
We characterize equilibrium payoffs of a delegated common agency game in a public good context where principals use smooth contribution schedules. We prove that under complete information, payoff vectors of equilibria with truthful schedules coincide with the set of smooth equilibrium payoffs, including non-truthful schedules. We next consider whether the presence of arbitrarily small amounts of asymmetric information is enough to refine this payoff set. Providing that the extensions of the equilibrium schedules beyond the equilibrium point are flatter than truthful schedules, the set of equilibrium payoffs is strictly smaller than the set of smooth (equivalently, truthful) equilibrium payoffs. Interestingly, some forms of asymmetric information do not sufficiently constrain the slopes of the extensions and fail to refine the payoff set. In the case of a uniform distribution of types and arbitrary out-of-equilibrium contributions, the refinement has no bite. If, however, one restricts out-of-equilibrium behavior in a natural way, the refinement is effective. Alternatively, we may consider an exponential distribution with unbounded support (and hence no out-of-equilibrium choices) and we find that the refinement selects a unique equilibrium payoff vector equal to Lindahl prices.As a separate contribution, equilibria with forcing contracts are also considered both under complete and asymmetric information. 相似文献
11.
We show the existence of an equilibrium in a model where private goods are allocated by markets and the public good (bad) is allocated by majority rule voting. 相似文献
12.
Rationalized subjective equilibria in repeated games 总被引:1,自引:0,他引:1
Abstract The purpose of this paper is to provide a new equilibrium concept of repeated games that involve incomplete information ( rationalized subjective equilibrium ) and a related framework ( subjective game ), and to analyse the relationships between players' subjective images of games and the realized outcomes. We demonstrate the relationships among rationalized subjective equilibria, subjective equilibria, and original Nash equilibria by providing several examples. We also present several theorems analogous to the ordinary folk theorem and a simple application using the Cournot duopoly model. JEL Classification: C70, C72
Equilibres subjectifs rationalisés dans des jeux répétés L'objectif de cet article est de proposer un nouveau concept d'équilibre dans les jeux répétés où l'information est incomplète (équilibre subjectif rationalisé) et un cadre d'analyse approprié( jeu subjectif ), ainsi que d'analyser les rapports entre les images subjectives que les acteurs ont des jeux et de leurs résultats. On montre les rapports entre équilibres subjectifs rationalisés, équilibres subjectifs, et équilibres à la Nash à l'aide de divers exemples. On présente aussi plusieurs théorèmes analogues au « ordinary folk theorem >> et une application simple utilisant le modèle de duopole de Cournot. 相似文献
Equilibres subjectifs rationalisés dans des jeux répétés L'objectif de cet article est de proposer un nouveau concept d'équilibre dans les jeux répétés où l'information est incomplète (équilibre subjectif rationalisé) et un cadre d'analyse approprié( jeu subjectif ), ainsi que d'analyser les rapports entre les images subjectives que les acteurs ont des jeux et de leurs résultats. On montre les rapports entre équilibres subjectifs rationalisés, équilibres subjectifs, et équilibres à la Nash à l'aide de divers exemples. On présente aussi plusieurs théorèmes analogues au « ordinary folk theorem >> et une application simple utilisant le modèle de duopole de Cournot. 相似文献
13.
Majority auction games are simultaneous sealed-bid auctions of identical objects among identical bidders who each want to win a specified fraction (more than a half) of the objects. Each bidder receives no benefit from winning less than the specified fraction and no additional benefit from winning more than it. Symmetric equilibria having simple, intuitive forms are shown to exist in first-price, second-price and all-pay versions of such games when the number of bidders is sufficiently large. This contrasts with earlier results for the two-bidder “pure chopstick” majority auction games where the only known equilibria are more complicated. 相似文献
14.
We present several new characterizations of correlated equilibria in games with continuous utility functions. These have the advantage of being more computationally and analytically tractable than the standard definition in terms of departure functions. We use these characterizations to construct effective algorithms for approximating a single correlated equilibrium or the entire set of correlated equilibria of a game with polynomial utility functions. 相似文献
15.
Willemien Kets 《Journal of Economic Theory》2011,146(1):300-325
This paper studies the robustness of symmetric equilibria in anonymous local games to perturbations of prior beliefs. Two priors are strategically close on a class of games if players receive similar expected payoffs in equilibrium under the priors, for any game in that class. I show that if the structure of payoff interdependencies is sparse in a well-defined sense, the conditions for strategic proximity in anonymous local games are strictly weaker than the conditions for general Bayesian games of Kajii and Morris (1998) [11] when attention is restricted to symmetric equilibria. Hence, by exploiting the properties of anonymous local games, it is possible to obtain stronger robustness results for this class. 相似文献
16.
Federico Echenique 《Economic Theory》2003,22(1):33-44
Summary. The literature on games of strategic complementarities (GSC) has focused on pure strategies. I introduce mixed strategies
and show that, when strategy spaces are one-dimensional, the complementarities framework extends to mixed strategies ordered
by first-order stochastic dominance. In particular, the mixed extension of a GSC is a GSC, the full set of equilibria is a
complete lattice and the extremal equilibria (smallest and largest) are in pure strategies. The framework does not extend
when strategy spaces are multi-dimensional. I also update learning results for GSC using stochastic fictitious play.
Received: October 16, 2000; revised version: March 7, 2002
RID="*"
ID="*" I am very grateful to Robert Anderson, David Blackwell, Aaron Edlin, Peter De Marzo, Ted O'Donoghue, Matthew Rabin,
Ilya Segal, Chris Shannon, Clara Wang and Federico Weinschelbaum for comments and advise. 相似文献
17.
We characterize the essential stability of games with a continuum of players, where strategy profiles may affect objective functions and admissible strategies. Taking into account the perturbations defined by a continuous mapping from a complete metric space of parameters to the space of continuous games, we prove that essential stability is a generic property and every game has a stable subset of equilibria. These results are extended to discontinuous large generalized games assuming that only payoff functions are subject to perturbations. We apply our results in an electoral game with a continuum of Cournot-Nash equilibria, where the unique essential equilibrium is that only politically engaged players participate in the electoral process. In addition, employing our results for discontinuous games, we determine the stability properties of competitive prices in large economies. 相似文献
18.
William H. Sandholm 《Journal of Economic Theory》2007,136(1):641-667
We study the evolutionary stability of purified equilibria of two-player normal form games, providing simple sufficient conditions for stability and for instability under the Bayesian best response dynamic. 相似文献
19.
The paper investigates the conditions under which an abstractly given market game will have the property that if there is a continuum of traders then every noncooperative equilibrium is Walrasian. In orther words, we look for a general axiomatization of Cournot's well-known result. Besides some convexity, continuity, and nondegeneracy hypotheses, the crucial axioms are: anonymity (i.e., the names of traders are irrelevant to the market) and aggregation (i.e., the net trade received by a trader depends only on his own action and the mean action of all traders). It is also shown that the same axioms do not guarantee efficiency if there is only a finite number of traders. Some examples are discussed and a notion of strict noncooperative equilibrium for anonymous games is introduced. 相似文献