Geodesics on the equilibrium manifold

We show the existence of a Riemannian metric on the equilibrium manifold such that a minimal geodesic connecting two (sufficiently close) regular equilibria intersects the set of critical equilibria in a finite number of points. This metric represents a solution to the following problem: given two (sufficiently close) regular equilibria, find the shortest path connecting them which encounters the set of critical equilibria in a finite number of points. Furthermore, this metric can be constructed in such a way to agree, outside an arbitrary small neighborhood of the set of critical equilibria, to any given metric with economic meaning.     

Evolution and market behavior with endogenous investment rules

In a repeated market for short-lived assets, we investigate wealth-driven selection among investment rules that depend on endogenous market variables, such as current and past prices. We study the random dynamical system describing prices and wealth dynamics and characterize local stability of the long-run equilibria in which one or a group of traders dominate. Multiplicity of stable and unstable equilibria, leading to path dependency and persistent heterogeneity, turns out to be a common phenomenon generated by two different mechanisms. Firstly, conditioning investment decisions on endogenous market variables implies that the relative performance of investment rules, in terms of average growth rates, may be different for different prevailing prices, so that the market may fail to select a global winner. Secondly, the feedback existing between past asset prices and current investment decisions can lead to a form of deterministic overshooting.     

An exact non-cooperative support for the sequential Raiffa solution

This article provides an exact non-cooperative foundation of the sequential Raiffa solution for two-person bargaining games. Based on an approximate foundation due to Myerson (1991) for any two-person bargaining game (S, d) an extensive form game G^S,d is defined that has an infinity of weakly subgame perfect equilibria whose payoff vectors coincide with that of the sequential Raiffa solution of (S, d). Moreover all those equilibria share the same equilibrium path consisting of proposing the Raiffa solution and accepting it in the first stage of the game.By a modification of G^S,d the analogous result is provided for subgame perfect equilibria. These results immediately extend to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium.     

Long-term interest rates,risk premia and unconventional monetary policy

We study two kinds of unconventional monetary policies: announcements about the future path of the short-term rate and long-term nominal interest rates as operating instruments of monetary policy. We do so in a model where the risk premium on long-term debt is, in part, endogenously determined. We find that both policies are consistent with unique equilibria, that, at the zero lower bound, announcements about the future path of the short-term rate can lower long-term interest rates through their impact both on expectations and on the risk premium and that long-term interest rate rules perform as well as, and at times better than, conventional Taylor rules. With simulations, we show that long-term interest rate rules generate sensible dynamics both when in operation and when expected to be applied.     

Experimental evidence of bank runs as pure coordination failures

We investigate how coordination requirement, measured by the coordination parameter, affects the occurrence of miscoordination-based bank runs in controlled laboratory environments. We identify an indeterminacy region of the coordination parameter such that games with the parameter within the region have varying coordination outcomes and exhibit persistent path dependence. Experimental economies with the parameter above (below) the region stay close or converge to the run (non-run) equilibrium. Switches between the two equilibria occur even with fixed economic fundamentals. The experimental results are well accounted for by a version of the evolutionary algorithm that uses experimentation rates estimated from the experimental data.     

Consistent collusion-proofness and correlation in exchange economies

We present a feasible strategic market mechanism with finitely many agents whose Nash, semi-strong Nash and coalition-proof Nash equilibria fully implement the Walrasian equilibria. We define a strategic equilibrium concept, called correlated semi-strong equilibrium, and show that the Walrasian equilibria can be implemented by these equilibria, and also by the coalition-proof correlated equilibria of our mechanism. We show that these two concepts, suitably modified with transfers, fully implement the Pareto optimal allocations.     

Multilateral negotiations and formation of coalitions

This paper analyses properties of games modeling multilateral negotiations leading to the formation of coalitions in an environment with widespread externalities. The payoff generated by each coalition is determined by an exogenous partition function (the parameter space). We show that in almost all games, except in a set of measure zero of the parameter space, the Markov perfect equilibrium value of coalitions and the state transition probability that describe the path of coalition formation is locally unique and stable. Therefore, comparative statics analysis are well-defined and can be performed using standard calculus tools. Global uniqueness does not hold in general, but the number of equilibria is finite and odd. In addition, a sufficient condition for global uniqueness is derived, and using this sufficient condition we show that there is a globally unique equilibrium in three-player superadditive games.     

Equilibrium with coordination

The obvious equilibrium concepts in the simplest institutions for transferring ownership of commodities—bilateral exchange—are neither Nash equilibria nor cooperative equilibria. To study such equilibria as special cases of equilibria of a social system it is necessary to introduce coordination. Two or more agents coordinate their actions, if, when they consider an alternative to a state, they take as given—for agents with whom they coordinate—the alternative state. If there is no coordination we obtain Nash equilibrium as a special case. If there is complete coordination we obtain optimality as a special case. The main result is an existence theorem for a social system with coordination. This theorem is then applied to prove existence of exchange equilibria in an economy with bilateral exchange.     

Second‐Price Auctions with Different Participation Costs

This paper studies equilibria of second‐price auctions in independent private value environments with different participation costs. Two types of equilibria are identified: monotonic equilibria in which a bidder with a lower participation cost results in a lower cutoff for submitting a bid, and nonmonotonic equilibria in which a lower participation cost results in a higher cutoff. We show that there always exists a monotonic equilibrium, and further, that the monotonic equilibrium is unique for either concave distribution functions or strictly convex distribution functions with nonincreasing reverse hazard rates. There exist nonmonotonic equilibria when the distribution functions are strictly convex and the difference of the participation costs is sufficiently small. We also provide comparative static analysis and study the limiting properties of equilibria when the difference in bidders’ participation costs approaches zero.     

Equilibrium theory with a measure space of possibly satiated consumers

Walras equilibria may not exist when consumers’ preferences are possibly satiated. To overcome this difficulty, several extended notions of equilibria have been proposed and all reduce to Walras equilibria under nonsatiation and free disposal. This includes the notions of equilibria with slack (also called dividend equilibria) as by Drèze and Müller [J. Economic Theory 23 (1980) 131], Makarov [J. Mathematical Economics 8 (1981) 87], Aumann and Drèze [Econometrica 54 (1986) 1271], Mas-Colell [Equilibrium theory with possibly satiated preferences, in: Majumdar, M. (Ed.), Proceedings of the Essays in Honour of David Gale on Equilibrium and Dynamics, Macmillan, London, pp. 201–213], monetary equilibria as by Kajii [J. Mathematical Economics 25 (1996) 75], or weak equilibria as by Polemarchakis and Siconolfi [J. Mathematical Economics 22 (1993) 85], which are all defined when there are finitely many consumers. This includes also the notion of free disposal equilibrium, when markets clear in a weak sense, allowing free disposal. Our paper considers an economy with a measure space of consumers and provides a general existence result of equilibria for the various existing notions. This result extends in particular the result by Hildenbrand [Econometrica 38 (1970) 608] on the existence of Walras equilibria.     

Convergence in games with continua of equilibria

In game theory, the question of convergence of dynamical systems to the set of Nash equilibria has often been tackled. When the game admits a continuum of Nash equilibria, however, a natural and challenging question is whether convergence to the set of Nash equilibria implies convergence to a Nash equilibrium. In this paper we introduce a technique developed in Bhat and Bernstein (2003) as a useful way to answer this question. We illustrate it with the best-response dynamics in the local public good game played on a network, where continua of Nash equilibria often appear.     

Note on the optimality of unemployment equilibria

An equilibrium concept for an economy with rigid prices has been given by Drèze (1975). He formulated a model where for some commodity, either the supplies or the demands are rationed. In this note we discuss ‘unemployment equilibria’, i.e., fixed price equilibria for which the quantity rationing affects the supplies only. It can be proved that there exists a set of unemployment equilibria. Therefore we consider the question whether it is possible to characterize the set of undominated unemployment equilibria.     

Ramsey equilibrium with liberal borrowing

This paper considers a multi-agent one-sector Ramsey equilibrium growth model with borrowing constraints. The extreme borrowing constraint used in the classical version of the model, surveyed in Becker (2006), and the limited form of borrowing constraint examined in Borissov and Dubey (2015) are relaxed to allow more liberal borrowing by the households. A perfect foresight equilibrium is shown to exist in this economy. We describe the steady state equilibria for the liberal borrowing regime and show that as the borrowing regime is progressively liberalized, the steady state wealth inequality increases. Unlike the case of a limited borrowing regime, an equilibrium path need not converge in the case of liberal borrowing regime. We show through an example that a two period cyclic equilibrium exists when agents are allowed to borrow against their two period future wage income. This result is similar to the possibility of non-convergent equilibrium capital stock sequences in the model with no borrowing.     

Convergence to competitive equilibria and elimination of no-trade (in a strategic market game with limit prices)

The strategic market games literature contains many results that predict Walrasian equilibria in the competitive limit. However, they usually come at the expense of ad hoc assumptions that rule out “pathological” no trade equilibria. This paper studies a strategic market game with limit prices. The set of Nash equilibrium allocations of this game converges to the set containing all competitive equilibria and no-trade, when players are replicated. Moreover, two rounds of iterated deletion of weakly dominated strategies eliminate the no-trade equilibria. Hence, replication paired with two rounds of iterated dominance gives a clean prediction of competitive equilibrium.     

Global indeterminacy and equilibrium selection in a model with depletion of non-renewable resources

We use the principles of global bifurcation analysis to explore the role of fiscal policy in a model where non-renewable depletion presents stock effects. Initially, we show that fiscal policy may induce the onset of two coexisting steady states, one of which is characterized by a lower depletion rate and higher income (virtuous steady state) than the other (bad steady state). Then, we shed light on the ability of an endogenous fiscal policy to act as an equilibrium selection device. We find that when the economy is sufficiently patient and exhibits low capital returns and environmental parameters, fiscal policy can create a continuum of equilibria that leads to the virtuous steady state. In the opposite situation of an impatient economy, which has high capital returns and environmental parameters, fiscal policy can only create one perfect-foresight path (a heteroclinic trajectory) through which the economy can approach the virtuous steady state.     

A characterization of equilibria in the Groves–Ledyard mechanism

In this paper, we characterize all interior and boundary equilibria of the Groves–Ledyard mechanism for a large class of economies and determine their stability properties. We show that the mechanism admits three types of equilibria: a symmetric, efficient, stable interior equilibrium, a large set of asymmetric, efficient, unstable, interior equilibria, and a large set of asymmetric, inefficient, stable boundary equilibria. We further show that asymmetric equilibria fail to exist for large values of the punishment parameter or if the message space is bounded sufficiently. The boundary equilibria previously had not been located nor had the instability of the asymmetric equilibria been known. Interestingly, the stability of the symmetric equilibrium rests on two dynamics that individually produce instability.     

Monotone comparative statics for games with strategic substitutes

Under some conditions, parameterized games with strategic substitutes exhibit monotone comparative statics of equilibria. These conditions relate to a tradeoff between a direct parameter effect and an opposing, indirect strategic substitute effect. If the indirect effect does not dominate the direct effect, monotone comparative statics of equilibria are guaranteed. These conditions are available for best-response functions, differentiable payoff functions, and general payoff functions. Results are extended to correspondences, the analysis applies to asymmetric equilibria, and several examples are provided.     

Matching models with a conservation law: The existence and global structure of the set of stationary equilibria

We study random matching models where there is a set of infinitely lived agents, and in each period agents are pairwise matched to each other and play a stage game. We investigate the basic structure of equilibria in such models: the existence of equilibria and the global structure of the set of equilibria. Specifically, we focus on models with a conservation law, which typically holds in economies having some assets, such as money. In such models, under certain regularity conditions the set of equilibria is one-dimensional and each connected component of it is a piecewise smooth one-dimensional manifold being homeomorphic to either the unit circle or the unit interval. Moreover, in an endpoint of an interval all agents have the same amount of assets.