Financial Cryptography: Algorithmic Mechanisms for a Hedonic Game

A (or a group of) selling agent wants to allocate and sell a (or a set of) parcel of land optimally and fairly to a buying agent within the capacity constraint of the selling agent and budget constraint of the buying agent. This problem has been solved by combining the concept of algorithmic cooperative game theory and financial cryptography. This is an approach for a group of decision-making agents to reach a mutually beneficial agreement through compromise and stable matching of preference. The work presents a cooperative game and a set of algorithmic coordination mechanisms: SBSS, SBMS (for collective and non-collective bargaining in holdout problem) and MBSS. The game is characterized by a set of agents, inputs, strategic moves, revelation principle, payment function and outputs. The coordination mechanisms are designed based on domain planning, rational fair data exchange and compensation negotiation. These mechanisms preserve the privacy of strategic data through secure multi-party computation (SMC), more specifically solving Yao’s millionaire problem. The mechanisms are analyzed from the perspectives of revelation principle, computational intelligence and communication complexity. The communication complexity depends on the time constraint of the negotiating agents, their information state and the number of negotiation issues. The computational complexity depends on the valuation of pricing plan, compensation estimation and private comparison. It is a mixed strategy game; both sequential and simultaneous moves can be applied intelligently to search a neighborhood space of core solutions.