Quotient spaces of boundedly rational types

By identifying types whose low-order beliefs up to level li about the state of nature coincide, weobtain quotient type spaces that are typically smaller than the original ones, preserve basic topologicalproperties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash(li; l-i)-equilibria capture players inability to distinguish types belonging to the same equivalence class.The case with uncertainty about the vector of levels (li; l-i) is also analyzed. Two examples illustratethe constructions.

Credit constraints in general equilibrium: Experimental results

Our work attempts to investigate the influence of credit tightness orexpansion on activity and relative prices in a multimarket set-up. We report on somedouble- auction, two-market experiments where subjects had to satisfy an inequalityinvolving the use of credit. The experiments display two regimes, characterizedby high and low credit availability. The critical value of credit at the commonboundary of the two regimes has a compelling interpretation as the maximal credituse at the Arrow-Debreu equilibrium of the abstract economy naturally associatedto our experimental environment. Our main results are that changes in theavailability of credit: (a): have minor and unsystematic effects on quantitiesand relative prices in the high-credit regime, (b): have substantial effects, bothon quantities and relative prices, in the low-credit regime.

Invariance and randomness in the Nash program for coalitional games

By introducing physical outcomes in coalitional games we note that coalitional games and social choice problems are equivalent (implying that so are the theory of implementation and the Nash program). This facilitates the understanding of the role of invariance and randomness in the Nash program. Also, the extent to which mechanisms in the Nash program perform ``real implementation'' is examined.

Short-term investment and equilibrium multiplicity

I study the effects of the heterogeneity of traders'horizon in the context of a 2-period NREE model whereall traders are risk averse. Owing to inventory effects,myopic trading behavior generates multiplicity ofequilibria. In particular, two distinct patterns arise.Along the first equilibrium, short term tradersanticipate higher second period price reaction toinformation arrival and, owing to risk aversion,scale back their trading intensity. This, in turn,reduces both risk sharing and information impoundinginto prices enforcing a high returns' volatility-lowprice informativeness equilibrium. In the second one,the opposite happens and a low volatility-high priceinformativeness equilibrium arises.

On some geometry and equivalence classes of normal form games

Equivalence classes of normal form games are defined using the geometryof correspondences of standard equilibiurm concepts like correlated, Nash,and robust equilibrium or risk dominance and rationalizability. Resultingequivalence classes are fully characterized and compared across differentequilibrium concepts for 2 x 2 games. It is argued that the procedure canlead to broad and game-theoretically meaningful distinctions of games aswell as to alternative ways of viewing and testing equilibrium concepts.Larger games are also briefly considered.

The evolution of conventions under incomplete information

We formulate an evolutionary learning process in the spirit ofYoung (1993a) for games of incomplete information. The process involves trembles. For many games, if the amount of trembling is small, play will be in accordance with the games' (semi-strict) Bayesian equilibria most of the time. This supports the notion of Bayesian equilibrium. Further, often play will most of the time be in accordance with exactly one Bayesian equilibrium. This gives a selection among the Bayesian equilibria. For two specific games of economic interest wecharacterize this selection. The first is an extension to incomplete information of the prototype strategic conflict known as Chicken. The second is an incomplete information bilateral monopoly, which is also an extension to incompleteinformation of Nash's demand game, or a simple version ofthe so-called sealed bid double auction. For both gamesselection by evolutionary learning is in favor of Bayesianequilibria where some types of players fail to coordinate, such that the outcome is inefficient.

Implementation, elimination of weakly dominated strategies and evolutionary dynamics

This paper is concerned with the realism of mechanisms that implementsocial choice functions in the traditional sense. Will agents actually playthe equilibrium assumed by the analysis? As an example, we study theconvergence and stability properties of Sj\"ostr\"om's (1994) mechanism, onthe assumption that boundedly rational players find their way to equilibriumusing monotonic learning dynamics and also with fictitious play. Thismechanism implements most social choice functions in economic environmentsusing as a solution concept the iterated elimination of weakly dominatedstrategies (only one round of deletion of weakly dominated strategies isneeded). There are, however, many sets of Nash equilibria whose payoffs maybe very different from those desired by the social choice function. Withmonotonic dynamics we show that many equilibria in all the sets ofequilibria we describe are the limit points of trajectories that havecompletely mixed initial conditions. The initial conditions that lead tothese equilibria need not be very close to the limiting point. Furthermore,even if the dynamics converge to the ``right'' set of equilibria, it stillcan converge to quite a poor outcome in welfare terms. With fictitious play,if the agents have completely mixed prior beliefs, beliefs and play convergeto the outcome the planner wants to implement.

Testing calibrated general equilibrium models

This paper illustrates the philosophy which forms the basis of calibrationexercises in general equilibrium macroeconomic models and the details of theprocedure, the advantages and the disadvantages of the approach, with particularreference to the issue of testing ``false'' economic models. We provide anoverview of the most recent simulation--based approaches to the testing problemand compare them to standard econometric methods used to test the fit of non--lineardynamic general equilibrium models. We illustrate how simulation--based techniques can be used to formally evaluate the fit of a calibrated modelto the data and obtain ideas on how to improve the model design using a standardproblem in the international real business cycle literature, i.e. whether amodel with complete financial markets and no restrictions to capital mobility is able to reproduce the second order properties of aggregate savingand aggregate investment in an open economy.

Equilibrium unemployment insurance

In this paper, we incorporate a positive theory of unemployment insuranceinto a dynamic overlapping generations model with search-matching frictionsand on-the-job learning-by-doing. The model shows that societies populatedby identical rational agents, but differing in the initial distributionof human capital across agents, may choose very different unemploymentinsurance levels in a politico-economic equilibrium. The interactionbetween the political decision about the level of the unemployment insuranceand the optimal search behavior of the unemployed gives rise to aself-reinforcing mechanism whichmay generate multiple steady-stateequilibria. In particular, a European-type steady-state with highunemployment, low employment turnover and high insurance can co-exist withan American-type steady-state with low unemployment, high employment turnoverand low unemployment insurance. A calibrated version of the model featurestwo distinct steady-state equilibria with unemployment levels and durationrates resembling those of the U.S. and Europe, respectively.

Generic finiteness of equilibrium payoffs for bimatrix games

It is shown that in any affine space of payoff matrices the equilibriumpayoffs of bimatrix games are generically finite.

Tracking the invisible hand: Convergence of double auctions to competitive equilibrium

Economics is the science of want and scarcity. We show that want andscarcity, operating within a simple exchange institution (double auction),are sufficient for an economy consisting of multiple inter--related marketsto attain competitive equilibrium (CE). We generalize Gode and Sunder's(1993a, 1993b) single--market finding to multi--market economies, andexplore the role of the scarcity constraint in convergence of economies to CE.When the scarcity constraint is relaxed by allowing arbitrageurs in multiple markets to enter speculative trades, prices still converge to CE,but allocative efficiency of the economy drops. \\Optimization by individual agents, often used to derive competitive equilibria,are unnecessary for an actual economy to approximately attain such equilibria.From the failure of humans to optimize in complex tasks, one need not concludethat the equilibria derived from the competitive model are descriptivelyirrelevant. We show that even in complex economic systems, such equilibriacan be attained under a range of surprisingly weak assumptions about agentbehavior.

A note on the convergence to competitive equilibria in economies with moral hazard

We examine the conditions under which competitive equilibria can beobtained as the limit, when the number of strategic traders getslarge, of Nash equilibria in economies with asymmetric informationon agents' effort and possibly imperfect observability of agents'trades. Convergence always occur when either effort is publiclyobserved (no matter what is the information available tointermediaries on agents' trades); or effort is private informationbut agents' trades are perfectly observed; or no information at allis available on agents' trades. On the other hand, when eachintermediary can observe its trades with an agent, but not theagent's trades with other intermediaries, the (Nash) equilibriawith strategic intermediaries do not converge to any of thecompetitive equilibria, for an open set of economies. The source ofthe difficulties for convergence is the combination of asymmetricinformation and the restrictions on the observability of tradeswhich prevent the formation of exclusive contractual relationshipsand generate barriers to entry in the markets for contracts.