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1.
We establish the existence of subgame perfect equilibria in general menu games, known to be sufficient to analyze common agency problems. Our main result states that every menu game satisfying enough continuity properties has a subgame perfect equilibrium. Despite the continuity assumptions that we make, discontinuities naturally arise due to the absence, in general, of continuous optimal choices for the agent. Our approach, then, is based on (and generalizes) the existence theorem of [Simon, L., Zame, W., 1990. Discontinuous games and endogenous sharing rules. Econometrica 58 (4), 861–872] designed for discontinuous games. 相似文献
2.
Maxwell B. Stinchcombe 《Games and Economic Behavior》2005,50(2):332-365
Infinite normal form games that are mathematically simple have been treated [ Harris, C.J., Stinchcombe, M.B., Zame, W.R., in press. Nearly compact and continuous normal form games: characterizations and equilibrium existence. Games Econ. Behav.]. Under study in this paper are the other infinite normal form games, a class that includes the normal forms of most extensive form games with infinite choice sets.Finitistic equilibria are the limits of approximate equilibria taken along generalized sequences of finite subsets of the strategy spaces. Points must be added to the strategy spaces to represent these limits. There are direct, nonstandard analysis, and indirect, compactification and selection, representations of these points. The compactification and selection approach was introduced [Simon, L.K., Zame, W.R., 1990. Discontinuous games and endogenous sharing rules. Econometrica 58, 861–872]. It allows for profitable deviations and introduces spurious correlation between players' choices. Finitistic equilibria are selection equilibria without these drawbacks. Selection equilibria have drawbacks, but contain a set-valued theory of integration for non-measurable functions tightly linked to, and illuminated by, the integration of correspondences. 相似文献
3.
Luciano I. de Castro 《Economic Theory》2011,48(1):67-85
Many conditions have been introduced to ensure equilibrium existence in games with discontinuous payoff functions. This paper
introduces a new condition, called regularity, that is simple and easy to verify. Regularity requires that if there is a sequence
of strategies converging to s* such that the players’ payoffs along the sequence converge to the best-reply payoffs at s*, then s* is an equilibrium. We show that regularity is implied both by Reny’s better-reply security and Simon and Zame’s endogenous
sharing rule approach. This allows us to explore a link between these two distinct methods. Although regularity implies that
the limits of e{\epsilon}-equilibria are equilibria, it is in general too weak for implying equilibrium existence. However, we are able to identify
extra conditions that, together with regularity, are sufficient for equilibrium existence. In particular, we show how regularity
allows the technique of approximating games both by payoff functions and space of strategies. 相似文献
4.
Guilherme Carmona 《Journal of Economic Theory》2009,144(3):1333-1340
We introduce a notion of upper semicontinuity, weak upper semicontinuity, and show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. We show that our result generalizes the pure strategy existence theorem of Dasgupta and Maskin [P. Dasgupta, E. Maskin, The existence of equilibrium in discontinuous economic games, I: Theory, Rev. Econ. Stud. 53 (1986) 1-26] and that it is neither implied nor does it imply the existence theorems of Baye, Tian, and Zhou [M. Baye, G. Tian, J. Zhou, Characterizations of the existence of equilibria in games with discontinuous and non-quasiconcave payoffs, Rev. Econ. Stud. 60 (1993) 935-948] and Reny [P. Reny, On the existence of pure and mixed strategy equilibria in discontinuous games, Econometrica 67 (1999) 1029-1056]. Furthermore, we show that an equilibrium may fail to exist when, while maintaining weak payoff security, weak upper semicontinuity is weakened to reciprocal upper semicontinuity. 相似文献
5.
Guilherme Carmona 《Economic Theory》2011,48(1):31-45
We introduce a new condition, weak better-reply security, and show that every compact, locally convex, metric, quasiconcave
and weakly better-reply secure game has a Nash equilibrium. This result is established using simple generalizations of classical
ideas. Furthermore, we show that, when players’ action spaces are metric and locally convex, it implies the existence results
of Reny (Econometrica 67:1029–1056, 1999) and Carmona (J Econ Theory 144:1333–1340, 2009) and that it is equivalent to a recent
result of Barelli and Soza (On the Existence of Nash Equilibria in Discontinuous and Qualitative Games, University of Rochester,
Rochester, 2009). Our general existence result also implies a new existence result for weakly upper reciprocally semicontinuous
and weakly payoff secure games that satisfy a strong quasiconcavity property. 相似文献
6.
I consider n-person normal form games where the strategy set of each player is a non-empty compact convex subset of an Euclidean space, and the payoff function of player i is continuous in joint strategies and continuously differentiable and concave in the player i's strategy. No further restrictions (such as multilinearity of the payoff functions or the requirement that the strategy sets be polyhedral) are imposed. I demonstrate that the graph of the Nash equilibrium correspondence on this domain is homeomorphic to the space of games. This result generalizes a well-known structure theorem in [Kohlberg, E., Mertens, J.-F., 1986. On the strategic stability of equilibria. Econometrica 54, 1003–1037]. It is supplemented by an extension analogous to the unknottedness theorems in [Demichelis S., Germano, F., 2000. Some consequences of the unknottedness of the Walras correspondence. J. Math. Econ. 34, 537–545; Demichelis S., Germano, F., 2002. On (un)knots and dynamics in games. Games Econ. Behav. 41, 46–60]: the graph of the Nash equilibrium correspondence is ambient isotopic to a trivial copy of the space of games. 相似文献
7.
8.
Adib Bagh 《Journal of Economic Theory》2010,145(3):1244-1268
We introduce a notion of variational convergence for sequences of games and we show that the Nash equilibrium map is upper semi-continuous with respect to variationally converging sequences. We then show that for a game G with discontinuous payoff, some of the most important existence results of Dasgupta and Maskin, Simon, and Reny are based on constructing approximating sequences of games that variationally converge to G. In fact, this notion of convergence will help simplify these results and make their proofs more transparent. Finally, we use our notion of convergence to establish the existence of a Nash equilibrium for Bertrand-Edgeworth games with very general forms of tie-breaking and residual demand rules. 相似文献
9.
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
10.
We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models
that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our
experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson
and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash
equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying
coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough
experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this
hypothesis, we use a different game with incomplete information, related to a complete information game where learning and
prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium
within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently
similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.
相似文献
11.
Pavlo Prokopovych 《Economic Theory》2011,48(1):5-16
We propose a single framework for studying the existence of approximate and exact pure strategy equilibria in payoff secure
games. Central to the framework is the notion of a multivalued mapping with the local intersection property. By means of the
Fan-Browder collective fixed point theorem, we first show an approximate equilibrium existence theorem that covers a number
of known games. Then a short proof of Reny’s (Econometrica 67:1029–1056, 1999) equilibrium existence theorem is provided for
payoff secure games with metrizable strategy spaces. We also give a simple proof of Reny’s theorem in its general form for
metric games in an appendix for the sake of completeness. 相似文献
12.
We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove limit uniqueness: as the signal noise vanishes, the game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and van Damme (Econometrica 61 (1993) 989-1018) for two-player, two-action games. The surviving profile, however, may depend on fine details of the structure of the noise. We provide sufficient conditions on payoffs for there to be noise-independent selection. 相似文献
13.
Yuichi Yamamoto 《Journal of Economic Theory》2009,144(2):802-824
The present paper studies repeated games with private monitoring, and characterizes the set of belief-free equilibrium payoffs in the limit as the discount factor approaches one and the noise on private information vanishes. Contrary to the conjecture by Ely et al. [J.C. Ely, J. Hörner, W. Olszewski, Belief-free equilibria in repeated games, Econometrica 73 (2005) 377-415], the equilibrium payoff set is computed by the same formula, no matter how many players there are. As an application of this result, a version of the folk theorem is established for N-player prisoner's dilemma games. 相似文献
14.
Endogenous timing in a mixed oligopoly with semipublic firms 总被引:1,自引:0,他引:1
An endogenous order of moves is analyzed in a mixed market where a firm jointly owned by the public sector and private domestic
shareholders (a semipublic firm) competes with n private firms. We show that there is an equilibrium in which firms take production decisions simultaneously. This result
is strikingly different from that obtained by Pal (Econ Lett 61:181–185, 1998), who shows that when a public firm competes with n private firms all firms producing simultaneously in the same period cannot be sustained as a Subgame Perfect Nash Equilibrium
outcome. Our result differs from that of Pal (Econ Lett 61:181–185, 1998) for two reasons: firstly, we consider that there is a semipublic firm rather than a public firm. Secondly, Pal (Econ Lett
61:181–185, 1998) considers that the public firm is less efficient than private firms while in our paper all firms are equally efficient. 相似文献
15.
We provide approximation results for Nash equilibria in possibly discontinuous games when payoffs and strategy sets are perturbed. We then prove existence results for a new “finitistic” infinite-game generalization of Selten’s (Int J Game Theory 4: 25–55, 1975) notion of perfection and study some of its properties. The existence results, which rely on the approximation theorems, relate existing notions of perfection to the new specification. 相似文献
16.
Summary. We show, by employing a density result for probability measures, that in games with a finite number of players and ∞-dimensional
pure strategy spaces Nash equilibria can be approximated by finite mixed strategies. Given ε>0, each player receives an expected
utility payoff ε/2 close to his Nash payoff and no player could change his strategy unilaterally and do better than ε.
Received: July 15, 1997; revised version: February 6, 1998 相似文献
17.
Siegfried K. Berninghaus Karl-Martin Ehrhart Marion Ott Bodo Vogt 《Journal of Evolutionary Economics》2007,17(3):317-347
It is the main aim of our paper to study network formation in experimental setups in discrete and continuous time. Our design
is inspired by the theoretical model on network formation by Bala and Goyal (Econometrica, 68(5): 1181–1229, 2000) as well as the experiments by Callander and Plott (J. Public Econ., 89: 1469–1495, 2005) and Falk and Kosfeld (IEW Working Paper, University of Zürich, Zürich, Switzerland, No. 146, 2003). In particular, we analyze the role of star-shaped networks which are strict Nash-equilibria of the corresponding network
formation game. Our experimental results show that strict Nash networks prove to be a good indicator for predicting network
formation, particularly in continuous time. In explaining our results, it turns out that, among others, the complexity in
coordinating on stars, the inequity aversion against unequal payoff distribution in the network, and the groups’ degrees of
activity are the most important determinants for the formation of strict Nash networks.
相似文献
18.
We model strategic competition in a market with asymmetric information as a noncooperative game in which each seller competes
for a buyer of unknown type by offering the buyer a catalog of products and prices. We call this game a catalog game. Our main objective is to show that catalog games have Nash equilibria. The Nash existence problem for catalog games is particularly
contentious due to payoff discontinuities caused by tie-breaking. We make three contributions. First, we establish under very
mild conditions on primitives that no matter what the tie-breaking rule, catalog games are uniformly payoff secure, and therefore have mixed extensions which are payoff secure. Second, we show that if the tie-breaking rule awards the sale
to firms which value it most (i.e., breaks ties in favor of firms which stand to make the highest profit), then firm profits
are reciprocally upper semicontinuous (i.e., the mixed catalog game is reciprocally upper semincontinuous). This in turn implies
that the mixed catalog game satisfies Reny’s condition of better-reply security—a condition sufficient for existence (Reny
in Econometrica 67:1029–1056, 1999). Third, we show by example that if the tie-breaking rule does not award the sale to firms
which value it most (for example, if ties are broken randomly with equal probability), then the catalog game has no Nash equilibrium.
This paper was written while the second author was Visiting Professor, Centre d’Economie de la Sorbonne, Universite Paris
1, Pantheon-Sorbonne. The second author thanks CES and Paris 1, and in particular, Bernard Cornet and Cuong Le Van for their
support and hospitality. The second author also thanks the C&BA and EFLS at the University of Alabama for financial support.
Both authors are grateful to Monique Florenzano and to participants in the April 2006 Paris 1 NSF/NBER Decentralization Conference
for many helpful comments on an earlier version of the paper. Finally, both authors are especially grateful to an anonymous
referee whose thoughtful comments led to substantial improvements in the paper. Monteiro acknowleges the financial support
of Capes-Cofecub 468/04. 相似文献
19.
We explore the implications of the farsightedness assumption on the conjectures of players in a coalitional Great Fish War
model with symmetric players, derived from the seminal model of Levhari and Mirman (Bell J Econ 11:649–661, 1980). The farsightedness assumption for players in a coalitional game acknowledges the fact that a deviation from a single player
will lead to the formation of a new coalition structure as the result of possibly successive moves of her rivals in order
to improve their payoffs. It departs from mainstream game theory in that it relies on the so-called rational conjectures, as opposed to the traditional Nash conjectures formed by players on the behavior of their rivals. For values of the biological parameter and the discount factor more plausible
than the ones used in the current literature, the farsightedness assumption predicts a wide scope for cooperation in non-trivial
coalitions, sustained by credible threats of successive deviations that defeat the shortsighted payoff of any prospective
deviator. Compliance or deterrence of deviations may also be addressed by acknowledging that information on the fish stock
or on the catch policies actually implemented may be available only with a delay (dynamic farsightedness). In that case, the
requirements are stronger and the sizes and number of possible farsighted stable coalitions are different. In the sequential
move version, which could mimic some characteristics of fishery models, the results are not less appealing, even if the dominant
player or dominant coalition with first move advantage assumption provides a case for cooperation with the traditional Nash
conjectures. 相似文献
20.
We study infinitely repeated games with perfect monitoring, where players have β-δ preferences. We compute the continuation payoff set using recursive techniques and then characterize equilibrium payoffs. We then explore the cost of the present-time bias, producing comparative statics. Unless the minimax outcome is a Nash equilibrium of the stage game, the equilibrium payoff set is not monotonic in β or δ. Finally, we show how the equilibrium payoff set is contained in that of a repeated game with smaller discount factor. 相似文献