Dynamic signaling with stochastic stakes

We study dynamic signaling in a game of stochastic stakes. Each period, privately informed agent binary type chooses whether to continue receiving return that is an increasing function both her reputation and exogenous public stakes variable or irreversibly exit the game. A strong has dominant strategy continue. In unique perfect Bayesian equilibrium, weak plays mixed depends only on current historical minimum she builds by continuing when reach new minimum. discuss applications corporate management, online vendor reputation, limit pricing with demand.