Market Games in Large Economies with a Finite Number of Types

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     

On Forward Induction and Evolutionary and Strategic Stability

We analyze which normal form solution concepts capture the notion of forward induction, as defined by E. van Damme (1989, J. Econ. Theory48, 476-496) in the class of generic two player normal form games preceded by an outside option. We find that none of the known strategic stability concepts (including Mertens stable sets and hyperstable sets) capture this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (J. Swinkels, 1992, J. Econ. Theory57, 306-332) is always consistent with forward induction. Journal of Economic Literature Classification Number: C72.     

Understanding some recent existence results for discontinuous games

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.     

The Zilcha criteria for dynamic inefficiency reconsidered

We reconsider necessary and sufficient conditions for dynamic inefficiency given in Zilcha (J Econ Theory 52:364–379, 1990, J Econ Theory 55:1–16, 1991) and a critique by Rangazas and Russell (2005). First, we show that the characterization given in Zilcha (1990) for nonstationary economies is correct and correct Zilcha’s proof. Second, using this insight, we complement Rangazas and Russell’s (Econ Theory 26:701–716, 2005) discussion of the counterexamples to Zilcha (J Econ Theory 55:1–16, 1991). Third, we discuss consequences of our results for applied tests of (in-)efficiency based on the Zilcha criteria. We would like to thank Itzhak Zilcha, and in particular Peter Rangazas and Steve Russell for detailed and very helpful comments.     

On purification of measure-valued maps

This paper presents new methods to obtain purification results for continuum games, which don’t make use of the “many more players than strategies” assumption (Yannelis in Econ Theory (in press) 2007) or of Loeb spaces (Loeb and Sun in Illinois J Math 50, 747–762, 2006). The approach presented doesn’t use nonstandard analysis; it is based on standard measure theory and in particular on the super-nonatomicity notion introduced in Podczeck (J Math Econ (in press) 2007). Thanks to Erik Balder, Peter Loeb, Yeneng Sun, and Nicholas Yannelis for helpful comments.     

Cournot–Nash equilibria in continuum games with non-ordered preferences

In the usual framework of continuum games with externalities, we substantially generalize Cournot–Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79–94; On the existence of Cournot–Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207–223; A unifying pair of Cournot–Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437–470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237–246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9–15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345–348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econ. 3 (1976) 313–316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233–245].     

Dynamic psychological games

The motivation of decision makers who care for various emotions, intentions-based reciprocity, or the opinions of others may depend directly on beliefs (about choices, beliefs, or information). Geanakoplos, Pearce and Stacchetti [J. Geanakoplos, D. Pearce, E. Stacchetti, Psychological games and sequential rationality, Games Econ. Behav. 1 (1989) 60-79] point out that traditional game theory is ill-equipped to address such matters, and they pioneer a new framework which does. However, their toolbox - psychological game theory - incorporates several restrictions that rule out plausible forms of belief-dependent motivation. Building on recent work on dynamic interactive epistemology, we propose a more general framework. Updated higher-order beliefs, beliefs of others, and plans of action may influence motivation, and we can capture dynamic psychological effects (such as sequential reciprocity, psychological forward induction, and regret) that were previously ruled out. We develop solution concepts, provide examples, explore properties, and suggest avenues for future research.     

Bayesian–Walrasian equilibria: beyond the rational expectations equilibrium

In general rational expectations equilibrium (REE), as introduced in Radner (Econometrica 47:655–678, 1978) in an Arrow–Debreu–McKenzie setting with uncertainty, does not exist. Moreover, it fails to be fully Pareto optimal and incentive compatible and is also not implementable as a perfect Bayesian equilibrium of an extensive form game (Glycopantis et al. in Econ Theory 26:765–791, 2005). The lack of all the above properties is mainly due to the fact that the agents are supposed to predict the equilibrium market clearing price (as agent’s expected maximized utility is conditioned on the information that equilibrium prices reveal), which leads inevitably to the presumption that agents know all the primitives in the economy, i.e., random initial endowments, random utility functions and private information sets. To get around this problematic equilibrium notion, we introduce a new concept called Bayesian–Walrasian equilibrium (BWE) which has Bayesian features. In particular, agents try to predict the market-clearing prices using Bayesian updating and evaluate their consumption in terms of Bayesian price estimates, which are different for each individual. In this framework agents maximize expected utility conditioned on their own private information about the state of nature, subject to a Bayesian estimated budget constraint. Market clearing is not an intrinsic part of the definition of BWE. However, both in the case of perfect foresight and in the case of symmetric information BWE leads to a statewise market clearing; it then becomes an ex post Walrasian equilibrium allocation. This new BWE exists under standard assumptions, in contrast to the REE. In particular, we show that our new BWE exists in the well-known example in Kreps (J Econ Theory 14:32–43, 1977), where REE fails to exist. This work was done in the Spring of 2005, when EJB was a visiting professor at the University of Illinois.     

Payoff dominance and risk dominance in the observable delay game: a note

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.      

Noise-independent selection in multidimensional global games

This paper examines many-player many-action global games with multidimensional state parameters. It establishes that the notion of noise-independent selection introduced by Frankel, Morris and Pauzner [D. Frankel, S. Morris, A. Pauzner, Equilibrium selection in global games with strategic complementarities, J. Econ. Theory 108 (2003) 1–44] for one-dimensional global games is robust when the setting is extended to the one proposed by Carlsson and Van Damme [H. Carlsson, E. Van Damme, Global games and Equilibrium selection, Econometrica 61 (1993) 989–1018]. More precisely, our main result states that if an action profile of some complete information game is noise-independently selected in one-dimensional global games, then it is also noise-independently selected in all multidimensional global games.     

Agreeing on generalised Darwinism: a response to Pavel Pelikan

Pelikan (J Evol Econ 21:341–366, 2011) develops an interesting conceptual framework that adds to prior work on generalised Darwinism. Despite claims to the contrary we show that it is similar to the approach developed by Hodgson and Knudsen (J Evol Econ 16(4):343–366, 2006a, J Econ Behav Organ 75(1):12–24, 2010a, b), Aldrich et al. (J Evol Econ 18(5):577–596, 2008) and others. Pelikan also mischaracterises the Hodgson–Knudsen position over Lamarckism. We show why the term is misleading (rather than strictly wrong) when applied to social evolution.     

Self-enforced collusion through comparative cheap talk in simultaneous auctions with entry

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.     

Leading-by-example and signaling in voluntary contribution games: an experimental study

We report experimental results on the effect of leadership in a voluntary contribution game. Consistent with recent theories we find that leading-by-example increases contributions and earnings in an environment where a leader has private information about the returns from contributing (Hermalin in Am Econ Rev 88:1188–1206, 1998; Vesterlund in J Public Econ 87:627–657, 2003). In contrast the ability to lead-by-example has no effect on total contributions and earnings when such returns are commonly known. In our environment the success of leadership therefore appears to be driven by signaling rather than by nonpecuniary factors such as reciprocity. This paper was started while the authors were visiting the Harvard Business School during the fall of 2000. We are grateful for their hospitality and financial support. Vesterlund acknowledges support from the National Science Foundation and Potters from the Royal Netherlands’ Academy of Arts and Sciences. We thank Henrik Orzen for assistance in conducting the experiment. We also thank David Cooper and an anonymous referee who helped us improve the paper. Finally we thank Chris Anderson, Jim Andreoni, John Duffy, Simon Gaechter, Ernan Haruvy, Muriel Niederle, Jack Ochs, Elke Renner, Al Roth, participants at ESA-meetings (Barcelona, 2001), the Leadership and Social Interactions Workshop (Lyon, 2003), SITE (Stanford, 2004) and seminar participants at Alabama, CMU, Duke, Keele, Maryland, Nottingham, NYU, Pittsburgh, OSU, and York for valuable comments.     

Post-earnings announcement drift: Spanish evidence

This paper analyses whether earnings announcements in the Spanish stock market are followed in subsequent months by a return drift in the same direction as the earnings surprise. Two alternative earnings surprise measures are used and they both provide strong post-earnings announcement drifts. In order to find an explanation for this anomaly we first make several unconditional adjustments, which include the CAPM, the Fama–French (J Financ Econ 33:3–56, 1993) three-factor model, a liquidity factor, controlling portfolios by size and book-to-market ratio, and controlling for the momentum effect. Second, we make a conditional analysis following two different approaches: (i) studying the relation with the business cycle and (ii) studying whether this phenomenon can be explained through a conditional version of the CAPM and the Fama-French model. None of these adjustments are able to satisfactorily capture the Spanish post-earnings announcement drift. A final analysis offers some slight evidence in favour of the limits-to-arbitrage explanation. A previous version of this paper is available in the Working Paper Series of FUNCAS (no. 221, 2005), who we thank for their collaboration in the research diffusion in Spain. We also acknowledge the financial support of the Ministerio de Ciencia y Tecnología (SEJ2005-09372/ECON), Conselleria d’Empresa, Universitat i Ciència (GV06/196) and University of Alicante (GRJ06-03). This version has benefited from interesting comments made by Gonzalo Rubio, Belén Nieto, Natividad Blasco, Renata Herrerías and Carina Sponholtz, as well as by various anonymous referees. Any remaining errors are the sole responsibility of the authors.     

Large economies with differential information and without free disposal

We consider exchange economies with a continuum of agents and differential information about finitely many states of nature. It was proved in Einy et al. (Econ Theory 18, 321–332, 2001) that if we allow for free disposal in the market clearing (feasibility) constraints then an irreducible economy has a competitive (or Walrasian expectations) equilibrium, and moreover, the set of competitive equilibrium allocations coincides with the private core. However when feasibility is defined with free disposal, competitive equilibrium allocations may not be incentive compatible and contracts may not be enforceable (see e.g. Glycopantis et al. in Econ Theory 21, 495–526, 2002). This is the main motivation for considering equilibrium solutions with exact feasibility. We first prove that the results in Einy et al. (Econ Theory 18, 321–332, 2001) are still valid without free-disposal. Then, motivated by the issue of contracts’ execution, we adapt the incentive compatibility property introduced in Krasa and Yannelis (Econometrica 62, 881–900, 1994) and we prove that every Pareto optimal exact feasible allocation is incentive compatible, implying that contracts of competitive or core allocations are enforceable. We would like to thank two anonymous reviewers and the Associate Editor for their valuable suggestions and remarks. This work was partially done while V.F. Martins-da-Rocha was visiting the Dipartimento di Matematica e Informatica of the Università degli Studi di Perugia. We thank the audience of the First General Equilibrium Workshop at Rio. Section 6 dealing with contract enforcement and coalitional incentive compatibility has benefited from discussions with J. Correia-da-Silva, W. Daher, F. Forges, C. Hervès-Beloso, E. Moreno-García, K. Podczeck, Y. Vailakis and N.C. Yannelis.     

A replication note on unemployment in the OECD since the 1960s: what do we know?

Nickell et al. (Econ J 115(500):1–27, 2005) argue that unemployment rates cointegrate with labour market institutions in a panel of OECD countries. This paper replicates their Maddala–Wu panel cointegration test and shows that this test is only valid when (i) the number of countries tends to infinity and (ii) the underlying country-specific cointegration tests are independent. Their finding of cointegration does not survive when small sample properties and heterogeneous cross-sectional dependencies are taken into account. We acknowledge financial support from the Interuniversity Attraction Poles Program, Belgian Science Policy, contract no. P5/21. The usual disclaimer applies.     

Coordination of mobile labor

We study coordination failures in many simultaneously occurring coordination problems. Players encounter one of the problems but have the outside option of migrating to one of the remaining ones. Drawing on the global games approach, we show that such a mobile game has a unique equilibrium that allows us to examine comparative statics. The endogeneity of the outside option value and of the migration activity leads to non-monotonicity of welfare with respect to mobility friction; high mobility may hurt players. We apply these “general equilibrium’’ findings to the problem of the labor market during industrialization as described by Matsuyama [Increasing returns, industrialization and indeterminacy of equilibrium, Quart. J. Econ. 106 (1991) 617-650].     

State-owned enterprises as indirect instruments of entry regulation

In the context of mixed markets, Matsumura and Kanda (J Econ 84(1): 27–48, 2005) show that social welfare in free entry equilibrium is maximized when there exists a public firm in the market. En passant, these authors state that this outcome is connected to the entry-deterring influence of a public firm. In this way, they counter-act the excess entry problem of Mankiw and Whinston (Rand J Econ 17(1): 48–58, 1986). We explain this result arguing that the state-owned firm can be an indirect instrument to regulate entry. In fact, under free entry equilibrium welfare may be greater with the presence of a public firm than with a social planner.      

Equilibrium price formation in markets with differentially informed agents

We consider a pure exchange economy with a finite set of types of agents which have incomplete and asymmetric information on the states of nature. Our aim was to describe the equilibrium price formation and analyze how the lack of information may affect the allocation of resources. To do so, we adapt to an asymmetric information scenario a variant of the Shapley–Shubik game introduced by Dubey and Geanakoplos (J Math Econ 39:391–400, 2003 ).     

Forward contracts and competition

This paper examines the strategic use of forward contracts in an industry where downstream firms must buy an essential input from imperfectly competitive upstream suppliers. When a single large firm and a fringe of firms exist downstream, the large firm buys forward contracts from the fringe, i.e. there is horizontal subcontracting from the large firm to the firms on the fringe, in order to make the spot market less competitive. Hence our paper argues that horizontal subcontracting becomes an anti-competitive device. We also compare the strategies of buying forward contracts and purchasing productive capacity and we find that both are equivalent tools. When the downstream industry has instead several large firms, they have a “horizontal” incentive to sell forward contracts in order to gain market share, but the former “vertical” incentive to buy them persists. In this case, forward contracting may then lead to less competition in the spot market. We are indebted to Ramon Faulí-Oller, José Manuel Ordó?ez and Juan Carlos Reboredo for their helpful comments and suggestions on an earlier draft. We also gratefully acknowledge the valuable observations made by two anonymous referees and a Co-Editor that led to substantial improvements. Of course, the usual disclaimer applies. Antelo acknowledges financial support from the Xunta de Galicia (Grant PGIDIT02PXIA20101PR) and Bru that from the Spanish Ministerio de Ciencia y Tecnología (Grant PB98-1402).