A Preliminary Study Of Bonanno's Logic Research On Backward Induction

Backward induction is a classic algorithm for refining equilibrium in dynamic game neutron game.The backward induction applies the strategy model generally,which would be subjectively or objectively counterfactually involved in the cognitive description theory of backward induction.However,the states involved are only specified in the actual decision-making of the participants in the simulated game process and do not involve the hypothetical selection of historical game subjects that have not been implemented in the simulated game process from Bonanno's research on Nash equilibrium and backward induction.Generally,a dynamic game with perfect information provides a model to describe the Nash equilibrium solution and the refined equilibrium solution of the subgame,which can avoid the counterfactuality of the backward induction in some degree.It is worth mentioning that the belief discussed by Bonanno in dynamic games with perfect information is neither the final characterization of game beliefs in reality nor the subjective prediction of game beliefs in the mind of a particular game subject,it is a simulated game of reality at the negotiation stage.Because the depicted belief is a historical belief,with no consideration of the initial belief,there is no need to update the belief.The goal of theoretical research is to solve problems and to serve reality.Based on this spirit,in this article,we attempt to analysis Bonanno's research on backward induction,then combine it with concrete examples and talk about its application.The original intention of this article is mainly to provide some theoretical guidance for the game activities carried out in reality.Based on the above original intention,this article is mainly dedicated to the following research:For the first,we make a preliminary introduction to the basic concepts in game theory,such as what is a dynamic game with perfect information,the concept of Nash equilibrium,and conceptual analysis of backward induction,finally,a brief introduction to the basic concepts in the dynamic cognitive logic.For the second,we introduce the main research on backward induction in Bonanno's article"Behavior and deliberation in perfect-information games:Nash equilibrium and backward induction"in 2018.In this article,the author first adopted the traditional game logic based on the definition of game history for the extended game,and questioned the precise prediction ability of the game subject,that is to say,the game subject can only analyze the beliefs about what might happen when he takes effective actions in the realized history,and does not have the ability to accurately predict the actions of future game players,indicating the counterfactuality of the strategy model,so as to the perfect information.Secondly,the Nash equilibrium result set is characterized by TRC?T represents the state set with correct beliefs,R represents the rationality,and C represents the accuracy?.Finally,the incident induction I_TRCRC is used to further characterize the reverse induction method result set.For the third,we combine the classic games recorded in ancient Chinese literature with Bonanno's research method on reverse induction as a case study,and we specifically describe the belief model of backward induction in this case and belief characterize it,further more,we use the deduction rules of propositional logic and the belief operator to derive the refined equilibrium solution of the subgame.Summary,we conclude with a preliminary discussion of Bonanno's contribution to the theoretical research of backward induction.How to apply the theoretical research of backward induction to life,and to more effectively guide some game problems in reality,some brief thoughts and prospects are put forward.