Reputational cheap talk with misunderstanding

We consider a cheap talk game with a sender who has a reputational concern for an ability to predict a state of the world correctly, and where receivers may misunderstand the message sent. When communication between the sender and each receiver is private, we identify an equilibrium in which the sender only discloses the least noisy information. Hence, what determines the amount of information revealed is not the absolute noise level of communication, but the extent to which the noise level may vary. The resulting threshold in transmission noise for which information is revealed may differ across receivers, but is unrelated to the quality of the information channel. When information transmission has to be public, a race to the bottom results: the cut-off level for noise of transmitted information now drops to the lowest cut-off level for any receiver in the audience.     

Computationally restricted unmediated talk under incomplete information

Summary. We show the role of unmediated talk with computational complexity bounds as both an information transmission and a coordination device for the class of two-player games with incomplete information and rational parameters. We prove that any communication equilibrium payoff of such games can be reached as a Bayesian-Nash equilibrium payoff of the game extended by a two phase universal mechanism of interim computationally restricted pre-play communication. The communication protocols are designed with the help of modern cryptographic tools. A familiar context in which our results could be applied is bilateral trading with incomplete information.Received: 9 September 2002, Revised: 14 March 2003, JEL Classification Numbers: C72. Correspondence to: Amparo UrbanoWe wish to thank financial aid from the Valencian Institute of Economic Research (IVIE) and partial support by DIGCYT under project PB95 - 1074. A previous version of this work appears as IVIE Working Paper WP-AD 99-07, under the title: "Unmediated talk under incomplete information".     

A note on cheap talk and burned money

Austen-Smith and Banks [Cheap talk and burned money, J. Econ. Theory 91(1) (2000) 1-16] study how money burning can expand the set of pure cheap talk equilibria of Crawford and Sobel [Strategic information transmission, Econometrica 50(6) (1982) 1431-1451]. I identify an error in the main Theorem of Austen-Smith and Banks, and provide a variant that preserves some of the important implications. I also prove that cheap talk can be influential with money burning if and only if it can be influential without money burning. This strengthens a result of Austen-Smith and Banks, but uncovers other errors in their analysis. Finally, an open conjecture of theirs is proved correct.     

Existence of Sparsely Supported Correlated Equilibria

We show that every N-player K ₁ × ... × K _N game possesses a correlated equilibrium with at least zero entries. In particular, the largest N-player K × ... × K games with unique fully supported correlated equilibrium are two-player games. We thank an anonymous referee for most useful comments. The first author acknowledges financial support from Spanish Ministry of Science and Technology, grant SEJ2004-03619, and in form of a Ramón y Cajal fellowship. The second author acknowledges support by the PASCAL Network of Excellence under EC grant no.506778, as well as from Spanish Ministry of Science and Technology and FEDER, grant BMF2003-03324. Both authors also acknowledge financial support from BBVA grant “Aprender a jugar.”     

The replicator dynamics does not lead to correlated equilibria

It is shown that, under the replicator dynamics, all strategies played in correlated equilibrium may be eliminated, so that only strategies with zero marginal probability in all correlated equilibria survive. This occurs in particular in a family of 4×4 games built by adding a strategy to a Rock-Paper-Scissors game.     

Correlated equilibrium and sunspot equilibrium

Summary We show by an example that the sunspot equilibria of a competitive economy are not equivalent to the correlated equilibria if sunspots generate transfers between (extrinsic) states of nature (through a contingent commodities market). Nevertheless, we prove that the sunspot equilibrium allocations of a standard overlapping generations economy coincide with the (strategic form) correlated equilibrium allocations of a natural market game mimicking the economy.     

A note on the value of public information in monopoly

The paper shows that in the standard model of monopoly with asymmetric information and second-degree price discrimination, the monopolist prefers to reveal public information under a form of stochastic dependence that is weaker than the affiliation of private values, private signals, and public signals.      

Message spaces for perfect correlated equilibria

Summary. We show that a perfect correlated equilibrium distribution of an N-person game, as defined by Dhillon and Mertens (1996) can be achieved using a finite number of copies of the strategy space as the message space.Received: 31 August 2004, Revised: 1 April 2005, JEL Classification Numbers: C72.Srihari Govindan: Correspondence toGovindan would like to thank the Social Sciences and Humanities Research Council of Canada for research support.     

A note on public debt, tax-exempt bonds, and Ponzi games

By issuing tax-exempt bonds, the government can incur debt and never pay back any principal or interest, even if the economy without public debt evolves on a dynamically efficient growth path. The welfare effects of such a Ponzi type borrowing scheme are mixed. The current young will unambiguously benefit. Depending on preferences and the aggregate technology, a finite number of subsequent generations may also benefit. However, the welfare of all generations thereafter will be lower than in the economy without public debt.     

A note on asymmetric and mixed strategy equilibria in the search-theoretic model of fiat money

Summary. The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y in (0,1). Here I construct an asymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N in (0,1) of agents always accept money and 1-N never accept money. Counter to what has been conjectured previously, I find N > y. I also introduce evolutionary dynamics, and show that the economy converges to monetary exchange iff the initial proportion of agents accepting money exceeds N. Received: September 10, 1997; revised version: April 24, 1998     

Whatever you say, your reputation precedes you: Observation and cheap talk in the trust game

Behavior in trust games has been linked to general notions of trust and trustworthiness, important components of social capital. In the equilibrium of a trust game, the investor does not invest, foreseeing that the allocator would keep all of the returns. We use a human-subjects experiment to test the effects of changes to the game designed to increase cooperation and efficiency. We add a pre-play stage in which the investor receives a cheap-talk message from the allocator, observes the allocator's previous decision, or both. None of these changes alter the game's theoretical predictions. We find that allowing observation results in substantially higher cooperation and efficiency, but cheap talk has little effect.     

A note on lindahl taxes when public goods are inputs to household production

This note explores the incidence of benefit taxation when public goods yield utility only indirectly, as inputs to household production. It provides a condition for tax progression in terms of measurable parameters. The result is contrasted with the usually considered case of public goods being ordinary consumption goods, in which the parameters that indicate whether benefit taxation would be progressive are inestimable because of the preference revelation problem.I am grateful to two referees for insisting on clarifications and for providing useful suggestions.