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Bargaining solutions to the problem of exchange of uncertain ventures Weerahandi, Samaradasa

Abstract

Consider the betting problem where two individuals negotiate to determine the amount each will bet. It has already been established that when the two bettors both have concave utility functions, there exist mutually beneficial bets (i.e. bets giving positive utility to both players) merely if players' subjective probabilities on the betting event differ. It is shown here that this result can be generalized to the case of more general utility functions. The results are extended to a more general situation, that of a stochastic exchange. It is shown that the set of all feasible solutions available for exchange for two risk averters is a convex set with a known boundary. After defining a solution for the members of a class of exchange models it is shown in the third chapter that the 'size' of the exchange prescribed by the solution tends to increase with the participants' initial wealth and with multiplicative shifts of the random variable characterizing the exchange. Furthermore the size of the exchange may increase or decrease due to an additive shift of this random variable. In Chapter 4 it is shown by an axiomatic method that an individual engaged in bargaining with incomplete information finds his 'fair' demand (offer) by maximizing a generalized Nash function, GNF; this GNF is found to be the product of his utility and a general mean of his opponent's uncertain utility (from first individual's point of view). This general mean is characterized by a parameter whose value may vary from person to person. Continuing the study on bargaining under incomplete information, a best bargaining strategy is developed in the last chapter using the technique of 'Backward Induction'. A criterion for comparing available bargaining strategies is also established.

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