Markovian Embeddings for Coalitional Bargaining Games

We examine the Markovian properties of coalition bargaining games, in particular, the case where past rejected proposals cannot be repeated. We propose a Markovian embedding with filtrations to render the sates Markovian and thus, fit into the framework of stochastic games. Coalitional bargaining games CBG are sequential games where one agent at random proposes a coalition formation while the others provide responses on whether to accept or reject the proposal. A CBG can we framed as a stochastic game where the game states are configured by two sequential actions: the proposals over coalition members and the corresponding responses. The state dynamics are determined by the agent's preferences and the rewards are assigned once a proposed coalition is accepted. The order of coalition proposals is a crucial factor in determining the convergence of CBG Okada (1996); however, it has not received sufficient attention in the existing literature Rubinstein (1982); Okada (1996); Chatterjee et al. (1993) and a thorough analysis is missing.