Contests with Alternative Public‐Good Prizes

I study contests in which a society of players compete, by expending irreversible effort, over which one of alternative prizes should be awarded to them by the decision maker. The prizes are public goods and/or public bads for the players. The players choose their effort levels simultaneously and independently. I define each player's valuation spread as the difference between his valuations for the two public‐good/public‐bad prizes. I establish that the players' equilibrium effort levels depend solely on their valuation spreads, and that the players never expend positive effort for both prizes in equilibrium. Further, I establish that in equilibrium only players with the widest positive valuation spread and players with the widest negative valuation spread expend positive effort. Finally, I establish that the equilibrium effort level expended for each prize and the equilibrium total effort level are determined only by the widest positive valuation spread and the widest negative valuation spread.     

Lotteries vs. All‐Pay Auctions in Fair and Biased Contests

The form of contests for a single fixed prize can be determined by a designer who maximizes the contestants' efforts. This article establishes that, under common knowledge of the two asymmetric contestants' prize valuations, a fair Tullock‐type endogenously determined lottery is always superior to an all‐pay‐auction; it yields larger expected efforts (revenues) for the contest designer. If the contest can be unfair (structural discrimination is allowed), then the designer's payoff under the optimal lottery is equal to his expected payoff under the optimal all‐pay auction.     

DISCRIMINATION IN A MODEL OF CONTESTS WITH INCOMPLETE INFORMATION ABOUT ABILITY

We study contests with private information and identical contestants, where contestants' efforts and innate abilities generate output of varying qualities. The designer's revenue depends on the quality of the output, and she offers a reward to the contestant achieving the highest quality. We characterize the equilibrium behavior, outcomes, and payoffs for both nondiscriminatory and discriminatory (where the reward is contestant‐dependent) contests. We derive conditions under which the designer obtains a larger payoff when using a discriminatory contest and describe settings, where these conditions are satisfied.     

An Eaton–Kortum model of trade and growth

We combine a multi‐country, continuum‐good Ricardian model of Eaton and Kortum (2002) with a multi‐country AK model of Acemoglu and Ventura (2002) to examine how trade liberalization affects countries' growth rates and extensive margins of trade over time. Focusing on the three‐country case, we obtain three main results. First, a permanent fall in any trade cost raises the balanced growth rate. Second, trade liberalization increases the liberalizing countries' long‐run fractions of exported varieties to all destinations. Third, the long‐run effects of trade liberalization are different from its short‐run effects, which can reverse the welfare implications of the static Eaton–Kortum model.     

Group Contests with Internal Conflict and Power Asymmetry

We investigate simultaneous inter‐ and intra‐group conflict in the shadow of within‐group power asymmetry and complementarity in members' group‐conflict efforts. A more symmetric group faces a higher degree of internal conflict, and might expend more effort in external conflict when the group‐conflict effort technology is highly complementary. Depending on the degree of complementarity, the stronger player's relative contribution to external conflict might be higher in a more asymmetric group and, as a result, it is possible for the weaker player to earn a higher payoff. In the absence of any complementarity, the rent‐dissipation is non‐monotonic with the within‐group power asymmetry.     

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.     

INDUCING VARIETY: A THEORY OF INNOVATION CONTESTS

This article analyzes the design of innovation contests when the quality of an innovation depends on the research approach, but the best approach is unknown. Inducing a variety of research approaches generates an option value. We show that suitable contests can induce such variety. The buyer‐optimal contest is a bonus tournament, where suppliers can choose only between a low bid and a high bid. This contest implements the socially optimal variety for a suitable parameter range. Finally, we compare the optimal contest to scoring auctions and fixed‐prize tournaments.     

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.     

Long‐run Lunacy,Short‐run Sanity: a Simple Model of Trade with Labor Market Turnover*

It is often argued that international trade is all about long‐run relationships. In this paper, we argue that this view is flawed when factor markets are characterized by turnover. Toward that end, we provide a simple dynamic model of trade with labor market turnover and show that the relationship between the economy's short‐run and long‐run behavior is more complex than in traditional trade models. For example, in the short run, the economy may produce outside of its long‐run frontier. We show that focusing on long‐run relationships can lead one to draw faulty policy conclusions, while focusing on its short‐run behavior restores sanity. The implication is that in the presence of factor market turnover, international trade issues can only be understood by studying the entire dynamic path of the economy. Long‐run relationships should be ignored.     

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.     

The Impact of Payoff Interdependence on Trust and Trustworthiness

Abstract. In one‐shot investment games where each player's payoff is a convex combination of own and other's profit, we measure trust by the amount given to the trustee and trustworthiness by the amount returned to the trustor by the trustee. Does the degree of payoff interdependence increase both trust and trustworthiness or one but not the other or neither of them? According to our experimental data, trust remains unaffected by the extent of interdependence whereas trustworthiness reacts positively to it.     

INCOMPLETE INFORMATION GAMES WITH MULTIPLE PRIORS*

We present a model of incomplete information games, where each player is endowed with a set of priors. Upon arrival of private information, it is assumed that each player “updates” his set of priors to a set of posterior beliefs, and then evaluates his actions by the most pessimistic posterior beliefs. So each player's preferences may exhibit aversion to ambiguity or uncertainty. We define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players’ views on uncertainty about the environment affect the strategic outcomes.     

A NOTE ON NEGATIVE ELECTORAL ADVERTISING: DENIGRATING CHARACTER VS. PORTRAYING EXTREMISM

In this expository note, we extend the model of Harrington and Hess (1996) by incorporating valence advertising. There is a two‐candidate electoral contest. Candidates inherit a certain position indicating their ideological platform in an unidimensional policy space. They also inherit a certain valence index which is a comprehensive term for personal traits that are desirable to all voters such as integrity. The candidates can subsequently influence these using negative advertising with regard to both ideological and valence factors. We find that when the available resources are sufficiently small and certain reasonable assumptions are fulfilled, the candidate with the higher initial valence index will run a relatively personal campaign while the candidate with the lower initial valence index will run an ideological campaign.     

Multi-activity contests

In many contests, players can influence their chances of winning through multiple activities or “arms”. We develop a model of multi-armed contests and axiomatize its contest success function. We then analyze the outcomes of the multi-armed contest and the effects of allowing or restricting arms. Restricting an arm increases total effort directed to other arms if and only if restricting the arm balances the contest. Restricting an arm tends to reduce rent dissipation because it reduces the discriminatory power of the contest. But it also tends to increase rent dissipation if it balances the contest. Less rent is dissipated if an arm is restricted as long as no player is excessively stronger than the other with that arm. If players are sufficiently symmetric in an arm, both players are better off if that arm is restricted. Nevertheless, players cannot agree to restrict the arm if their costs of using the arm are sufficiently low.     

Equilibrium opacity in ultimatum‐offer bargaining

We consider ultimatum bargaining between a seller and a buyer of an asset. They know each other's valuation of the asset. Both can defer their decisions to delegates. These delegates have opaque preferences. Seller and buyer choose the opacity of their delegate. For the seller's delegate this choice is restricted to a random reservation price drawn from the set of symmetric two‐point distributions around the seller's true reservation price. The opacity choice of the buyer's delegate is restricted to a random willingness‐to‐pay drawn from the set of symmetric two‐point distribution around the buyer's true willingness‐to‐pay. We characterize the set of pure‐strategy equilibria in their delegation choices. Multiple equilibria arise. Except for two corner solutions, both players will exploit the strategy of opacity. A large set of efficient equilibria exist. For these, opacity choices do not reduce the probability of transacting, but benefit the buyer compared with the no‐delegation equilibrium. We also study the robustness of the results with respect to the player's ability to also resort to a tougher delegate in addition to the opacity choice.     

Asymmetric technologies in contests

I consider a contest between two risk-neutral players over a common-value prize, in which one player has a linear cost-of-effort function and the other a strictly convex cost-of-effort function f. I show that if the value of the prize is above (below) a certain threshold level, then the equilibrium aggregate effort in this contest is larger (smaller) than in a contest in which both players are characterized by the strictly convex cost-of-effort function f, and smaller (larger) than in a contest in which both players are characterized by a linear cost-of-effort function. Therefore, in contrast to the general result in the literature, asymmetry in contests can increase competition.     

MIMICKING THE WINNER LEADS TO WAR: AN EVOLUTIONARY ANALYSIS OF CONFLICT AND COOPERATION*

This note applies an evolutionary analysis to Skaperdas's (1992) static model of conflict and cooperation, in which agents are faced with trade‐offs between joint production and share competition. We adopt the stochastic evolution approach, and assume that each agent occasionally mimics the action of the winner of the stage. In contrast to Skaperdas's results that justify full or partial cooperation in productive activity, the long‐run equilibrium must exhibit total conflict; nobody engages in production at all.     

Gambling in contests

This paper presents a strategic model of risk-taking behavior in contests. Formally, we analyze an n-player winner-take-all contest in which each player decides when to stop a privately observed Brownian motion with drift. A player whose process reaches zero has to stop. The player with the highest stopping point wins. Unlike the explicit cost for a higher stopping time in a war of attrition, here, higher stopping times are riskier, because players can go bankrupt. We derive a closed-form solution of a Nash equilibrium outcome. In equilibrium, highest expected losses occur at an intermediate negative value of the drift.     

Truthtelling in Matching Markets

We analyze a search and matching model with non‐transferable utility and asymmetric information. Randomly paired agents go through an evaluation phase, at the end of which they discover each other's types and choose to match or not. Before deciding to enter this phase, agents can communicate through cheap talk. We provide conditions for this communication to be informative, and we examine how it affects agents' welfare. We show that communication is Pareto‐improving only when the matching is assortative in the absence of communication and left unchanged by information transmission.     

Are property rights enough?Re‐evaluating a big‐bang claim1

We investigate the claim made by proponents of the big‐bang strategy that the establishment of property rights in an economy in transition creates its own demand for the enforcement of laws to protect those rights. Our model contains a government engaging in activities to accomplish objectives that depend on public support for the enforcement of the rule of law and agents who interpret the level of activities of the government as indications of the government's intent to enforce the rule of law. Agents, using the level of government activities as an input to their decisions, choose whether to support the government's objectives. We establish conditions under which the level of activities chosen by the government maximizes its benefits, and simultaneously induces the constituency to support enforcement of the rule of law. These conditions provide a basis for the argument for the implementation of the big‐bang policy. When these conditions do not hold, however, we show that the level of activities that maximizes the government's benefits may have only a minor impact on support for the enforcement of the rule of law. Two characteristics play an important role in these conditions: the initial level of crime and the types of activities the government chooses to undertake. We present examples showing that the initial level of crime has the more dramatic effect on subsequent support for the rule of law.