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1.
This paper presents a survey of the use of homotopy methods in game theory. Homotopies allow for a robust computation of game-theoretic
equilibria and their refinements. Homotopies are also suitable to compute equilibria that are selected by various selection
theories. We present the relevant techniques underlying homotopy algorithms. We give detailed expositions of the Lemke–Howson
algorithm and the van den Elzen–Talman algorithm to compute Nash equilibria in 2-person games, and the Herings–van den Elzen,
Herings–Peeters, and McKelvey–Palfrey algorithms to compute Nash equilibria in general n-person games. We explain how the main ideas can be extended to compute equilibria in extensive form and dynamic games, and
how homotopies can be used to compute all Nash equilibria. 相似文献
2.
Informationally robust equilibria (IRE) are introduced in Robson (Games Econ Behav 7: 233–245, 1994) as a refinement of Nash equilibria for strategic games. Such equilibria are limits of a sequence of (subgame
perfect) Nash equilibria in perturbed games where with small probability information about the strategic behavior is revealed
to other players (information leakage). Focusing on bimatrix games, we consider a type of informationally robust equilibria
and derive a number of properties they form a non-empty and closed subset of the Nash equilibria. Moreover, IRE is a strict
concept in the sense that the IRE are independent of the exact sequence of probabilities with which information is leaked.
The set of IRE, like the set of Nash equilibria, is the finite union of polytopes. In potential games, there is an IRE in
pure strategies. In zero-sum games, the set of IRE has a product structure and its elements can be computed efficiently by
using linear programming. We also discuss extensions to games with infinite strategy spaces and more than two players.
The authors would like to thank Marieke Quant for her helpful comments. 相似文献
3.
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
4.
Takeshi Momi 《Economic Theory》2008,36(3):503-513
In this note, we emphasize the role of consumers’ risk aversion in the non-existence of sunspot equilibria in incomplete market
economies. We prove that there are no sunspot equilibria if the fundamentals of the underlying economy admit a unique equilibrium
for any distribution of endowments. This substantiates Mas-Colell’s (Economic analysis of markets and games: essays in honor
of Frank Hahn. MIT, Cambridge, 1992) conjecture. We also prove that, in a two-consumer economy, no sunspot equilibrium exists
under the more relaxed condition that the underlying economy admits a unique equilibrium for the initial endowment. This is
a generalization of Corollaries 1 and 2 of Hens and Pilgrim (Econ Theory 24:583–602, 2004).
相似文献
5.
6.
Anne Balthasar 《Economic Theory》2010,42(1):39-54
We analyze the relationships of the van den Elzen–Talman algorithm, the Lemke–Howson algorithm and the global Newton method
for equilibrium computation by Govindan and Wilson. For two-player games, all three can be implemented as complementary pivoting
algorithms. The algorithms by Lemke and Howson and by van den Elzen and Talman start at a pair of strategies: the first method
at a pure strategy and its best reply, the latter anywhere in the strategy space. However, we show that even with the same
starting point they may find different equilibria. Our second result is that the van den Elzen–Talman algorithm is a special
case of the global Newton method, which was known only for the Lemke–Howson algorithm. More generally, the global Newton method
implements the linear tracing procedure for any number of players. All three algorithms find generically only equilibria of
positive index. Even though the van den Elzen–Talman algorithm is extremely flexible in the choice of starting point, we show
that there are generic coordination games where the completely mixed equilibrium, which has positive index, is generically
not found by the algorithm. 相似文献
7.
Erik J. Balder 《Economic Theory》2011,48(1):47-65
For games with discontinuous payoffs Simon and Zame (Econometrica 58:861–872, 1990) introduced payoff indeterminacy, in the form of endogenous sharing rules, which are measurable selections of a certain payoff
correspondence. Their main result concerns the existence of a mixed Nash equilibrium and an associated sharing rule. Its proof
is based on a discrete approximation scheme “from within” the payoff correspondence. Here, we present a new, related closure
result for games with possibly noncompact action spaces, involving a sequence of Nash equilibria. In contrast to Simon and
Zame (Econometrica 58:861–872, 1990), this result can be used for more involved forms of approximation, because it contains more information about the endogenous
sharing rule. With such added precision, the closure result can be used for the actual computation of endogenous sharing rules
in games with discontinuous payoffs by means of successive continuous interpolations in an approximation scheme. This is demonstrated
for a Bertrand type duopoly game and for a location game already considered by Simon and Zame. Moreover, the main existence
result of Simon and Zame (Econometrica 58:861–872, 1990) follows in two different ways from the closure result. 相似文献
8.
Ping Zhang 《Experimental Economics》2009,12(2):202-219
We compare uniform price auctions with fixed price offerings in Initial Public Offerings (IPO) using laboratory experiments.
The experimental environment is based on the Biais and Faugeron-Grouzet (J. Financ. Intermed. 11:9–36, 2002) model. Standard predictions based on tacit collusion equilibria (TCE) suggest lower revenues in uniform price auctions,
although alternative equilibria allow for higher revenues. In our experiment, there is no evidence that TCE are played. The
experiment suggests that the uniform price auctions are superior to fixed price offerings in terms of raising revenues.
Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users. 相似文献
Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users. 相似文献
9.
We examine whether the payoff dominant sequential-move (Stackelberg) outcome is realized when timing is endogenized. We adopt
the observable delay game formulated by Hamilton and Slutsky [Games Econ Behav 2(1):29–46, 1990]. We find that if one sequential-move
outcome is payoff dominant, either (i) the outcome both players prefer is the unique equilibrium; or (ii) two sequential-move
outcomes are equilibria and the one both players prefer is risk dominant. In other words, no conflict between payoff dominance
and risk dominance in the observable delay game exists, in contrast to other games such as (non pure) coordination games.
We also find that even if one of two sequential-move outcomes is the unique equilibrium outcome in the observable delay game,
it does not imply that the equilibrium outcome is payoff dominant to the other sequential-move outcome.
相似文献
10.
Christopher Sleet 《Economic Theory》2001,17(2):371-397
Summary. This paper considers the existence and computation of Markov perfect equilibria in games with a “monotone” structure. Specifically,
it provides a constructive proof of the existence of Markov perfect equilibria for a class of games in which a) there is a
continuum of players, b) each player has the same per period payoff function and c) these per period payoff functions are
supermodular in the player's current and past action and have increasing differences in the player's current action and the
entire distribution of actions chosen by other players. The Markov perfect equilibria that are analyzed are symmetric, not
in the sense that each player adopts the same action in any period, but rather in the sense that each player uses the same
policy function. Since agents are typically distributed across many states they will typically take different actions.
The formal environment considered has particular application to models of industries (or economies) in which firms face costs
of price adjustment. It is in this context that the results are developed.
Received: November 9, 1999; revised version: February 10, 2000 相似文献
11.
We study market games derived from an exchange economy with a continuum of agents, each having one of finitely many possible
types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley–Shubik
theorem on market games (Shapley and Shubik in J Econ Theory 1:9–25, 1969), there might be a (fuzzy) game in which each of
its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market
game, a game needs also to be homogeneous.
We also study investment games – which are fuzzy games obtained from an economy with a finite number of agents cooperating
in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore
introduce and analyze the new notion of comprehensive core. This solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an
allocation in games with a large number of players.
Some of the results in this paper appear in a previous draft distributed by the name “Cooperative investment games or Population
games”.
An anonymous referee of Economic Theory is acknowledged for his/her comments 相似文献
12.
We study a two-sector model with heterogeneous agents and borrowing constraint on labor income. We show that the relative
capital intensity difference across sectors is crucial for the conditions required to get indeterminacy and endogenous fluctuations.
The main result shows that when the consumption good is sufficiently capital intensive, local indeterminacy arises while the
elasticities of capital–labor substitution in both sectors are slightly greater than unity and the elasticity of the offer
curve is low enough. Locally indeterminate equilibria are thus compatible with a low elasticity of intertemporal substitution
in consumption and a low elasticity of the labor supply. As recently shown in empirical analysis, these conditions appear
to be in accordance with macroeconomic evidences.
We would like to thank R. Becker, J.P. Drugeon and an anonymous referee for useful comments and suggestions. The current version
also benefited from a presentation at the conference “Public Economic Theory 04”, Beijing, August 2004. 相似文献
13.
Julio Dávila 《Economic Theory》1998,12(1):213-223
Summary. It is shown in this note that in an incomplete markets economy with uncountably many states of the world there may be uncountably
many isolated equilibria as well as uncountably many non-isolated equilibria. Moreover, both subsets can be simultaneously
of second category. Therefore, none of the subsets can be considered negligible with respect to the other, neither from a
cardinality point of view nor from a topological one. Unfortunately, this fact prevents from claiming that these economies
may have “typically” determinate equilibria – even though uncountably many of them – as would have been desirable for comparative
statics exercises.
Received: May 19, 1995; revised version: March 24, 1997 相似文献
14.
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
15.
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
16.
Steven Russell 《Economic Theory》2003,22(1):111-140
Summary. This paper uses a general equilibrium model to study the determination of the exchange rate in an economy with fundamental
uncertainty. The model has steady state equilibria in which the exchange rate is constant. These equilibria may coexist with
“quasi-fundamental” equilibria – nonstationary equilibria in which the exchange rate displays stochastic fluctuations that
are correlated with the fluctuations in fundamental random variables. The quasi-fundamental equilibria are Pareto dominated
by the corresponding constant-exchange-rate steady states. They also converge to these steady states, inevitably or with positive
probability.
Received: October 2, 1999; revised version: March 26, 2002
RID="*"
ID="*" This paper began as a joint project with Alex Mourmouras, who has made many helpful comments and suggestions but is
not responsible for any errors or deficiencies. In addition, I thank an anonymous referee for helpful comments. 相似文献
17.
The Dixit (Econ J 90:95–106, 1980) hypothesis that incumbents use investment in capacity to deter potential entrants has found
little empirical support. Bagwell and Ramey (J Econ 27:660–680, 1996) propose a model where, in the unique game-theoretic
prediction based on forward induction or iterated elimination of weakly-dominated strategies, the incumbent does not have
the strategic advantage. We conduct an experiment with games inspired by these models. In the Dixit-style game, the incumbent
monopolizes the market most of the time even without the investment in capacity. In our Bagwell-and-Ramey-style game, the
incumbent also tends to keep the market, in contrast to the predictions of an entrant advantage. Nevertheless, we find strong
evidence that forward induction affects the behavior of most participants. The results of our games suggest that players perceive
that the first mover has an advantage without having to pre-commit capacity. In our Bagwell–Ramey game, evolution and learning
do not drive out this perception. We back these claims with data analysis and a theoretical framework for dynamics.
Financial support by the Spanish Ministerio de Ciencia and Tecnología (SEC2002-01352 and SEJ2006-11665-C02-01) and the Barcelona Economic Program of CREA and excellent research assistance by
David Rodríguez are gratefully acknowledged. The authors thank Aurora García Gallego and Armin Schmutzler for helpful comments. 相似文献
18.
Antonio Miralles 《Economic Theory》2010,42(3):523-538
Campbell (J Econ Theory 82:425–450, 1998) develops a self-enforced collusion mechanism in simultaneous auctions based on complete
comparative cheap talk and endogenous entry, with two bidders. His result is difficult to generalize to an arbitrary number
of bidders, since the entry-decision stage of the game is characterized by strategic substitutes. This paper analyzes more-than-two-bidder,
symmetric-prior cases. Two results are proved: (1) as the number of objects grows large, a full comparative cheap talk equilibrium
exists and it yields asymptotically fully efficient collusion; and (2) there is always a partial comparative cheap talk equilibrium.
All these results are supported by intuitive equilibria at the entry-decision stage (J Econ Theory 130:205–219, 2006; Math
Soc Sci 2008, forthcoming). Numerical examples suggest that full comparative cheap talk equilibria are not uncommon even with
few objects. 相似文献
19.
Moshe Babaioff Robert Kleinberg Christos H. Papadimitriou 《Games and Economic Behavior》2009,67(1):22
We study the equilibria of non-atomic congestion games in which there are two types of players: rational players, who seek to minimize their own delay, and malicious players, who seek to maximize the average delay experienced by the rational players. We study the existence of pure and mixed Nash equilibria for these games, and we seek to quantify the impact of the malicious players on the equilibrium. One counterintuitive phenomenon which we demonstrate is the “windfall of malice”: paradoxically, when a myopically malicious player gains control of a fraction of the flow, the new equilibrium may be more favorable for the remaining rational players than the previous equilibrium. 相似文献
20.
Alberto Martin 《Economic Theory》2007,31(2):371-386
Dubey and Geanakoplos (Q J Econ 117:1529–1570, 2002) have developed a theory of competitive pooling, which incorporates adverse
selection and signaling into general equilibrium. By recasting the Rothschild–Stiglitz model of insurance in this framework,
they find that a separating equilibrium always exists and is unique.
We prove that their uniqueness result is not a consequence of the framework, but rather of their definition of refined equilibria.
When other types of perturbations are used, the model allows for many pooling allocations to be supported as such: in particular,
this is the case for pooling allocations that Pareto dominate the separating equilibrium. 相似文献