We study elections with three candidates under plurality voting. A candidate is a Condorcet loser if the majority of the voters place that candidate at the bottom of their preference rankings. We first show that a Condorcet loser might win the election in a three-way race. Next we introduce to the model an endorser who has private information about the true probability distribution of the preferences of the voters. Observable endorsements facilitate coordination among voters who may otherwise split their votes and lead to the victory of the condorcet loser. When the endorser has an ideological bias towards one of the candidates, the coordination impact of endorsements remains unaltered, moreover the endorser successfully manipulates the outcome of the election in favor of his bias, even if his ideological bias is known by the voters. The results are true for any endorsement cost and any magnitude of bias as long as the electorate is large enough.

We model a long-run relationship as an infinitely repeated game played by two equally patient agents. In each period, the agents play an extensive-form game of perfect information. There is incomplete information about the type of player 1 while player 2’s type is commonly known. We show that a sufficiently patient player 1 can leverage player 2’s uncertainty about his type to secure his highest payoff in any perfect Bayesian equilibrium of the repeated game.

We study a class of moral hazard games between a long lived seller and an infinite sequence of buyers. We assume that buyers cannot observe past signals. To facilitate the analysis of applications such as online auctions (e.g. eBay), online shopping search engines (e.g. BizRate.com) and consumer reports, we assume that a central mechanism observes all past signals, and makes public announcements every period. The set of announcements and the mapping from observed signals to the set of announcements is called a rating system. We show that, absent reputation effects, information censoring cannot improve attainable payoffs. However, if there is an initial probability that the seller is a commitment type that plays a particular strategy every period, then there exists a rating system and an equilibrium of the resulting game such that, the expected present discounted payoff of the seller is almost his Stackelberg payoff after every history. This is in contrast to Cripps, Mailath and Samuelson (2004), where it is shown that reputation effects do not last forever in such games if buyers can observe all past signals. We also construct rating systems that increase payoffs of almost all buyers, while decreasing the sellers payoff.

We study the impact of unobservable replacements on the sustainability of reputation e¤ects in frequently repeated games played by a long run player facing a sequence of short run players. At the beginning of every period the long-run player is replaced with a new long run player with probability (1-λ) ∈ (0,1). The new long run player is either a commitment type who plays the same strategy in every period when he is in the game, or a normal type. The Long run player’s choice of stage game strategy is imperfectly observed by the short run players. We show that the long run player’s payo¤, in any Nash equilibrium, is bounded below by what he could get by committing to his most favorite commitment type strategy after every history of the game, even as his rate of impatience (1-δ) vanishes at the same rate as his replacement probability. Hence arbitrarily infrequent replacements are su¢ cient to prevent reputations and their e¤ects from disappearing when the stage game is played frequently enough.

Cripps et al. (2005) conjectured that in an infinitely repeated game with two equally patient players, if there is positive probability that the players could be Stackelberg types, then equilibrium behavior would resemble a war of attrition, i.e., a two-sided reputation result would hold. In this note we show that this conjecture is indeed true for a wide set of stage games for which the one-sided reputation result of Atakan and Ekmekci (2008) holds.

Previous work shows that reputation results may fail in repeated games between two long-run players with equal discount factors. We restrict attention to an infinitely repeated game where two players with equal discount factors play a simultaneous move stage game where actions of player 2 are imperfectly observed. The set of commitment types for player 1 is taken as any (countable) set of infinite automata. In this context, for a restricted class of stage games, we provide a one sided reputation result. If player 1 is a particular commitment type with positive probability and player 2's actions are imperfectly observed, then player 1 receives his highest payoff, compatible with individual rationality, in any Bayes-Nash equilibria, as agents become patient.

We study the equilibrium payoffs of a long-run player who plays a fixed-stage game of imperfect public monitoring against an infinite sequence of opponents each of whom plays only once. We show that for any δ < 1, there exists an η > 0 such that if in the repeated game where player 1's discount factor is δ and the probability with which she is a commitment type is less than η, long-run player's any equilibrium payoff is close to some equilibrium payoff in the complete information version of the repeated game. This means that under imperfect public monitoring, introducing arbitrarily small incomplete information cannot open the possibility of equilibrium payoffs for the long-run player that are far away from the complete information equilibrium payoff set.

In a two-sided search market agents are paired to bargain over a unit surplus. The matching market serves as an endogenous outside option for agents in a bargaining relationship. Behavioral agents are (strategically inflexible) commitment types that demand a constant portion of the unit surplus. The steady state frequency of behavioral types in the market is determined in equilibrium. We show, even if behavioral types are negligible, they substantially effect the terms of trade and efficiency. In an unbalanced market where the entering flow of one side is short, bargaining follows equilibrium play in a bargaining game with one-sided reputation, the terms of trade are determined by the commitment types on the short side, and commitment types improve efficiency. In a balanced market where the entering flows of the two sides are equal, bargaining follows equilibrium play in a bargaining game with two-sided reputation and commitment types cause inefficiency. An inefficient equilibrium with persistent delays and break-ups is constructed. The magnitude of inefficiency is determined by the inflexible demands of the commitment types and is independent of the fraction of the commitment types entering the market.