On Independence of Irrelevant Alternatives and Dynamic Programming in Dynamic Bargaining Games

Abstract

We consider bargaining games where the players control a dynamic system and the feasible set consists of utility gains over multiple time periods. It is assumed that the players can make binding contracts over the time horizon in question and that they are allowed to monitor the contract as the game evolves. A property of the bargaining solution arising in this situation is its dynamic consistency. A weaker form of it was recently proposed by Ehtamo and Ruusunen, who also showed that it is equivalent to the independence of irrelevant alternatives property. Here it is shown that independence of irrelevant alternatives property serves as Bellman’s principle of optimality for multi-period bargaining games. Namely, if the bargaining solution is independent of irrelevant alternatives, then the contract and the corresponding cooperative policies can be obtained backwards by applying dynamic programming.KeywordsBargaining SolutionBargaining GameNash Bargaining SolutionUtility GainDynamic ConsistencyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.