The Mechanism of Transaction: Value Equilibrium Model of A Bargaining Game Between Two Rational Agents

Transactions are the most common phenomenon in market economy. But in theoretical research, modeling a transaction is a complex problem unsolved. In this paper, firstly, natural rationality (A) is defined as nonlinear function of agent\´s benefit (B) and cost (C), and _A=max(B/C₎. This mathematical model of natural rationality can be considered as one answer to Aumann\´s "open problem". Secondly, Three basic definitions of neutrality value system for market economy are constructed: commodity value, seller value and buyer value. Thirdly, value equilibrium of a bargaining game is modeled when the seller value is equal to the buyer value, and equilibrium price solution in a transaction is obtained. Finally, On these basis, the sequential bargaining process between two rationality agents (a seller and a buyer) is modeled in a time series by analytical geometry.