A note on cheap talk and burned money

Austen-Smith and Banks [Cheap talk and burned money, J. Econ. Theory 91(1) (2000) 1-16] study how money burning can expand the set of pure cheap talk equilibria of Crawford and Sobel [Strategic information transmission, Econometrica 50(6) (1982) 1431-1451]. I identify an error in the main Theorem of Austen-Smith and Banks, and provide a variant that preserves some of the important implications. I also prove that cheap talk can be influential with money burning if and only if it can be influential without money burning. This strengthens a result of Austen-Smith and Banks, but uncovers other errors in their analysis. Finally, an open conjecture of theirs is proved correct.     

Strategic candidacy for multivalued voting procedures

Dutta et al. (Econometrica 69 (2001) 1013) (Dutta, Jackson, and Le Breton—DJLeB) initiate the study of manipulation of voting procedures by a candidate who withdraws from the election. A voting procedure is candidate stable if this is never possible. We extend the DJLeB framework by allowing: (a) the outcome of the procedure to be a set of candidates; (b) some or all of the voters to have weak preference orderings of the candidates. When there are at least three candidates, any strongly candidate stable voting selection satisfying a weak unanimity condition is characterized by a serial dictatorship. This result generalizes Theorem 4 of DJLeB.     

On mixed markets with asymmetric information

In asymmetric information exchange economies involving both non-negligible and negligible agents, one should expect the failure of the private Core-Walras Equivalence Theorem. This paper shows that if “large” traders are similar to each other, then they lose their market power and hence the Equivalence Theorem can be restored. We also investigate on weaker equivalences among Walrasian expectations allocations, Aubin private core and private core allocations of the original mixed economy and the atomless one associated to it, without the assumption that all atoms are of the same type. Furthermore, extensions of Hervés-Moreno-Yannelis and Schmeidler Theorems (compare Hervés et al. in J Math Econ 41:844–856, 2005a; Schemidler in Econometrica 40:579–580, 1972) are given for differential information economies in which the feasibility constraints are imposed with an equality (exact feasibility).     

Network formation and stable equilibrium

We study the non-cooperative formation of a (directed) network that builds upon one-way immediate links. Our novel feature is that we require circular paths of links for productive activities. This captures more clearly the higher level of coordination that is often required for network formations than models such as those of Jackson and Wolinsky [A strategic model of social and economic networks, J. Econ. Theory 71 (1996) 44-74] and Bala and Goyal [A non-cooperative model of network formation, Econometrica 68 (2000) 1181-1229], in that in our model a single agent's unilateral action is limited in affecting the network structure. We completely characterize the class of Nash equilibria by showing that the minimality of a graph is both necessary and sufficient (Theorem 1). We also propose the concept of a stable network that is similar to the pairwise stability of Jackson and Wolinsky (1996). We show that stable equilibria are a wheel, a trivial network, or a sub-wheel partitioned network (Theorem 2). We modify the Bala and Goyal (2000) dynamic process with inertia, and obtain the convergence to stable equilibria regardless of the initial state (Theorem 3).     

On discounted dynamic programming with unbounded returns

In this paper, we apply the idea of k-local contraction of Rincón-Zapatero and Rodriguez-Palmero (Econometrica 71:1519–1555, 2003; Econ Theory 33:381–391, 2007) to study discounted stochastic dynamic programming models with unbounded returns. Our main results concern the existence of a unique solution to the Bellman equation and are applied to the theory of stochastic optimal growth. Also a discussion of some subtle issues concerning k-local and global contractions is included.     

Evolution, bargaining, and time preferences

I include a role for time preferences within a version of the Young (J Econ Theory 59:145–168, 1993b) evolutionary model of bargaining. With or without time preferences, the stochastic stable convention yields a generalized version of the Nash (Econometrica 18:155–162, 1950) Bargaining Solution. When time preferences are added to the model, agents’ discount factors enter into the stochastically stable convention in a natural manner. That is, an agent’s discount factor acts as a bargaining weight within the Nash Bargaining Solution. By taking appropriate limits, an evolutionary foundation for the Rubinstein (Econometrica 50:97–110, 1982) Bargaining Solution is provided. I thank Lew Evans, Jack Leach, Collin Starkweather, Aaron Strong, a referee and associate editor. All errors are my own.     

Stochastic stability in networks with decay

This paper considers a stylized model of network formation in which relations among agents are subject to frictions, as described in Bala and Goyal [A non cooperative model of network formation, Econometrica 68 (2000) 1181-1231]. We analyze the process of network formation in a dynamic framework where self-interested individuals can form or delete links and, occasionally, make mistakes. Then, using stochastic stability, we identify the network structures to which the formation process will converge.     

Markov Equilibria of Stochastic Games with Complementarities

The existence of Markov equilibria for stochastic games with a continuum of states is a complex issue for which no general result holds as yet. In this article, the problem is solved for a class of stochastic games that satisfy assumptions of complementarity and monotonicity. The proof of existence relies on results from lattice programming. In the Markov equilibria singled out by the Theorem of Existence, the policies and continuation values are increasing and Lipschitz continuous functions of the state variable.Journal of Economic LiteratureClassification Numbers: C62, C73.     

An equilibrium closure result for discontinuous games

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.     

Arbitrage-free valuation of interest rate securities under forward curves with stochastic speed and acceleration

Arbitrage-free models for valuing interest rate securities posit that stochastic changes in spot or forward interest rates (forward rate “speed”) follow a diffusion process. This paper extends the Heath, Jarrow and Morton [Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuations, Econometrica 60 (1992) 77-105], HJM framework by allowing diffusive shocks to both the “speed” and “acceleration” of forward rates. The arbitrage-free restriction on forward rates is identified and involves volatilities of the speed and acceleration dynamics and their correlation. Although the extended forward rates remain in the diffusive framework and evolve continuously, they may exhibit large changes over short intervals (as with jumps) due to stochastic acceleration. Comparisons of bond prices show that the proposed model generates more complex and intricate shapes for the restricted forward curve with the same number of stochastic factors and volatility.     

Stochastic mechanisms in settings without monetary transfers: The regular case

We analyze relative performance of stochastic and deterministic mechanisms in an environment that has been extensively studied in the literature on communication (e.g., [Vincent P. Crawford, Joel Sobel, Strategic information transmission, Econometrica 50 (6) (1982) 1431-1451]) and optimal delegation (e.g., [Bengt Holmström, On the theory of delegation, in: M. Boyer, R.E. Kihlstrom (Eds.), Bayesian Models in Economic Theory, North-Holland, 1984, pp. 115-141]): a principal-agent model with hidden information, no monetary transfers, and single-peaked preferences. We demonstrate that under the common assumption of quadratic payoffs and a certain regularity condition on the distribution of private information and the agent's bias, the optimal mechanism is deterministic. We also provide an explicit characterization of this mechanism.     

Testing the balanced growth hypothesis: evidence from China

We investigate whether China’s experience during 1952–2004 supports the balanced growth entailment of the neoclassical growth model. Estimation of long-run relations among output, consumption and investment for the full period reject the balanced growth hypothesis for both the national and regional economies. When the economic reforms of the late 1970s are modelled as a structural break by the methods of Johansen et al. (Economet J 3(2):216–249, 2000) and Perron (Econometrica 57(6):1361–1401, 1989), we find some evidence of balanced growth in the pre-break period but in the post-break period the ‘great ratios’ are trend-stationary, precluding fully balanced growth, though permitting a common (stochastic) productivity trend.      

Information and size of coalitions

We consider a set of asymmetrically informed agents, where the information of each trader is susceptible of being altered when she becomes a member of a coalition. For this, we consider a general rule that depending on the coalition, a signal (or an information partition) is assigned to each member of the coalition. We set examples showing that Grodal’s (Econometrica 40:581–583, 1972), Schmeidler’s (Econometrica 40:579–580, 1972) and Vind’s (Econometrica 40:585–586, 1972) core characterizations of a continuum economy may fail in this general informational setting. However, under mild assumptions on the rule, we extend Schmeidler’s and Vind’s results to economies that allocate information to agents in each coalition according to the rule. We then focus on information mechanisms based on the size of coalitions and provide a general characterization result for the corresponding cores. Moreover, we pay close attention to the rule that assigns the shared information to each member of specific coalitions. We prove that the resulting cores are exactly the same independently of whether arbitrarily small or large coalitions share information.     

Price dynamics in an exchange economy

The pure exchange model is the foundation of the neoclassical theory of value, yet equilibrium predictions and price adjustment dynamics for this model remained untested prior to the experiment reported in this paper. With the exchange economy replicated several times, prices and allocations in most experiment sessions adjust toward the competitive equilibrium in continuous double auction trading, though adjustment is much slower than in previous commodity flow (or perishable good) double auction market experiments. Price adjustment is evaluated by comparing its extent within each market replication (or trading period) to its extent across trading periods. More price adjustment occurs within trading periods than across trading periods, so price adjustment data are evaluated with the disequilibrium Hahn process model (Hahn and Negishi in Econometrica 30:463–469, 1962) of within-period trades. This paper introduces a stochastic version the Hahn process model and demonstrates that a linear approximation to this stochastic model yields an autoregressive process with a near unit root when the adjustment rate is low. In effect, the autoregressive price adjustment model studied extensively by time series econometricians over the past 30 years can be viewed as a reduced form of a stochastic disequilibrium exchange economy price adjustment model. Estimation of the model demonstrates that price adjustment in the exchange economy experiment is considerably slower than in economies without income effects, which suggests that the price discovery process may be a significant factor in the slow adjustment documented by applied econometricians.     

Equilibrium selection in global games with strategic complementarities

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.     

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.     

Corrigendum to “Stable matchings and preferences of couples” [J. Econ. Theory 121 (1) (2005) 75–106]

We correct an omission in the definition of the domain of weakly responsive preferences introduced in [B. Klaus, F. Klijn, Stable matchings and preferences of couples, J. Econ. Theory 121 (2005) 75–106] or KK05 for short. The proof of the existence of stable matchings [KK05, Theorem 3.3] and a maximal domain result [KK05, Theorem 3.5] are adjusted accordingly.     

Generalized risk-dominance and asymmetric dynamics

This paper proposes two (ordinal and cardinal) generalizations of [J.C. Harsanyi, R. Selten, A General Theory of Equilibrium Selection in Games, MIT Press, Cambridge, MA and London, 1988] risk-dominance to multi-player, multi-action games. There are three reasons why generalized risk-dominance (GR-dominance) is interesting. Extending the logic of risk-dominance, GR-dominant actions can be interpreted as best responses to conjectures that satisfy a certain type of symmetry. Second, in a local interaction game of [G. Ellison, Learning, local interaction, and coordination, Econometrica 61 (5) (1993) 1047], if an action is risk-dominant in individual binary interactions with neighbors, it is also GR-dominant in the large game on a network. Finally, we show that GR-dominant actions are stochastically stable under a class of evolutionary dynamics. The last observation is a corollary to new abstract selection results that applies to a wide class of so-called asymmetric dynamics. In particular, I show that a (strictly) ordinal GR-dominant profile is (uniquely) stochastically stable under the approximate best-response dynamics of [M. Kandori, G.J. Mailath, R. Rob, Learning, mutation, and long run equilibria in games, Econometrica 61 (1) (1993) 29]. A (strictly) cardinal GR-dominant equilibrium is (uniquely) stochastically stable under a class of payoff-based dynamics that includes [L.E. Blume, The statistical-mechanics of strategic interaction, Games Econ. Behav. 5 (3) (1993) 387-424]. Among others, this leads to a generalization of a result from [G. Ellison, Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution, Rev. Econ. Stud. 67 (230) (2000) 17] on the -dominant evolutionary selection to all networks and the unique selection to all networks that satisfy a simple, sufficient condition.     

Koopmans recursive preferences and income convergence

Stiglitz (Econometrica 37 (1969) 382) shows income convergence in a many-agent Solow growth model with integrated capital markets (ICM). The many-agent Ramsey model (MARM) without ICM also gives income convergence. With a MARM, equal discount rates, and ICM, convergence of incomes (as opposed to product per capita) cannot occur. These results depend upon fixed saving propensities (Stiglitz) or separable additive preferences (Ramsey). Non-convergence of incomes is shown when preferences are identical Koopmans separable (KS). Endogenous discount rates may violate KS. A model for that case is developed when, even under favourable assumptions, oscillations or chaotic dynamics may result.     

Optimal guessing: Choice in complex environments

In this paper, we extend the analysis of our earlier work on boundedly rational learning in an i.i.d. setting [Easley and Rustichini, Econometrica 67 (1999) 1157-1184] to complex decision problems. We show that the axioms from our earlier analysis can be applied in this more complex setting, and along with some new axioms, they asymptotically yield expected utility maximization. Perhaps most important is our demonstration of a simple procedure that insures expected payoff maximization no matter what Markov process the underlying process on states follows. We view this result as providing a positive learning result for all worlds in which learning is possible.