Low information nash equilibria for oligopolistic markets

This paper deals with an infinite horizon n firm oligopoly in which firms are assumed to have incomplete information about one another's actions and profit functions. An equilibrium concept is defined that is similar to the Nash non-cooperative equilibrium, but is suitable for the information assumptions of the model. The equilibrium uses a type of bounded rationality which makes firms' computations relatively easy. This is due to an implicit assumption that computation is costly and a Bayesian approach is prohibitively costly. This low information Nash equilibrium is proved to exist, and, in addition, an adaptive expectations decision process is described which, if followed by all firms, leads to the low information Nash equilibrium.     

General equilibrium in economies with uncertain delivery

We consider a general equilibrium model of trade ex ante with differential information in which agents choose plans of state-contingent lists of bundles. Being unable to verify that the state of nature is s and not t, an agent has to accept the delivery of any bundle in the list for delivery in state s or in the list for delivery in state t. Under the assumption that each state of nature can be verified by at least one agent, we establish existence of equilibrium and we show that the equilibrium allocation satisfies a notion of coalitional incentive compatibility.     

The level of R&D spending in the variety-based endogenous growth model

We show that equilibrium endogenous growth may be excessive in the variety-based endogenous growth modelà la5 . This result is obtained by relaxing the assumption on the constant elasticity of the demand function for intermediate goods.     

The role of independence in the Green-Lin Diamond-Dybvig model

Green and Lin study a version of the Diamond-Dybvig model with a finite number of agents, independence (independent determination of each agent's type), and sequential service. For special preferences, they show that the ex ante first-best allocation is the unique equilibrium outcome of the model with private information about types. Via a simple argument, it is shown that uniqueness of the truth-telling equilibrium holds for general preferences—and, in particular, for a constrained-efficient allocation whether first-best or not. The crucial assumption is independence.     

How strong is the case for a populist central banker? A note

Conventional wisdom holds that a conservative central banker reduces equilibrium inflation with no cost in terms of real activity. More recently, this proposition has been turned around in models with inflation averse wage setters who are Stackelberg leaders vis-à-vis the central bank: In this case a populist central banker with no interest in inflation was shown to lead to the first-best equilibrium. This note demonstrates that the Stackelberg assumption is crucial for this result and that the Nash solution of the same model does not generally support the case for a populist central banker.     

Existence and Welfare Properties of Equilibrium in an Exchange Economy with Multiple Divisible and Indivisible Commodities and Linear Production Technologies

In this paper we consider a class of economies with a finite number of divisible commodities, linear production technologies, and indivisible goods and a finite number of agents. This class contains several well-known economies with indivisible goods and money as special cases. It is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities, if each agent initially owns a sufficient amount of one of the divisible commodities, and if a “no production without input”-like assumption on the production sector holds, then there exists a competitive equilibrium for any economy in this class. The usual convexity assumption is not needed here. Furthermore, by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds. We further obtain a second welfare theorem stating that under some conditions a Pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well-chosen redistribution of the total initial endowments. Journal of Economic Literature Classification Numbers: D4, D46, D5, D51, D6, D61.     

On the generic nonexistence of pure strategy nash equilibria in continuous games

S. Srivastava (J. Econ. Theory 36 (1985), 26–35) states that in the space of continuous games an open and dense subset does not have a pure strategy. Nash equilibrium. The purpose of this note is twofold: first, to show that without a connectedness assumption on the strategy sets of the players this statement is false; second, to provide correct proofs of his main results.     

Linear and non-linear price decentralization

Compendious and thorough solutions to the existence of a linear price equilibrium problem, the second welfare theorem, and the limit theorem on the core are provided for exchange economies whose consumption sets are the positive cone of arbitrary ordered Fréchet spaces—dispensing entirely with the assumption that the vector ordering of the commodity space is a lattice. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory vector orderings that are not lattices, which arise in the typical model of portfolio trading with missing options. The assumptions are on the primitives of the model. They are bounds on the marginals of non-linear prices and for ω-proper economies they are both sufficient and necessary.     

Nash equilibrium search for the best alternative

In a recent paper, Weitzman (Econometrica47 (1979) 641–654) described a policy of “optimal search for the best alternative.” The present paper is concerned with the development and characterization of a policy of “Nash equilibrium search for the best alternative.” Specifically, it is shown that, under certain monotonicity assumptions, and under the assumption that firms have incomplete information regarding the results of rivals' search behavior, a Nash equilibrium search policy exists and has the same form as Weitzman's optimal search policy.     

Job matching and the distribution of producer surplus

We study wage determination in the Jovanovic model of matching, relaxing the standard assumption that wages continuously adjust to reflect on-the-job performance and studying aggregation of ex-ante heterogeneous career paths. We assume that workers have no bargaining power and consider an equilibrium where individual workers' age-earnings profiles are piecewise constant, reflecting their outside earning opportunities at each point in time. Turnover results from employers' firing decisions rather than from workers' quitting decisions, and the equilibrium delivers realistic cross-sectional and time-series implications. Employees receive only a portion rather than the whole of the ex-ante producer's surplus from established matches, and have individual incentives to lobby for increased job security. Inefficiently low aggregate turnover may result if such lobbying efforts are successful.     

We can't disagree forever

Under the assumption of common priors, if the information partitions of two agents are finite, then simply by communicating back and forth and revising their posteriors the two agents will converge to a common equilibrium posterior, even though they may base their posteriors on quite different information. Furthermore, given any integer, n, one can construct an example in which the revision process not only takes n steps to converge, but no evident revision occurs—for (n?1) steps both agents repeat the same conflicting posteriors—until the last step, when the two agents decide to agree. Common knowledge of each other's posterior does not necessarily lead agents to the posterior they would have agreed upon had information been directly exchanged. On the other hand, the examples that are characterized by a discrepancy between the direct and indirect communication equilibrium, are rare: with probability 1, the revision process constructed here leads the two agents in one step to the direct communication equilibrium.     

The efficiency of competitive mechanisms under private information

We consider the efficiency properties of exchange economies where privately informed traders behave strategically. Specifically, a competitive mechanism is any mapping of traders’ reports about their types to an equilibrium price vector and allocation of the reported economy. In our model, some traders may have non-vanishing impact on prices and allocations regardless of the size of the economy. Although truthful reporting by all traders cannot be achieved, we show that, given any desired level of approximation, there is such that any Bayesian-Nash equilibrium of any competitive mechanism of any private information economy with or more traders leads, with high probability, to prices and allocations that are close to a competitive equilibrium of the true economy. In particular, allocations are approximately efficient. A key assumption is that there is small probability that traders behave non-strategically.     

Implementation,Elimination of Weakly Dominated Strategies and Evolutionary Dynamics

This paper studies convergence and stability properties of T. Sjöström's (1994, Games Econom. Behav.6, 502–511) mechanism, under the assumption that boundedly rational players find their way to equilibrium using monotonic evolutionary dynamics and best-reply dynamics. This mechanism implements most social choice functions in economic environments using as a solution concept one round of deletion of weakly dominated strategies and one round of deletion of strictly dominated strategies. However, there are other sets of Nash equilibria, whose payoffs may be very different from those desired by the social choice function. With monotonic dynamics, all these sets of equilibria contain limit points of the evolutionary dynamics. Furthermore, even if the dynamics converge to the “right” set of equilibria (i.e., the one which contains the solution of the mechanism), it may converge to an equilibrium which is worse in welfare terms. In contrast with this result, any interior solution of the best-reply dynamics converges to the equilibrium whose outcome the planner desires. Journal of Economic Literature Classification Numbers: C72, D70, D78.     

SIZE,OPENNESS, AND MACROECONOMIC INTERDEPENDENCE

One common, simplifying assumption in open economy macroliterature is that the rest of the world can be thought of as a representative economy. This article formally investigates conditions under which this assumption can be justified using a multicountry general equilibrium model as a laboratory. We derive the conditions that ensure the existence of the equilibrium and study the properties of the equilibrium using large N asymptotics. Thereby, we show that the two‐country framework is a valid approximation only for economies that have diversified trade linkages and only when there is no globally dominant economy among the foreign economies.     

Fault tolerance in large games

A Nash equilibrium is an optimal strategy for each player under the assumption that others play according to their respective Nash strategies, but it provides no guarantees in the presence of irrational players or coalitions of colluding players. In fact, no such guarantees exist in general. However, in this paper we show that large games are innately fault tolerant. We quantify the ways in which two subclasses of large games – λ-continuous games and anonymous games – are resilient against Byzantine faults (i.e. irrational behavior), coalitions, and asynchronous play. We also show that general large games have some non-trivial resilience against faults.     

Overlapping expectations and Hart's conditions for equilibrium in a securities model

Hart (J. Econ. Theory9 (1974), 293–311) gave conditions for equilibrium to exist in a securities model where each agent undertakes asset transactions to maximize expected utility of wealth. These conditions rule out agents wanting to undertake unbounded balanced transactions to reach a Pareto superior allocation given their expectations. With mild extra assumptions to make agents unwilling to risk incurring unbounded losses on their portfolios, Hart's conditions become equivalent to an assumption of “overlapping expectations,” which is comparable to a much weaker form of Green's “common expectations” (Econometrica41 (1973), 1103–1124).     

The capital gain lock-in effect and perfect substitutes

This paper analyses the effect of investors' accrued capital gains on optimal portfolio composition and equilibrium returns under the assumption that investors are able to re-balance with perfect substitute securities. No-dominance arguments are used to show that pricing differences because of accrued capital gains do not arise among securities which are perfect substitutes. These arguments are insufficient, however, to prevent pricing differences because of accrued capital gains among securities which are not perfect substitutes. Trading rules are developed which outline the conditions necessary for the realisation of accrued capital gains and the deferral of capital losses. These trading rules also provide guidance on which securities investors should sell, given their tax basis, when re-balancing their portfolios.     

Implementation with partial provability

We extend implementation theory by allowing the social choice function to depend on more than just the preferences of the agents and allowing agents to support their statements with hard evidence. We show that a simple condition on evidence is necessary for the implementation of a social choice function f when the preferences of the agents are state independent and sufficient for implementation for any preferences (including state dependent) with at least three agents if the social planner can perform small monetary transfers beyond those called for by f. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under a boundedness assumption. For both results, transfers only occur out of equilibrium. The use of evidence enables implementation which is robust in the sense that the planner needs little information about agents? preferences or beliefs and agents need little information about each others? preferences. Our results are robust to evidence forgery at any strictly positive cost.     

INFLATION AND THE PUBLIC DEFICIT WHEN THE UTILITY OF MONEY IS INSATIABLE*

When the marginal utility of money is positive even at very high levels of the asset (Yoshiyasu Ono's, 1994, assumption), the relationship between inflation and the public deficit at full employment may result in a unique perverse equilibrium where higher deficits reduce inflation. If there are two equilibria, the low inflation equilibrium is one where the perverse effect between inflation and the public deficit prevails; while in the high inflation equilibrium higher public deficits increase inflation. These results contrast sharply with traditional results found in the literature.     

Entrepreneurs' capital accumulation behavior and long-run equilibrium

The purpose of this paper is to derive some interesting results on long-run equilibrium by considering entrepreneurs' capital accumulation behavior explicitly. Our framework is a two class, two production sector model in order to analyze the dynamic stability properties in the cases of Kaldor's saving assumption and Pasinetti's saving assumption. We shall introduce a further adjustment mechanism: the speeding up (slowing down) of capital accumulation in that sector in which the rate of profit is higher (lower).