Belief-free equilibria in games with incomplete information

We de ne belief-free equilibria in two-player games with incomplete information as se- quential equilibria for which players' continuation strategies are best-replies, after every history, independently of their beliefs about the state of nature. We characterize a set of payos that includes all belief-free equilibrium payos. Conversely, any payo in the interior of this set is a belief-free equilibrium payorepeated game with incomplete information; Harsanyi doctrine; belief-free equilibria

Belief-free Equilibria in games with incomplete information

In this paper, the authors define belief-free equilibria in two-player games with incomplete information as sequential equilibria for which players’ continuation strategies are best-replies, after every history, independently of their beliefs about the state of nature. They characterize a set of payoffs that includes all belief-free equilibrium payoffs. Conversely, any payoff in the interior of this set is a belief-free equilibrium payoff.game theory; equilibria; information

Linkage principle, Multi-dimensional Signals and Blind Auctions

We compare the seller’s expected revenue in a second price sealed bid auction for a single object in which bidders receive multidimensional signals. Bidders’ valuations for the object depend on their signals and a signal observed privately by the seller. We show in various examples that the seller can be better off not revealing publicly his signal. Hence the linkage principle does not necessarily hold when bidders receive multidimensional signals.Auction Theory; Linkage Principle; Multidimensional Signals; Blind Auctions

Preopening and equilibrium selection

In this paper, the authors introduce a form of pre-play communication that we call "preopening". During the preopening, players announce their tentative actions to be played in the underlying game. Announcements are made using a posting system which is subject to stochastic failures. Posted actions are publicly observable and players payo¤s only depend on the opening outcome, i.e. the action pro…le that is posted at the end of the preopening phase. We show that when the posting failures hit players idiosyncratically all equilibria of the preopening game lead to the same opening outcome that corresponds to the most "sensible" pure Nash equilibrium of the underlying game. By contrast preopening does not operate an equilibrium selection when posting failure hits players simultaneously.Preopening; equilibrium selection; bargaining; cheap talk

Reputation as an Entry Barrier in the Credit Rating Industry

We study competition between an incumbent Credit Rating Agency (CRA) and a sequence of entrant CRAs that are potentially more e¤ective but whose ability in appraising default risk is unproven when they enter the market. We show that free entry competition fails to select the most competent CRA as long as two conditions are met. First, investors and issuers trust the incumbent CRA to provide a sincere, although imperfect, assessment. Second, CRAs cannot charge higher fees for low rating than for high rating. Then, a rather incompetent CRA can dominate the market without concerns about entry. We derive policy implications.Credit Rating, Entry Barrier, Reputation, Credit Constraint, Private Information

Risk aversion and herd behavior in financial markets

We show that differences in investors risk aversion can generate herd behavior in stock markets where assets are traded sequentially. This in turn prevents markets from being efficient in the sense that financial market prices do not converge to the asset's fundamental value. The informational efficiency of the market depends on the distribution of the risky asset across risk averse agents. These results are obtained without introducing multidimensional uncertainty.herd behavior; stock markets; efficiency

Market efficiency and Price Formation when Dealers are Asymmetrically Informed

We consider the effect of asymmetric information on price formation process in a quote-driven market where one market maker receives a private signal on the security's fundamental. A model is presented where market makers repeatedly compete in prices: at each stage a bid-ask auction occurs and the winner trades the security against liquidity traders. We show that at equilibrium the market is not strong-form efficient until the last stage. We characterize a reputational equilibrium in which the informed market maker will aspect market beliefs, possibly misleading them, in the sense that he will push the uninformed participants to think the value of the risky asset is different from the realized one. At this equilibrium a price leadership effect arises, quotes are never equal to the expected value of the asset given the public information, the informed market maker expected payoff is positive and the information revelation speed is slower than in an analogous order-driven market.bid-ask prices; asymmetric information; repeated auction; insider trading

Market informational inefficiency, risk aversion and quantity grid

In this paper we show that long run market informational inefficiency is perfectly compatible with standard rational sequential trade models. Our inefficiency result is obtained taking into account two features of actual financial markets: tradable quantities belong to a quantity grid and traders and market makers do not have the same degree of risk aversion. The implementation of our model for reasonable values of the parameters suggests that the long term deviations between asset prices and fundamental value are important. We explain the ambiguous role of the quantity grid in exacerbating or mitigating market inefficiency. We show that stock splits can improve the information content of the order flow and consequently increase price volatility.informational efficiency; quantity grid; stock splits

Belief-free Equilibria in Games with Incomplete Information: Characterization and Existence

We characterize belief-free equilibria in infinitely repeated games with incomplete information with N \ge 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; conversely, any point in the interior of this set is a belief-free equilibrium payoff vector when players are sufficiently patient. Further, we provide necessary conditions and sufficient conditions on the information structure for this set to be non-empty, both for the case of known-own payoffs, and for arbitrary payoffs.Repeated games with incomplete information, Harsanyi doctrine, Belief-free equilibria