Chapter 1 suggests "soft debt" as a social convention that facilitates long-term reciprocal relationships. In each round of a two-player repeated game, one player develops a need for help from his counterpart, who may or may not be able to help. Unlike the existing favor trading models, the benefit and cost involved in each round, as well as the roles of potential receiver and provider of help, are randomly drawn. In addition, instead of automatically accepting help whenever it is offered by the provider, the receiver can decline the offer. If help is rendered, a soft debt is tacitly accrued by the receiver to the provider and added to the soft debt balance between them. A player is said to follow a soft debt strategy if his decisions about offering and soliciting help depend on the entire history only through the soft debt balance. His counterpart's expected future value of the relationship therefore also depends on the balance. This consideration creates intertemporal incentives that promote reciprocity. Soft transactions occur when help is traded between players following soft debt strategies. Under discrete benefits, there exist stationary Markov equilibria in which the players trade as long as the debt balance does not exceed a certain limit. The first best allocation is never achieved, but all trades that do occur in the equilibria are efficient. The model provides a unifying framework for decision making when both hard and soft transactions are available (e.g. hiring a mover versus asking a friend to help move to a new home). Chapter 2 emphasizes that when the benefits and costs are random, the favors do not necessarily result in positive surpluses. The players then need to consider not only whether the counterparts are trustworthy, but also whether the favor is efficient and whether the expected value of future trades justify the current cost even if the counterpart is willing to cooperate. This chapter proposes a modified grim trigger strategy, called the "limited efficiency strategy," in which a player will help if and only if (i) the favor is efficient (ii) the cost incurred is below a certain threshold (iii) no one has ever defected. Multiple equilibria with trades exist.Chapter 3 presents an axiomatic approach to extend the Expected Utility Theorem to multi-periods. The standard time-separable form is recovered when the functions describing the risk and substitution attitudes are identical. Further, I argue that the standard analysis of risk aversion neglects the agent's option to trade his lottery outcome. With trading, an agent is not indifferent to the timing of resolution of lotteries on consumptions. It is straightforward to characterize risk attitudes and to compare risk aversiveness between agents (even with different ex post preferences). The approach can accommodate multiple goods in each period. Time consistency is discussed.
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