Repeated Elections with Asymmetric Information

An infinite sequence of elections with no term limits is modelled. In each period a challenger with privately known preferences is randomly drawn from the electorate to run against the incumbent, and the winner chooses a policy outcome in a one-dimensional issue space. One theorem is that there exists an equilibrium in which the median voter is decisive: an incumbent wins re-election if and only if his most recent policy choice gives the median voter a payoff at least as high as he would expect from a challenger. The equilibrium is symmetric, stationary, and the behavior of voters is consistent with both retrospective and prospective voting. A second theorem is that, in fact, it is the only equilibrium possessing the latter four conditions — decisiveness of the median voter is implied by them.     

Repeated Bargaining with Persistent Private Information

The paper analyses repeated contract negotiations involving the same buyer and seller where the contracts are linked because the buyer has persistent (but not full y permanent) private information. The size of the surplus being divided is specified as a two-state Markov chain with transitions that are synchronized with contract negotiation dates. Equilibrium involves information cycles triggered by the success or failure of aggressive demands made by the seller. Because there is persistence in the Markov chain generating the surplus, a successful demand induces the seller to make another aggressive demand in the next negotiation, since the buyer's acceptance reveals that the current surplus is large. Rejection of an aggressive demand, on the other hand, leads the seller to be pessimistic about the size of the surplus in the next contract, so the seller makes a "soft" offer that is sure to be accepted. Then, after several such offers have been accepted, the seller is optimistic enough to again make an aggressive demand, creating an information cycle. An interesting feature of this cycle is that the soft price is not constant, but declines as the cycle continues, so as to offset the buyer's option value of re-starting the cycle when the current state is bad. An explicit mapping is given for the relationship between the basic parameters and the equilibrium prices and quantities; in particular, there is a closed-form solution for the threshold belief that makes the seller indifferent between hard and soft offers.     

Contests with rank-order spillovers

This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player??s strategy generates direct or indirect affine ??spillover?? effects that depend on the rank-order of her decision variable. These effects arise in natural interpretations of a number of important economic environments, as well as in classic contests adapted to recent experimental and behavioral models where individuals exhibit inequality aversion or regret. We provide the closed-form solution for the symmetric Nash equilibria of this class of games, and show how it can be used to directly solve for equilibrium behavior in auctions, pricing games, tournaments, R&D races, models of litigation, and a host of other contests.     

Contests with size effects

In this paper we analyze the structure of contest equilibria with a variable number of individuals. First we analyze a situation where the total prize depends on the number of agents and where every single agent faces opportunity costs of investing in the contest. Second we analyze a situation where the agents face a trade-off between productive and appropriative investments. Here, the number of agents may also influence the productivity of productive investments. It turns out that both types of contests may lead to opposing results concerning the optimal number of individuals depending on the strength of size effects. Whereas in the former case individual utility is u-shaped when the number of agents increases, the opposite holds true for the latter case. We discuss the implications of our findings for the case of anarchic societies and market competition.     

Contests with Multi-tasking*

The standard contest model in which participants compete in a single dimension is well understood and documented. Multi‐dimension extensions are possible but are liable to increase the complexity of the contest structure, mitigating one of its main advantages: simplicity. In this paper we propose an extension in which competition ensues in several dimensions, and a competitor that wins a certain number of these is awarded a prize. The amount of information needed to run the contest is hence limited to the number of dimensions won by each player. We look at the design of this contest from the point of view of maximising effort in the contest (per dimension and totally), and show that there will be a tendency to run small contests with few dimensions. The standard Tullock model and its results are encompassed by our framework.     

Contests with limited resources

Many interesting phenomena (electoral competition, R&D races, lobbying) are instances of multiple simultaneous contests with unconditional commitment of limited resources. Specifically, the following game is analyzed. Two players compete in a number of simultaneous contests. The players have limited resources (budgets) and must decide how to allocate these to the different contests. In each contest the player who expends more resources than his adversary wins a corresponding prize. Mixed-strategy equilibria are characterized in the case of identical values and budgets and the connections with the classical Blotto game are analyzed.     

On the Existence and Uniqueness of Pure-Strategy Nash Equilibrium in Asymmetric Rent-Seeking Contests

There can be three types of heterogeneity among players in a rent‐seeking contest. First, effectiveness of player's effort on the winning probabilities may differ among players. Secondly, players may evaluate the rent or prize of the rent‐seeking contest differently. Thirdly, players may face different financial constraints. This article proves under standard assumptions in the literature that there exists a unique pure‐strategy Nash equilibrium in a general asymmetric rent‐seeking contest with these three types of heterogeneity among players.     

Asymmetric Information and Annuities

The standard Rothschild and Stiglitz (1976) and Wilson (1977) analysis of adverse selection economies is extended to a particular model of annuity market which features both elements of moral hazard and adverse selection. Individuals are heterogeneous with respect to time preferences and they make investments in health care that affect their survival probabilities. The main case considered is that where both preferences and investments (and hence the endogenous survival probabilities) are unobserved. Thus, the model captures a further source of inefficiency that is particular to annuity market: an endogenous correlation between the desire for annuities and the survival probabilities. The basic insights of Wilson (1977) —as worked out by Eckstein, Eichenbaum and Peled (1985) —are worth also in this new setting. When the equilibrium is separating, the government intervention may yield Pareto improvements. If the equilibrium is pooling, the government intervention may improve the well‐being of individuals affected by the inefficiencies and the negative externalities caused by the asymmetric information.     

A Model of Product Recalls with Asymmetric Information

This paper presents a model of involuntary product recall in which a firm has private information on its ability to produce safety. The ex post regulation of safety is motivated through a parametric imperfection in the product liability system which results in a firm under internalizing expected liability expenses. We treat the problem as one of mechanism design, where the regulator designs a recall procedure. This framework illuminates the point that recall is an interesting blend of ex ante and ex post regulation. We characterize a perfect recall procedure, contrast this with real world imperfect procedures, and study the interaction of the recall and the liability systems. Further, we analyze the interaction between optimal recall policy and product market structure.     

Contests with size effects through costs

Eggert and Kolmar [Eggert, W., Kolmar, M., in press. Contests with size effects. European Journal of Political Economy.] examine the effects of group size on individual and aggregate payoffs in contests where prizes increase in the number of players. In a reconsideration of their paper, this note examines contests in which the unit cost of effort decreases in the number of players. In contests for fixed prizes, an increase in the number of players decreases individual and aggregate payoffs. In contests in which players face a trade-off between appropriative and productive investments, an increase in the number of players decreases individual payoffs while increasing aggregate payoffs.     

Merging, Reputation, and Repeated Games with Incomplete Information

We relate and unify several results that appeared in the following domains: merging of probabilities, perturbed games and reputation phenomena, and repeated games with incomplete information. Journal of Economic Literature Classification Numbers: C72, D83.     

Contests with spying: A comment

The subject of the following comment is a paper by Baik and Shogren which has been published in this journal (Vol. 11, No. 3 (1995) pp. 441–451). In their game-theoretic model, Baik and Shogren connect the informational states of the agents in a way which leads to inconsistencies.     

Hybrid Contests

This paper examines hybrid contests where participants commit two types of resources to improve their probability of winning the prize. The first type is forfeited ex ante, before the prize is allocated, by winners and losers alike, while the second is committed ex ante by all contenders but expended ex post, after the prize is allocated, and only by the contestant that wins the prize. The model yields a number of interesting results. Among them is the finding that, as the number of contestants increases, the ex ante expenditures of individual contestants decrease while the ex post expenditure increases. Even more interesting, the total of the ex ante and ex post expenditures by the contenders in a hybrid contest may decrease with the number of competitors. The study also finds that there is no rent overdissipation, and compares the total expenditures in the contest and “all‐pay” allocation mechanisms.     

Tax Rate Harmonization,Renegotiation, and Asymmetric Tax Competition for Profits with Repeated Interaction

This paper analyzes a model of corporate tax competition with repeated interaction and with strategic use of profit shifting within multinationals. We show that international tax coordination is more likely to prevail if the degree of asymmetry in terms of productivity differences between countries is smaller, or if concealment costs of profit shifting are larger when the tax authorities adopt grim‐trigger strategies. Allowing for renegotiation in the tax harmonization process requires more patient tax authorities to implement tax harmonization as a weakly renegotiation‐proof equilibrium. In this case, we find somewhat paradoxical situations where higher costs of profit shifting make tax harmonization less sustainable.     

Market Selection and Asymmetric Information

We consider a dynamic general equilibrium asset pricing model with heterogeneous agents and asymmetric information. We show how agents' different methods of gathering information affect their chances of survival in the market depending upon the nature of the information and the level of noise in the economy.     

Multidimensional Bargaining Under Asymmetric Information

A buyer with private information regarding marginal valuation bargains with a seller to determine price and quantity of trade. Depending on parameter values, a high‐valuation buyer wants either to reveal information to create value or to conceal it to capture value. In the first case, equilibrium trades are efficient. In the second case, the low‐valuation buyer purchases less than her efficient quantity, and there can be a one‐period delay in trade. The quantity distortion is the only inefficiency that persists when time between offers approaches zero. There exist equilibria that are independent of the seller's prior beliefs.     

A Property of Nash Equilibria in Repeated Games with Incomplete Information

We consider two-person non-zero-sum infinitely repeated games with lack of information on one side. The characterization of Nash equilibrium payoffs obtained by Hart allows for complex strategies, which are actually required by some equilibrium payoffs in some games. We show that appropriate one-shot public communication mechanisms make Nash equilibrium payoffs achievable by means of simple strategies. Furthermore, these mechanisms satisfy a notion of self-fulfillment.Journal of Economic LiteratureClassification Numbers: D82, C72.     

Contests with a stochastic number of players

We study Tullock's (1980) n-player contest when each player has an independent probability 0 < p 1 of participating. A unique symmetric equilibrium is found for any n and p and its properties are analyzed. In particular, we show that for a fixed n > 2 individual equilibrium spending as a function of p is single-peaked and satisfies a single-crossing property for any two different numbers of potential players. However, total equilibrium spending is monotonically increasing in p and n. We also demonstrate that ex-post over-dissipation is a feature of the pure-strategy equilibrium in our model. It turns out that if the contest designer can strategically decide whether to reveal the actual number of participating players or not, then the actual number of participants is always revealed.     

Mispricing of Risk in Sovereign Bond Markets with Asymmetric Information

The likelihood that a government will repay its sovereign debt depends both on the amount of debt it issues and on the government's future ability to repay. Whilst the former is publicly observable, the government may have more information about the latter than investors. This paper shows that this asymmetric information problem impairs the market's ability to differentiate economies according to their fiscal sustainability, and can lead to a disconnect between bond prices and default risk. The model can help rationalise the behaviour of Eurozone bond prices prior to the recent European sovereign debt crisis.