Abstract
In the literature of franchising arrangements, the focus of most research is on a relationship in which a franchisor is the leader and franchisees are followers. This relationship implies no control by franchisees over the franchisor. In this paper, we intend to explore the role of efficiency transactions between a franchisor and a franchisee by means of chance cross-constrained game theory. The chance constraint is formed as follows. The probability that the franchisee's profit from the franchise is less than the maximum profit to him from other opportunities should be less than his loss tolerance. Based on this chance constraint, we formulate two franchise models, i.e. the chance cross-constrained two stage game model and the chance cross-constrained cooperative game model. In the two stage game model, the franchisor is assumed to be a leader who first specifies the fixed lump sum fees and royalties. The franchisee, as a follower, then decides on the retail price. In the cooperative game model, the channel profit is maximized for every Pareto payment scheme, but not for any other schemes. The choice of the best Pareto efficient payment scheme is discussed via alternative bargaining models taking channel members' preferences and risk attitudes into account.