In a correlated equilibrium, the players' choice of actions is affected by random, correlated messages that they receive from an outside source, or mechanism. This allows for more equilibrium outcomes than without such messages (pure-strategy equilibrium) or with statistically independent ones...

We examine multistage information transmission with voluntary monetary transfer in the framework of Crawford and Sobel (1982). In our model, an informed expert can send messages to an uninformed decision maker more than once, and the uninformed decision maker can pay money to the informed expert...

We analyze a cheap-talk model in which an informed sender and an uninformed receiver engage in a finite-period communication before the receiver chooses a project. During the communication phase, the sender sends a message in each period, and the receiver then voluntarily pays money for the...

This paper studies the incentives for interim voluntary disclosure of verifiable information in probabilistic all-pay contests with two-sided incomplete information. Private information may concern marginal cost, valuations, and ability. Our main result says that, if the contest is uniformly...

Applying unawareness belief structures introduced in Heifetz, Meier, and Schipper (2012), we develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower...

We show that, in a minimum effort game with incomplete information where player types are independently drawn, there is a largest and smallest Bayesian equilibrium, leading to the set of equilibrium payoffs (as evaluated at the interim stage) having a lattice structure. Furthermore, the range of...

This paper analyzes the signaling effect of bidding in a two-round elimination contest. Before the final round, bids in the preliminary round are revealed and act as signals of the contestants' private valuations. Depending on his valuation, a contestant may have an incentive to bluff or sandbag...

We define and analyze a "strategic topology" on types in the Harsanyi-Mertens-Zamir universal type space, where two types are close if their strategic behavior is similar in all strategic situations. For a fixed game and action define the distance between a pair of types as the difference...