Study On Multi-Agent Dynamic Game Theory With Time Constraints

The research on the long-term interaction process among multi-agents has great practical significance,so it is the focus of algorithmic game theory.In real life,we often encounter such a type of multi-agent dynamic game,in which one or more player(s)’ strategies have significant changes due to time constraints.In this thesis,we study Revision Game and Continuous Double Auction with time constraint.The deadline of Revision Game is the core feature that distinguishes it from other games.This paper studies the role of the uncertainty of the game’s deadline in Revision Game.By introducing the uncertainty of game’s deadline,this paper deduces the sufficient and necessary conditions for grim trigger equilibrium under any deadline distribution.Computing such a trigger equilibrium strategy requires recursively solving a set of differential equations and using a Bayesian update formula to update the posterior distribution of players’ beliefs about the game’s deadline distribution.Under such a trigger equilibrium strategy,players will first remain full cooperation level,and then gradually and slowly reduce the level of cooperation over time.The uncertainty of the game’s deadline has a huge impact on the player’s strategy,which is mainly reflected in the risk aversion term defined in this paper.Through in-depth theoretical illustration of the risk aversion term,it has been proved that as the uncertainty of the game’s deadline increases,players tend to deviate from the fully cooperative level earlier and cooperate to a lower degree.They will adopt a more conservative approach to change their actions and the equilibrium payoff will also decrease.In this paper,a large number of related experiments are done in the background of the Cournot oligarchic game,continuous prisoner’s dilemma and the public goods game.The influence of environmental parameters,which include the uncertainty of the game’s deadline,on the player’s strategy and revenue is studied.By introducing the uncertainty of the game’s deadline,it will increase the competition among players and reduce the collusion between players,so it can be used in the mechanism design field.Based on the multi-agent dynamic game theory,this thesis constructs a Continuous Double Auction environment with time constraints,and analyzes the time-constrained agent trading strategies in this environment,such as value trading agent strategies and market-making trading agent strategies.The item bidding problem with time constraints is constructed as a Markov sequence decision problem.This thesis proposed the corresponding reinforcement learning agent states,actions and reward function with time constraints.A new proximal policy optimization algorithm is proposed,which combines the time-constrained agent reward function,and the Generalized Advantage function estimation can better make decisions under the game end time limit.This thesis further introduces the LSTM algorithm and the Gated Transformer-XL algorithm to extract the features of the agent state sequence,and improves the proximal policy optimization algorithm,so that the reinforcement learning agent has long-term memory ability in the Continuous Double Auction game.Through comparative experiments,this thesis proves that the algorithms proposed have superiority in the Continuous Double Auction multi-agent dynamic game with time constraints.At the same time,a further theoretical analysis is carried out on the experimental results.