Cost-sharing in directed networks: Experimental study of equilibrium choice and system dynamics

This study reports the results of an experiment on directed networks with positive externalities induced by cost-sharing. Subjects participated in a network game in which they had to choose between private and public transportations. If a player chose public transportation, then she shared the travel cost equally with other players making the same choice, whereas if she chose private transportation, then her travel cost was fixed. Travel costs on the private route were manipulated across the two experimental conditions. In one condition, these costs were homogeneous among players; in the other condition, they were heterogeneous among players and only privately known. We found that half (none) of the player groups in the homogeneous (heterogeneous) condition converged toward the efficient equilibrium. Examination of the system dynamics shows that convergence toward efficiency was facilitated by: (1) the existence of an intermediate equilibrium choice; and (2) strategic teaching by which a farsighted player chooses strategies with poor short-term payoff in order to shift group decisions to the efficient equilibrium and thereby increase her own long-term benefit.     

Winner’s effort maximization in large contests

We investigate the temporal structure that maximizes the winner’s effort in large homogeneous contests. We find that the winner’s effort ranges from a lower bound of 0 to an upper bound of one third of the value of the prize, depending on the temporal structure; the upper (lower) bound is approached with an infinite number of players playing sequentially (simultaneously) in the first periods (period). Nevertheless, when the number of players is large but finite, we show that winner’s effort is maximized when all players play sequentially except in the very last period and that, within the family of such optimal temporal structures, more players play simultaneously in the very last period than sequentially in all other periods. Furthermore, out of all players, the percentage of those playing simultaneously in the very last period goes to 100% as the number of players grows larger and larger.     

Observing each other’s observations in a Bayesian coordination game

We study a Bayesian coordination game where agents receive private information on the game’s payoff structure. In addition, agents receive private signals that inform them of each other’s private information. We show, that once agents possess these different types of information, there exists a coordination game in the evaluation of this information. Even though the precisions of both signal types are exogenous, the precision with which agents forecast each other’s actions in equilibrium turns out to be endogenous. As a consequence, there exist multiple equilibria which differ with regard to the way that agents weight their private information to forecast each other’s actions.     

Sad-Loser contests

We consider asymmetric winner-reimbursed contests. It turns out that such contests (Sad-Loser) have multiple internal pure-strategy equilibria (where at least two players are active). We describe all equilibria and discuss their properties. In particular, we find (1) that an active player is indifferent among all her non-negative choices and her expected payoff is zero in any internal equilibrium, (2) that a higher-value (stronger) player always spends less than a lower-value (weaker) player and therefore always has a lower chance to win a Sad-Loser contest in any internal equilibrium, and (3) a sufficient condition for a net total spending to be higher in a Sad-Loser contest than in the corresponding asymmetric contest.     

Can learning cause shorter delays in reaching agreements?

This paper uses a continuous-time war of attrition model to investigate how learning about private payoffs affects delays in reaching agreement. At each point in time, players may receive a private Poisson signal that completely reveals the concession payoff to be high (good-news learning) or low (bad-news learning). In the good-news model, the expected delay is always non-monotonic in the learning rate: an increase in the learning rate prolongs delay in agreement if the learning rate is sufficiently low. In the bad-news model, numerical examples suggest learning prolongs delay as well.     

Do tournaments solve the adverse selection problem?

This paper provides a solution to a puzzle in the analysis of tournaments, that of why there is no agent discrimination or differential contracting in certain business practice settings. The paper examines the problem of a principal contracting with multiple agents whose activities are subject to common shocks. The presence of common shocks invites the use of relative performance evaluation to minimize the costs of moral hazard. But, in the additional presence of adverse selection, the analysis shows that there may be no need for ex ante screening through menus of offers. This is so because the principal becomes better informed ex post about agent types, via the realization of common uncertainty, and can effectively penalize or reward the agents ex post. Thus, unlike the standard adverse selection problem without common uncertainty where the principal always benefits from ex ante screening, it is shown that ex post sorting through relative performance evaluation reduces the scope for ex ante screening through menus, and can eliminate it completely if agents are known to not be very heterogeneous. This is consistent with observed practice in industries where the primary compensation mechanism is a cardinal tournament which is uniform among employees. The analysis connotes that by using relative instead of absolute performance measures, firms with employees who are not substantially heterogeneous not only can alleviate the agency problem, but there is also no need to extract the agents' ex ante private information about their innate abilities via a screening menu.     

Two-stage elimination contests with optimal head starts

We study two-stage elimination Tullock contests. In the first stage all the players compete against each other; then some advance to the second stage while the others are removed. The finalists compete against each other in the second stage, and one of them wins the prize. To maximize the expected total effort, the designer can give a head start to the winner of the first stage when he competes against the other finalists in the second stage. We show that the optimal head start, independent of the number of finalists, always increases the players’ expected total effort. We also show how the number of players and finalists affect the value of the optimal head start.     

Compensating the dead

An early death is, undoubtedly, a serious disadvantage. However, the compensation of short-lived individuals has remained so far largely unexplored, probably because it appears infeasible. Indeed, short-lived agents can hardly be identified ex ante, and cannot be compensated ex post. We argue that, despite those difficulties, a compensation can be carried out by encouraging early consumption in the life cycle. In a model with heterogeneous preferences and longevities, we show how a specific social criterion can be derived from intuitive principles, and we study the corresponding optimal policy under various informational assumptions.     

What restrictions do Bayesian games impose on the value of information?

In a Bayesian game players play an unknown game. Before the game starts some players may receive a signal regarding the specific game actually played. Typically, information structures that determine different signals, induce different equilibrium payoffs. In two-person zero-sum games the equilibrium payoff measures the value of the particular information structure which induces it. We pose a question as to what restrictions Bayesian games impose on the value of information. We provide answers for two kinds of information structures: symmetric, where both players are equally informed, and one-sided, where only one player is informed.     

Die Theorie globaler Spiele: Private Information als Mittel zur Vermeidung multipler Gleichgewichte

Investment decisions with network effects, refinancing illiquid firms, and speculative attacks are typical examples for coordination games with multiple equilibria. By introducing private information about payoff relevant parameters, the theory of global games embeds such coordination games in a stochastic environment, in which the game may have a unique equilibrium. This paper provides an introduction to the theory of global games and shows that it delivers a unique equilibrium if private information is sufficiently precise, while public information may lead to equilibria with self-fulfilling beliefs. This implies some criteria for optimal mechanisms of information dissemination. For example, a well-informed central bank can minimize the prior probability of currency crises by committing to provide information to private actors with small idiosyncratic errors.     

Repeated two-person zero-sum games with unequal discounting and private monitoring

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.     

Growth,speculation and sprawl in a monocentric city

An economic theory of sprawl in a growing, monocentric city is presented. Where decision-makers have perfect foresight, leapfrog development and discontinuous land-rent functions may occur and be efficient in both an ex post and ex ante sense. Where the extent of future growth is uncertain, decision-makers become speculators and the spatial pattern of development is more complicated. Ex post inefficiency generally occurs.     

The maturity structure of term premia with time-varying expected returns

This paper analyzes the maturity structure of term premia using McCulloch’s US Treasury yield curve data from 1953–91, allowing expected returns to vary across time. One, 3, 6, and 12 month holding period returns on maturities up to 5 years are projected on 3 ex ante variables to compute time-varying expected returns, and simulations are employed to generate distributions of conditionally expected return premia. The likelihood of expected returns monotonically increasing in maturity (as implied by the liquidity preference hypothesis) is relatively high when the yield curve is steep and interest rates are high, and with longer holding periods, but low in other cases. The hypothesis that intermediate maturity bonds have the highest expected returns (a “hump-shaped” maturity-return pattern) around the onset of recessions does not receive much support.     

Efficient Contests

In their seminal contribution, Lazear and Rosen (1981) show that wages based upon rank induce the same efficient effort as incentive‐based reward schemes. They also show that this equivalence result is not robust toward heterogeneity in worker ability, as long as ability is private information because it is not possible to structure contests to simultaneously satisfy self‐selection constraints and first‐best incentives. This paper demonstrates that efficiency can be achieved by a simple modification of the prize scheme in a mixed (heterogenous) contest where contestants learn their type after entry. If contestants know their type before entering the contest, rent extraction becomes an issue. Implications for optimal contest design are also explored. Finally, the relationship between effort maximizing contests and profit maximizing contests are discussed.     

An experiment of social learning with endogenous timing

In this paper, we experimentally investigate a social learning model with endogenous timing. Specifically, we focus on a model, in which two subjects are supposed to make a binary decision. One alternative is a safe action with a fixed payoff, while the other alternative is a risky action. The subjects can make their decisions in three stages. The safe action is reversible, but the risky action is not. A subject who delays his decision can observe the decision of the other subject in the earlier stages, and as a result, acquire more information. We show that players do delay their decisions in order to obtain more information. Furthermore, they delay especially when their private information does not particularly support the risky action. We also find evidence which suggests that risk aversion plays an important role in timing decisions, often leading to ex post inefficient outcomes.     

The political economy of ‘ordered competition’ in European telecoms

This article discusses the current efforts of policymakers to spur development of telecommunications infrastructure. It argues that the policy of ‘ordered competition’, widely implemented in this sector, has formed a highly beneficial environment for major players, who have the ability to influence the regulatory machine. The system protects the status quo, impedes the efficiency of the market process and allows unnecessary public subsidy of the industry's development. The main alternative to this regulatory regime is structural reform of the industry and the formation of a genuinely competitive marketplace which could function without ex ante regulation.     

Optimal contest design under reverse-lottery technology

In this paper, we study effort-maximizing contest design under the “reverse” nested lottery contest model of Fu et al. (2014) — which is the “mirror image” of the conventional nested lottery contest of Clark and Riis (1996). We show that under the reverse-lottery technology, a single-stage winner-take-all grand contest dominates all other feasible designs when the contest is sufficiently noisy. This result is in dramatic contrast to the conventional wisdom on the optimality of multistage elimination contests that is grounded under the conventional nested lottery contest technology in the literature. In the framework of a noisy-performance ranking model, the conventional and reverse models differ only in the noise on players’ performance. Our study therefore reveals the important role that the noise term plays in modeling imperfectly discriminatory contests.     

Social norms,coordination and collaboration in heterogeneous teams

This paper considers the coordinating role of social norms in a heterogeneous team of workers. We define an optimal unit of production as a form of organisation involving several teams and members, with the following properties: (i) a social norm operating to coordinate individual efforts; (ii) a team with heterogeneous skills, enabling generation of synergies. Our model suggests that competences of the best worker are transferred to his or her peers. This collaborative process enhances team efficiency but only if there is an implicit ex ante coordinating device based on social norms that discourage free riding. Copyright © 2008 John Wiley & Sons, Ltd.     

Innovation contests with entry auction

We consider innovation contests for the procurement of an innovation under moral hazard and adverse selection. Innovators have private information about their abilities, and choose unobservable effort in order to produce innovations of random quality. Innovation quality is not contractible. We compare two procurement mechanisms—a fixed prize and a first-price auction. Before the contest, a fixed number of innovators is selected in an entry auction, in order to address the adverse selection problem. We find that–if effort and ability are perfect substitutes–both mechanisms implement the same innovations in symmetric pure-strategy equilibrium, regardless of whether the innovators’ private information is revealed or not. These equilibria are efficient if the procurer is a welfare-maximizer.