Risk aversion in symmetric and asymmetric contests

We analyze existence, uniqueness and properties of equilibria in incompletely discriminating Tullock contests with logistic contest success functions, when contestants are risk averse. We prove that a Nash equilibrium for such a contest exists, but give an example of a symmetric contest with both symmetric and asymmetric equilibria, showing that risk aversion may lead to multiple equilibria. Symmetric contests have unique symmetric equilibria but additional conditions are necessary for general uniqueness. We also study the effects on incumbents of additional competitors entering the contest under these conditions and examine the effects of risk aversion on rent dissipation in symmetric and asymmetric contests.     

Sufficient conditions for the existence of sunspot equilibria

This paper reports on conditions on agents' preferences and endowments sufficient to guarantee the existence of sunspot equilibria in a simple overlapping generations model of pure exchange. Sunspot equilibria are those in which uncertainty extrinsic to the economy operates through expectations to yield a fulfilled expectations competitive equilibrium in which the extrinsic randomness has real effects on prices and allocations. The paper also provides necessary and sufficient conditions for these equilibria to have agents trading in a fixed stock of valued fiat money. The condition derived can be interpreted as requiring that intertemporal income effects appropriately dominate substitution effects.     

Variable rational partisan cycles and electoral uncertainty

Variable rational partisan theory of political business cycles suggests differences in inflation under left-wing and right-wing governments. Fluctuations of economic activity result from uncertainty about the electoral outcome and the exact timing of elections. However, the core hypothesis that post-electoral booms and recessions depend upon the degree of electoral uncertainty has rarely been tested. Using polling data, we provide empirical evidence in favor of the hypothesis of the existence of variable rational partisan cycles.     

Overlapping risk adjusted sets of priors and the existence of efficient allocations and equilibria with short-selling

The theory of existence of equilibrium with short-selling is reconsidered under risk and ambiguity modelled by risk averse variational preferences. No-arbitrage conditions are given in terms of risk adjusted priors. A sufficient condition for existence of efficient allocations is the overlapping of the interiors of the risk adjusted sets of priors or the inexistence of mutually compatible trades, with non-negative expectation with respect to any risk adjusted prior. These conditions are necessary when agents are not risk neutral at extreme levels of wealths. It is shown that the more uncertainty averse or risk averse the agents, the more likely are efficient allocations and equilibria to exist.     

Basins of attraction and equilibrium selection under different learning rules

A deterministic learning model applied to a game with multiple equilibria produces distinct basins of attraction for those equilibria. In symmetric two-by-two games, basins of attraction are invariant to a wide range of learning rules including best response dynamics, replicator dynamics, and fictitious play. In this paper, we construct a class of three-by-three symmetric games for which the overlap in the basins of attraction under best response learning and replicator dynamics is arbitrarily small. We then derive necessary and sufficient conditions on payoffs for these two learning rules to create basins of attraction with vanishing overlap. The necessary condition requires that with probability one the initial best response is not an equilibrium to the game. The existence of parasitic or misleading actions allows subtle differences in the learning rules to accumulate.     

ON THE ROLE OF THE PRIMARY SYSTEM IN CANDIDATE SELECTION

How does the type of the primary system affect political outcomes? We address this issue by constructing a simple model that accounts for intra‐party as well as inter‐party political competition. Our model suggests that allowing non‐partisan voters to participate in the primaries (i.e. a semi‐open primary system) indeed improves the chances of a moderate candidate getting elected. However, this need not necessarily happen in the case of a completely open primary system. Under such a system there arise multiple equilibria, some of which may lead to a greater degree of extremism than the closed primary system. Thus, our model contributes to the current debate on the choice of primary systems from an analytical perspective and helps explain some of the empirical findings.     

Intertemporal equilibria with Knightian uncertainty

We study a dynamic and infinite-dimensional model with incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents? multiple prior sets. A specific model with neither risk nor uncertainty at the aggregate level is considered. Risk is always fully insured. For small levels of ambiguity, there exists an equilibrium with inertia where agents also insure fully against Knightian uncertainty. When the level of ambiguity exceeds a critical threshold, full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all. We also show that equilibria with inertia are indeterminate.     

Voluntary participation and intergenerational risk sharing in a funded pension system

We explore the feasibility of a funded pension system with intergenerational risk sharing when participation in the system is voluntary. Typically, the willingness of the young to participate depends on their belief about the future young's willingness to do so. We characterise equilibria with voluntary participation and show that the likelihood of their existence increases with risk aversion and financial market uncertainty. We find that mandatory participation is often necessary to sustain a funded pension pillar and to let participants benefit from intergenerational risk sharing.     

The Structure of Sunspot Equilibria: The Role of Multiplicity

This paper examines the structure of sunspot equilibria in a standard two period exchange economy with real assets. We show that for a generic choice of utility functions and endowments, there exists an open set of real asset structures whose payoffs are independent of sunspots such that the economy with this asset structure has a regular sunspot equilibrium. An important implication of our result is that the multiplicity of non-sunspot equilibria is not necessary for the existence of sunspot equilibria. Our technique is general and can be applied to show the existence of sunspot equilibria in other frameworks.     

Knightian uncertainty and poverty trap in a model of economic growth

This paper explores how Knightian uncertainty affects dynamic properties in an economic growth model. The decision-making theory employed in the analysis is the theory of expected utility under a non-additive probability measure, i.e., the Choquet expected utility model of preference. We apply this decision-making theory to an overlapping generations model where producers face “uncertainty” in their technologies. When the producer is averse to uncertainty, the firm's profit function may not be differentiable. Therefore, the firm's decision to invest and hire labor becomes rigid for a certain measurable range of real interest rates. In dynamic equilibrium, the existence of firm-level rigidity causes discontinuity in the wage function; this makes multiple equilibria the more likely outcomes under the log utility and Cobb–Douglas production functions. In this paper, we show that even if aversion to uncertainty is small, the “poverty trap” can arise for a wide range of parameter values.     

Multiple equilibria in Tullock contests

We find the sufficient conditions for the existence of multiple equilibria in Tullock-type contests, and show that asymmetric equilibria arise even under symmetric prize and cost structures. We then present existing contests where multiple equilibria exist under reasonably weak conditions.     

History and Coordination Failure

An extensive literature discusses the existence of a virtuous circle of expectations that might lead communities to Pareto-superior states among multiple potential equilibria. It is generally accepted that such multiplicity stems fundamentally from the presence of positive agglomeration externalities. We examine a two-sector model in this class and look for intertemporal perfect foresight equilibria. It turns out that under some plausible conditions, positive externalities must coexist with external diseconomies elsewhere in the model, for there to exist equilibria that break free of historical initial conditions. Our main distinguishing assumption is that the positive agglomeration externalities appear with a time lag (that can be made vanishingly small). Then, in the absence of external diseconomies elsewhere, the long-run behaviour of the economy resembles that predicted by myopic adjustment. This finding is independent of the degree of forward-looking behavior exhibited by the agents.     

Economic growth and multiple equilibria: A critical note

Recent literature on economic growth points towards the possibility of the existence of multiple equilibria, under certain conditions. In this paper we use a growth model with a public health infrastructure to analyze, in detail, its local dynamics. The discussion of the existence of equilibria in the model reveals that some candidates for equilibria turn out to be non-relevant and are therefore ruled out. Indeed, multiple equilibria may only arise under restrictive parameter values, meaning that the so called “growth miracles” in some literature may be less likely to occur. Numerical computations illustrate that each relevant equilibrium exhibits local saddle-path stability.     

The Effects of Open Market Operations in a Model of Intermediation and Growth

This article presents a monetary growth model where spatial separation and limited communication create a role for banks. Monetary policy interacts with the financial system's liquidity provision to affect the existence, multiplicity, and dynamical properties of equilibria. Moderate levels of risk aversion and tight monetary policy can lead to multiple steady states. Dynamical equilibria can be indeterminate, with oscillatory paths. Thus financial market frictions are a source of indeterminacies and endogenous volatility. Under plausible conditions, tight monetary policy raises the nominal interest rate and inflation rate and reduces long run output. Thus, a central bank's liquidity provision can promote growth.     

Political Effects on Pension Underfunding

Pension underfunding in the public sector has received considerable attention recently and is often cited as the next looming crisis. The majority of recent research has focused on appropriately measuring the underfunding. In this paper, we employ a political economy framework to show that increases in partisan polarization and electoral uncertainty lead to greater underfunding. Using an unbalanced panel of individual pension plans, we find robust empirical evidence that higher legislative turnover rates, more electoral competition, and term limits all lead to more pension underfunding. The political environments of state and local governments play a pivotal role in pension underfunding.     

Instabilities and robust control in natural resource management

Most renewable natural resources exhibit marked demographic and environmental stochasticities, which are exarcebated in management decisions by the uncertainty regarding the choice of an appropriate model to describe system dynamics. Moreover, demand and supply analysis often indicates the presence of instabilities and multiple equilibria, which may lead to management problems that are intensified by uncertainty on the evolution of the resource stock. In this paper the fishery management problem is used as an example to explore the potential of robust optimal control, where the objective is to choose a harvesting rule that will work under a range of admissible specifications for the stock-recruitment equation. The paper derives robust harvesting rules leading to a unique equilibrium, which could be helpful in the design of policy instruments such as robust quota systems.

     

Threshold uncertainty in the private-information subscription game

We introduce threshold uncertainty, à la Nitzan and Romano (1990), into a private-values model of voluntary provision of a discrete public good. Players are allowed to make any level of contribution toward funding the good, which is provided if the cost threshold is reached. Otherwise, contributions are refunded. Conditions ensuring existence and uniqueness of a Bayesian equilibrium are established. Further restricting the threshold uncertainty to a uniform distribution, we show the equilibrium strategies are very simple, even allowing for any number of players with asymmetric distributions of values. Comparative statics with respect to changes in players' distributions are derived, allowing changes in both the intensity and the dispersion of values. For example, increased uncertainty, in the sense of mean-preserving spreads of players' distributions of values, increases equilibrium contributions. Finally, we show the equilibrium is interim incentive inefficient. The sharpness of our results greatly contrasts with the more qualified insights of earlier private-values models with known cost threshold, which relied on there being two symmetric players and generally exhibited multiple equilibria.     

The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition

Abstract. We analyze the Nash equilibria of a standard Bertrand model. We show that in addition to the marginal-cost pricing equilibrium there is a possibility for mixed-strategy equilibria yielding positive profit levels. We characterize these equilibria and find that having unbounded revenues is the necessary and sufficient condition for their existence. Hence, we demonstrate that under realistic assumptions the only equilibrium is marginal-cost pricing.     

Income distribution and equilibrium multiplicity in a stigma-based model of tax evasion

This paper incorporates continuous income distribution into the stigma-based model of tax compliance. The paper investigates the effect of income distribution on the existence of multiple equilibria, and characterizes the conditions under which multiple equilibria emerge. Precisely, multiple equilibria exist if taxpayer incomes are sufficiently homogeneous, because the ‘social coordination effect’ dominates the ‘individual characteristics effect’. Numerical simulations show that the main proposition is robust to allowing two-step audit policies on the part of the tax agency, under the presumption that the best (or good) equilibrium is selected whenever there are multiple equilibria. As a byproduct, the effect of various forms of tax reforms on the optimal two-step audit policy, the equilibrium compliance, and fiscal revenue is analyzed.     

Bayesian games with unawareness and unawareness perfection

Applying unawareness belief structures introduced in Heifetz et al. (Games Econ Behav 77:100–121, 2013a), we develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower awareness levels. We apply Bayesian games with unawareness to investigate the robustness of equilibria to uncertainty about opponents’ awareness of actions. We show that a Nash equilibrium of a strategic game is robust to unawareness of actions if and only if it is not weakly dominated. Finally, we discuss the relationship between standard Bayesian games and Bayesian games with unawareness.