Facilitating Consumer Learning in Insurance Markets: What Are the Welfare Effects?

We model a monopoly insurance market in which consumers can learn their accident risks at a cost c . We then examine the welfare effects of a policy that reduces c . If c is sufficiently small (c  < c ^*), the optimal contract is such that the consumer gathers information. For c  < c ^*, both the insurer and the consumer benefit from a policy that reduces c further. For c   >  c ^*, marginally reducing c hurts the insurer and weakly benefits the consumer. Finally, a reduction in c that is successful, meaning that the consumer gathers information after the reduction but not before it, can hurt both parties.     

Group efforts when performance is determined by the “best shot”

We investigate the private provision of a public good whose level is determined by the maximum effort made by a group member. Costs of effort are either commonly known or privately known. For symmetric perfect-information games, any number of players may be active and we characterize the unique (mixed-strategy) equilibrium in which active contributors use the same strategy. Increasing the number of active players leads to stochastically lower individual efforts and level of the public good. When information is private, the symmetric equilibrium is in pure strategies. Increasing the number of players yields a pointwise reduction in the equilibrium contribution strategy but an increase in equilibrium payoffs. Comparative statics with respect to costs and levels of risk aversion are derived. Finally, whether information is public or private, equilibria are inefficient—we provide mechanisms that improve efficiency.     

Bayesian Equilibrium in a Public Good Economy

This paper studies the provision of a public good via voluntary contributions in an economy with uncertainty and differential information. Consumers differ in their private information regarding their future endowment as well as in their preferences. Each consumer selects her consumption ex ante, i.e., before knowing the state of nature. Contributions to the provision of the public good are determined ex post, i.e., when the state of nature is realized. Assuming that some normality conditions hold, a Bayesian equilibrium exists. Further, equilibrium is unique, regardless of the number of consumers, when either (1) the information partitions of consumers can be ranked from the finest to the coarsest, or (2) there are only two types of consumers.     

Life insurer performance under the bailout of distressed asset purchases

ABSTRACT

The paper develops a structure-break contingent claim model to examine how government bailout affects a life insurer’s performance (policyholder protection and insurer survival). The distressed assets purchased by the government enhance the optimal insurer interest margin, and policyholder protection. Bailout as such helps the life insurer, implying a higher likelihood of survival in particular when a financial crisis deteriorates seriously, thereby contributing to the stability of the insurance system. In addition, we suggest that low participation of the profit-sharing policy increases insurer survival. This strategic participation effect becomes more significant when the economic state of structural break volatility is increased, and thus, enhancing insurer survival and solving financial problems.     

Incomplete information in rent-seeking contests

We consider a variant of the Tullock lottery contest. Each player’s constant marginal cost of effort is drawn from a potentially different continuous distribution. In order to study the impact of incomplete information, we compare three informational settings to each other; players are either completely informed, privately informed about their own costs, or ignorant of all cost realizations. For the first and the third setting, we determine the unique pure-strategy Nash equilibrium. Under private information, we prove existence of a pure-strategy Bayesian Nash equilibrium and identify a sufficient condition for uniqueness. Assuming that unit cost distributions all have the same mean, we show that under ignorance of all cost realizations ex ante expected aggregate effort is lower than under both private and complete information. Ex ante expected rent dissipation, however, is higher than in the latter settings if we focus on the standard lottery contest and assume costs are all drawn from the same distribution. Between complete and private information, there is neither a general ranking in terms of effort nor in terms of rent dissipation.     

Private value perturbations and informational advantage in common value auctions

We analyze the value of being better informed than one's rival in a two bidder, second price common value auction. Standard models of these auctions do not pin down relative bidding postures, but we show that by adding small amounts of private value information, a unique equilibrium can be restored. Additional common value information affects a bidder's payoff both directly, by increasing his information rent, and indirectly, by shifting the relative bidding posture of his opponent. Although the latter effect need not be positive, we establish broad conditions under which bidders with more information do better than their rivals. We turn to information acquisition and release and show that the desire to influence relative bidding postures can lead sellers to create new information rents (by releasing information privately to only one bidder) and bidders to forego information rents (instead choosing to gather information that a rival already has).     

Multi-stage sequential all-pay auctions

We study multi-stage sequential all-pay contests (auctions) where heterogeneous contestants are privately informed about a parameter (ability) that affects their cost of effort. We characterize the perfect Bayesian equilibrium of these contests and analyze the effect of the number of contestants and their types on the contestants׳ expected highest effort.     

Information Advantage in a Public Good Economy with Multiplicative Structure of Utilities

This paper extends results on information advantage in Cournot oligopoly to a public good economy with uncertainty and private information where the state‐dependent utilities have a multiplicative structure. We show that in a Bayesian–Nash equilibrium where consumers’ contributions are positive in all states of nature, a consumer with superior information is rewarded with a higher ex ante expected utility. Our counter example shows that in the case where one consumer does not contribute, information disadvantage might emerge. Thus, the interiority assumption is essential to obtain our results.     

Characterization and incentive compatibility of Walrasian expectations equilibrium in infinite dimensional commodity spaces

Summary. We consider a differential information economy with infinitely many commodities and analyze the veto power of the grand coalition with respect the ability of blocking non-Walrasian expectations equilibrium allocations. We provide two different Walrasian expectations equilibrium equivalence results. First by perturbing the initial endowments in a precise direction we show that an allocation is a Walrasian expectations equilibrium if and only if it is not privately dominated by the grand coalition. The second characterization deals with the fuzzy veto in the sense of Aubin but within a differential information setting. This second equivalence result provides a different characterization for the Walrasian expectations equilibrium and shows that the grand coalition privately blocks in the sense of Aubin any non Walrasian expectations equilibrium allocation with endowment participation rate arbitrarily close to the total initial endowment participation for every individual. Finally, we show that any no free disposal Walrasian expectations equilibria is coalitional Bayesian incentive compatible. Since the deterministic Arrow-Debreu-McKenzie model is a special case of the differential information economy model, one derives new characterizations of the Walrasian equilibria in economies with infinitely many commodities.Received: 29 October 2003, Revised: 24 February 2004, JEL Classification Numbers: D51, D82, D11. Correspondence to: Emma Moreno-GarcíaThe authors are grateful to an anonymous referee for his/her careful reading and helpful comments and suggestions.C. Hervés and E. Moreno acknowledge support by Research Grant BEC2000-1388-C04-01 (Ministerio de Ciencia y Tecnología and FEDER); and support by the Research Grant SA091/02 (Junta de Castilla y León).     

Socialization and altruism

An important problem in theoretical biology is to explain how altruism can have positive selection value. We model socialization as a costly public good that raises altruism and we study evolution equations for altruistic preferences. Stable cultural (social) equilibria exist in which socialization is supplied privately and property rights exist without civil government. In equilibrium, agents are altruistic in ways not explained by traditional biological theories. The theory essentially formalizes the story in Adam Smith'sTheory of Moral Sentiments.     

A MARKET WITH A SOCIAL CONSUMPTION EXTERNALITY*

We model a spatial market in which the utility of each consumer is affected by the consumers who buy precisely the same product. The marginal contribution of consumers x's purchase on consumer y depends on |x–y|, which declines as |x–y| increases. Such modelling of preferences fits goods that signal a consumer's place in society—clothing styles, automobiles and jewellry are examples. For 2n + 1 firms we find the unique symmetric equilibrium and derive comparative statics on the optimal number of firms, the largest number of firms the market can support, and the behaviour of profits per firm as n increases.     

Optimal Controls for a Large Insurance Under a CEV Model: Based on the Legendre Transform-Dual Method

The purpose of this paper is to consider the optimal proportional reinsurance and investment strategies for an insurance company. The insurer’s surplus process is approximated by a Brownian motion with drift. The insurance company can purchase proportional reinsurance and invest the surplus in a financial market which includes one risk-free asset and one risky asset whose price is modeled by a CEV model. The primary problem is changed to the dual problem by implying Legendre transform. When the objective of the insurance company is to maximize the expected logarithmic utility from terminal wealth, the closed-form expressions for the optimal reinsurance-investment policy which is different to the Merton case to the primal optimal problem are obtained and numerical simulations are provided to demonstrate our results. Moreover, we find an interesting result that risk exposure is non-monotonic in the cost of reinsurance.

     

The measure of blocking coalitions in differential information economies

We provide an evaluation of the measure of privately blocking coalitions in differential information economies. In the case of atomless economies, it is proved that for a Pareto optimal allocation that is not a Walrasian expectations equilibrium, to any symmetric profile there corresponds a ball such that "almost half” of the profiles it contains are privately blocking. Analogous results are proved in the case of finite differential information economies for generalized coalitions and social coalition structures. From a different point of view, the paper can be considered as a contribution showing private core equivalence theorems under restrictions on coalition formation. We thank an anonymous referee for observations and comments improving an earlier version of the present paper.     

Endogenous private information structures

We formally incorporate the option to gather information into a game and thus endogenize the information structure. We ask whether models with exogenous information structures are robust with respect to this endogenization. Any Nash equilibrium of the game with information acquisition induces a Nash equilibrium in the corresponding game with an exogenous structure. We provide sufficient conditions on the structure of the game for which this remains true when ‘Nash’ is replaced by ‘sequential’. We characterize the (sequential) Nash equilibria of games with exogenous information structures that can arise as a (sequential) Nash equilibrium of games with endogenous information acquisition.     

Competitive equilibrium when preferences change over time

Summary. We show the existence of a competitive equilibrium in an economy with many consumers whose preferences may change over time. The demand correspondence of an individual consumer is determined by the set of subgame-perfect equilibrium outcomes in his intrapersonal game. For additively separable preferences with concave period utility functions that are unbounded above, this demand correspondence will satisfy the usual boundary conditions. Whenever consumers can recall their own mixed actions, this correspondence is convex-valued. This ensures the existence of a symmetric competitive equilibrium.Received: 29 July 2004, Revised: 17 November 2004, JEL Classification Numbers: D51, D91, C73. Correspondence to: Thomas MariottiWe thank Michele Piccione for useful comments and suggestions. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

Optimal Contracting with Private Knowledge of Wealth and Ability

We examine the optimal design of contracts when an agent is privately informed about his wealth, his ability, and his effort supply. We find that the agent's wealth and ability act as perfect complements in determining the power of the incentive scheme under which he operates. Only if his ability and his wealth both increase can an agent be assured of operating under a more powerful scheme. Consequently, severe under-utilization of wealth and ability arise in equilibrium.     

Equilibrium selection through incomplete information in coordination games: an experimental study

We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.      

Endogenous residual claimancy by vertical hierarchies

In this note we study a model of vertical hierarchies where the allocation of residual claimancy is endogenous and is determined jointly with production and contractual decisions. We show that the (equilibrium) allocation of residual claimancy may be affected by production externalities across hierarchies in a non-trivial manner. Specifically, although revenue-sharing contracts foster agents’ (non-contractible) surplus enhancing effort, we show that principals dealing with exclusive and privately informed agents might still prefer to retain a share of the surplus from production when dealing with inefficient (high-cost) types. This is because reducing the surplus share of those types reduces the information rent given up to efficient (low-cost) types by means of a ‘generalized competing contracts’ effect.     

Unit Versus Ad Valorem Taxes: The Private Ownership of Monopoly in General Equilibrium

Employing a general equilibrium framework, Blackorby and Murty prove that, with a monopoly and under 100% profit taxation and uniform lump‐sum transfers, the utility possibility sets of economies with unit and ad valorem taxes are identical. This welfare equivalence is in contrast to most previous studies, which demonstrate the superiority of the ad valorem tax in a partial equilibrium framework. In this paper, we relax the assumption of 100% profit taxation and allow the consumers to receive profit incomes from ownership of shares in the monopoly firm. We find that, under certain regularity conditions, for any fixed vector of profit shares, the utility possibility sets of economies with unit and ad valorem taxes are not generally identical. But it does not imply that one completely dominates the other. Rather, the two utility possibility frontiers cross each other. Additionally, employing a standard partial equilibrium welfare analysis, we show that the Marshallian social surpluses resulting from the two tax structures are identical when the government can implement unrestricted transfers.     

Reinterpreting mixed strategy equilibria: a unification of the classical and Bayesian views

We provide a new interpretation of mixed strategy equilibria that incorporates both von Neumann and Morgenstern's classical concealment role of mixing, as well as the more recent Bayesian view originating with Harsanyi. For any two-person game, G, we consider an incomplete information game, in which each player's type is the probability he assigns to the event that his mixed strategy in G is “found out” by his opponent. We show that, generically, any regular equilibrium of G can be approximated by an equilibrium of in which almost every type of each player is strictly optimizing. This leads us to interpret i's equilibrium mixed strategy in G as a combination of deliberate randomization by i together with uncertainty on j's part about which randomization i will employ. We also show that such randomization is not unusual: for example, i's randomization is nondegenerate whenever the support of an equilibrium contains cyclic best replies.