In telling the tale of, and analyzing the decisions made by, an heir claimant to a large fortune, Lippman and McCardle (2004) introduce embedded Nash bargaining, an approach to modeling joint decision making. They embed several bargaining games in a joint decision tree and calculate the expected payoffs to the two sides if the Nash bargaining solution is used to generate the intermediate payoffs from bargaining. The purpose of the current paper is to provide theoretical underpinnings for that approach: we establish some general results regarding the existence, uniqueness, and comparative statics (with respect to costs, risk aversion, and time discounting) of the embedded Nash bargaining solution. In particular, when the disagreement payoff is random, we show that a decision maker's embedded Nash bargaining payoff decreases with both his risk aversion and impatience, and it increases with his opponent's risk aversion and impatience.
