Abstract
We analyze a repeated cheap-talk game in which the receiver is privately informed about the conflict of interest between herself and the sender and either the sender or the receiver controls the stakes involved in their relationship. We focus on payoff-dominant equilibria that satisfy a Markovian property and show that if the potential conflict of interest is large, then the stakes increase over time, i.e., “starting small” is the unique equilibrium arrangement. In each period, the receiver plays the sender's ideal action with positive probability and the sender provides full information as long as he has always observed his ideal actions in the past. We also show that as the potential conflict of interest increases, the extent to which the stakes are back-loaded increases, i.e., stakes are initially smaller but grow faster.
Highlights
We analyze a repeated cheap-talk game in which the receiver is privately informed about the conflict of interest between herself and the sender and either the sender or the receiver controls the stakes involved in their relationship
6See Section 5 for a discussion of the literature on gradualism and starting small. 7If the initial reputation of the receiver is not bad enough, the sender-optimal equilibrium is not optimal for the receiver. Even in this case, we show that the size of the stakes increases over time in the receiver-optimal equilibrium. 8As we will show subsequently, this is true except perhaps in the first period. 9We refer the reader to Chen et al (2008) and the references cited therein for justification of the most informativeness criterion in cheap-talk games
A collection σ =iN=1 constitutes an assessment and we focus our attention on perfect Bayesian equilibria (PBE) of the game that satisfy Properties 1 and 2 that we define below
Summary
We analyze a repeated cheap-talk game in which the receiver is privately informed about the conflict of interest between herself and the sender and either the sender or the receiver controls the stakes involved in their relationship. The stage game exhibits both conflict of interest, because of the possible bias, and common interest, because of the common preference for truthful communication These considerations imply that the sender (or the receiver) may choose the stakes in a strategic manner in order to utilize the reputational incentives and facilitate communication. Our results further imply that as the potential conflict of interest between the sender and the receiver increases, initial stakes become smaller but they grow faster This is due the fact that as the bias becomes larger, the future must become relatively more important in order to provide sufficient incentives to the biased receiver to play the unbiased action in the current period. We should note that since the sender fully reveals the state in every period as long as he observes the unbiased action, a payoff-dominant equilibrium is the most informative one on the equilibrium path. payoff-dominance is potentially a reasonable equilibrium selection in our context.
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