Mehmet Ekmekci

Sustainable reputations with rating systems

In a product choice game played 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 finite 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) [5], where it is shown that reputation effects do not last forever in such games if buyers can observe all past signals. We also construct finite rating systems that increase payoffs of almost all buyers, while decreasing the seller[modifier letter apostrophe]s payoff.

A two Sided Reputation Result with Long Run Players

We establish reputation results, under two sided incomplete information, for a class of repeated games. We consider a repeated game that satisfies the assumptions of either Atakan and Ekmekci (2012) [3] or Cripps et al. (2005) [6] and we assume that both players are Stackelberg types with positive probability. If the stage game is not a common interest game, then equilibrium play converges to the unique equilibrium of a continuous time war of attrition as the stage game is repeated arbitrarily frequently. Alternatively, if the stage game is a common-interest game, then the playersʼ equilibrium payoffs converge to their highest payoffs as the stage game is repeated arbitrarily frequently.

Impermanent types and permanent reputations

We study the impact of unobservable stochastic replacements for the long-run player in the classical reputation model with a long-run player and a series of short-run players. We provide explicit lower bounds on the Nash equilibrium payoffs of a long-run player, both ex-ante and following any positive probability history. Under general conditions on the convergence rates of the discount factor to one and of the rate of replacement to zero, both bounds converge to the Stackelberg payoff if the type space is sufficiently rich. These limiting conditions hold in particular if the game is played very frequently.

Manipulation through political endorsements

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.

Information in tender offers with a large shareholder

We study tender offers for a firm which is owned by one large shareholder who holds less than half of the total shares, and many small shareholders who each hold a unit share. Each shareholder is privately informed, yet uncertain, about the raider’s ability to improve the value of the firm, whereas the raider is unin- formed. In the benchmark model of complete information, the raider is unable to make a profit. As shown in Marquez and Y?lmaz (2008), the same obtains when the raider is facing only privately informed small shareholders. We show, however, that the combination of private information on the side of shareholders and the presence of a large shareholder can facilitate profitable takeovers. More precisely, for any given information structure, the raider can make a profit if the large shareholder holds a sufficiently large stake in the company. In the unique equilibrium outcome, neither the probability of a successful takeover nor the quilibrium price offer depends on the large shareholder’s information. Therefore, the large shareholder’s information is not reflected in the price. When the equilibrium price offer is positive, the large shareholder tenders all of his shares regardless of his information. Finally, we show that the same type of equilibria arise when there are several large shareholders, as long as their total stake in the company is smaller than one-half. Keywords: takeovers, tender offers, lemons problem, large shareholder. JEL Classification Numbers: D82, G34.

Integrating Schools for Centralized Admissions

As school districts integrate charter schools for centralized admissions in Denver, New Orleans, Newark and Washington D.C., some charter schools have stayed out of the system. This is counterintuitive as centralized clearinghouses are deemed beneficial to schools as well as students. We provide a new framework to study the incentives of a school to join a clearinghouse and we show that each school prefers to remain out of the system when others join it for the standard mechanisms used in practice for student assignment. Therefore, our analysis provides an explanation of why some charter schools have evaded the clearinghouse. To overcome this issue, we propose two schemes that can be used by policymakers to incentivize schools to join the system, which achieves the desired integration of schools to the clearinghouse.