This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor's subjective vi...This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor's subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets' prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.展开更多
A novel method for decision making with fuzzy probability assessments and fuzzy payoff is presented. The consistency of the fuzzy probability assessment is considered. A fuzzy aggregate algorithm is used to indicate t...A novel method for decision making with fuzzy probability assessments and fuzzy payoff is presented. The consistency of the fuzzy probability assessment is considered. A fuzzy aggregate algorithm is used to indicate the fuzzy expected payoff of alternatives. The level sets of each fuzzy expected payoff are then obtained by solving linear programming models. Based on a defuzzification function associated with the level sets of fuzzy number and a numerical integration formula (Newton-Cotes formula), an effective approach to rank the fuzzy expected payoff of alternatives is also developed to determine the best alternative. Finally, a numerical example is provided to illustrate the proposed method.展开更多
We study the effect of accumulative payoff on the evolution of cooperation in the evolutionary prisoner＇s dilemma on a square lattice. We introduce a decaying factor for the accumulative payoff, which characterizes t...We study the effect of accumulative payoff on the evolution of cooperation in the evolutionary prisoner＇s dilemma on a square lattice. We introduce a decaying factor for the accumulative payoff, which characterizes the extent that the historical payoff is accumulated. It is shown that for fixed values of the temptation to defect, the density of cooperators increases with the value of the decaying factor. This indicates that the more the historical payoff is involved, the more favourable cooperators become. In the critical region where the cooperator density converges to zero, cooperators vanish according to a power-law-like behaviour. The associated exponents agree approximately with the two-dimensional directed percolation and depend weakly on the value of the decaying factor.展开更多
In finite population games with weak selection and large population size, when the payoff matrix is constant, the one-third law serves as the condition of a strategy to be advantageous. We generalize the result to the...In finite population games with weak selection and large population size, when the payoff matrix is constant, the one-third law serves as the condition of a strategy to be advantageous. We generalize the result to the cases of environment-dependent payoff matrices which exhibit the feedback from the environment to the population. Finally, a more general law about cooperation-dominance is obtained.展开更多
In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theor...In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theorem of generalized minimax regret equilibrium point with scalar set payoffs holds. In other words, when the scalar set payoffs functions and feasible constraint mappings are slightly disturbed, by using Fort theorem and continuity results of set-valued mapping optimal value functions, we obtain a general stability theorem for generalized minimax regret equilibria with scalar set payoffs. At the same time, an example is given to illustrate our result.展开更多
This paper is concerned with nonzero-sum discrete-time stochastic games in Borel state and action spaces under the expected discounted payoff criterion.The payoff function can be unbounded.The transition probability i...This paper is concerned with nonzero-sum discrete-time stochastic games in Borel state and action spaces under the expected discounted payoff criterion.The payoff function can be unbounded.The transition probability is a convex combination of finite probability measures that are dominated by a probability measure on the state space and depend on the state variable.Under suitable conditions,the authors establish the existence of stationary almost Markov ε-equilibria and give an approximation method via some stochastic games with bounded payoffs.Finally,a production game is introduced to illustrate the applications of the main result,which generalizes the bounded payoff case.展开更多
By introducing state payoff vector to every state node on the connected graph in this paper,dynamic game is researched on finite graphs.The concept of simple strategy about games on graph defined by Berge is introduce...By introducing state payoff vector to every state node on the connected graph in this paper,dynamic game is researched on finite graphs.The concept of simple strategy about games on graph defined by Berge is introduced to prove the existence theorem of absolute equilibrium about games on the connected graph with state payoff vector.The complete algorithm and an example in the three-dimensional connected mesh-like graph are given in this paper.展开更多
This paper studies a class of strategic games,where players often collaborate with other players to form a group when making decisions,and the payoff functions of players in such games are presented as vector function...This paper studies a class of strategic games,where players often collaborate with other players to form a group when making decisions,and the payoff functions of players in such games are presented as vector functions.First,using the semi-tensor product(STP)method,it is proved that a finite game with vector payoffs is potential if and only if its potential equation has solution.By adding a suitable weight vector to the vector payoffs of each player,a finite game with vector payoffs that is not potential can be converted into a potential game.Second,as a natural generalization,the authors consider the verification problem of the group-based potential games with vector payoffs.By solving a linear potential equation,a simple formula is obtained to calculate the corresponding potential function.Finally,some examples are presented and discussed in detail to illustrate the theoretical results.展开更多
This paper studies the policy iteration algorithm(PIA)for zero-sum stochastic differential games with the basic long-run average criterion,as well as with its more selective version,the so-called bias criterion.The sy...This paper studies the policy iteration algorithm(PIA)for zero-sum stochastic differential games with the basic long-run average criterion,as well as with its more selective version,the so-called bias criterion.The system is assumed to be a nondegenerate diffusion.We use Lyapunov-like stability conditions that ensure the existence and boundedness of the solution to certain Poisson equation.We also ensure the convergence of a sequence of such solutions,of the corresponding sequence of policies,and,ultimately,of the PIA.展开更多
This paper concerns two-person zero-sum games for a class of average-payoff continuous-time Markov processes in Polish spaces.The underlying processes are determined by transition rates that are allowed to be unbounde...This paper concerns two-person zero-sum games for a class of average-payoff continuous-time Markov processes in Polish spaces.The underlying processes are determined by transition rates that are allowed to be unbounded,and the payoff function may have neither upper nor lower bounds.We use two optimality inequalities to replace the so-called optimality equation in the previous literature.Under more general conditions,these optimality inequalities yield the existence of the value of the game and of a pair of optimal stationary strategies.Under some additional conditions we further establish the optimality equation itself.Finally,we use several examples to illustrate our results,and also to show the difference between the conditions in this paper and those in the literature.In particular,one of these examples shows that our approach is more general than all of the existing ones because it allows nonergodic Markov processes.展开更多
This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounde...This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounded,and the payoff functions may be unbounded from above and from below.We give suitable conditions under which the existence of a Nash equilibrium is ensured.More precisely,using the socalled "vanishing discount" approach,a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to zero.Our results are illustrated with a birth-and-death game.展开更多
基金Supported by the Fundamental Research Funds for the Central University(10D10909)
文摘This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor's subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets' prices are discussed. Some properties of the maximal utility function with respect to the endowment are given.
文摘A novel method for decision making with fuzzy probability assessments and fuzzy payoff is presented. The consistency of the fuzzy probability assessment is considered. A fuzzy aggregate algorithm is used to indicate the fuzzy expected payoff of alternatives. The level sets of each fuzzy expected payoff are then obtained by solving linear programming models. Based on a defuzzification function associated with the level sets of fuzzy number and a numerical integration formula (Newton-Cotes formula), an effective approach to rank the fuzzy expected payoff of alternatives is also developed to determine the best alternative. Finally, a numerical example is provided to illustrate the proposed method.
基金supported by the National Natural Science Foundation of China (Grant Nos.70671079,60674050,60736022 and 60528007)the National Basic Research Program of China (Grant No.2002CB312200)+1 种基金the National High Technology Research and Development Program of China (Grant No.2006AA04Z258)11-5 Project (Grant No.A2120061303)
文摘We study the effect of accumulative payoff on the evolution of cooperation in the evolutionary prisoner＇s dilemma on a square lattice. We introduce a decaying factor for the accumulative payoff, which characterizes the extent that the historical payoff is accumulated. It is shown that for fixed values of the temptation to defect, the density of cooperators increases with the value of the decaying factor. This indicates that the more the historical payoff is involved, the more favourable cooperators become. In the critical region where the cooperator density converges to zero, cooperators vanish according to a power-law-like behaviour. The associated exponents agree approximately with the two-dimensional directed percolation and depend weakly on the value of the decaying factor.
文摘In finite population games with weak selection and large population size, when the payoff matrix is constant, the one-third law serves as the condition of a strategy to be advantageous. We generalize the result to the cases of environment-dependent payoff matrices which exhibit the feedback from the environment to the population. Finally, a more general law about cooperation-dominance is obtained.
文摘In this paper, we first introduce the notion and model of generalized minimax regret equilibria with scalar set payoffs. After that, we study its general stability theorem under the conditions that the existence theorem of generalized minimax regret equilibrium point with scalar set payoffs holds. In other words, when the scalar set payoffs functions and feasible constraint mappings are slightly disturbed, by using Fort theorem and continuity results of set-valued mapping optimal value functions, we obtain a general stability theorem for generalized minimax regret equilibria with scalar set payoffs. At the same time, an example is given to illustrate our result.
基金supported by the National Key Research and Development Program of China under Grant No.2022YFA1004600the National Natural Science Foundation of China under Grant No.11931018+1 种基金the Guangdong Basic and Applied Basic Research Foundation under Grant No.2021A1515010057the Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University under Grant No.2020B1212060032。
文摘This paper is concerned with nonzero-sum discrete-time stochastic games in Borel state and action spaces under the expected discounted payoff criterion.The payoff function can be unbounded.The transition probability is a convex combination of finite probability measures that are dominated by a probability measure on the state space and depend on the state variable.Under suitable conditions,the authors establish the existence of stationary almost Markov ε-equilibria and give an approximation method via some stochastic games with bounded payoffs.Finally,a production game is introduced to illustrate the applications of the main result,which generalizes the bounded payoff case.
基金supported by National Natural Science Foundation of China (Grant Nos.70571040,70871064)the International (Regional) Joint Research Program of China (Grant Nos.70711120204,71011120107)the Innovation Project of Graduate Education in Shandong Province,China (Grant No.SDYC08045)
文摘By introducing state payoff vector to every state node on the connected graph in this paper,dynamic game is researched on finite graphs.The concept of simple strategy about games on graph defined by Berge is introduced to prove the existence theorem of absolute equilibrium about games on the connected graph with state payoff vector.The complete algorithm and an example in the three-dimensional connected mesh-like graph are given in this paper.
基金the National Natural Science Foundation of China under Grant Nos.61903236,62073202,and 61803240Shandong Provincial National Science Foundation under Grant No.ZR2018BF021China Postdoctoral Science Foundation under Grant No.2017M622262。
文摘This paper studies a class of strategic games,where players often collaborate with other players to form a group when making decisions,and the payoff functions of players in such games are presented as vector functions.First,using the semi-tensor product(STP)method,it is proved that a finite game with vector payoffs is potential if and only if its potential equation has solution.By adding a suitable weight vector to the vector payoffs of each player,a finite game with vector payoffs that is not potential can be converted into a potential game.Second,as a natural generalization,the authors consider the verification problem of the group-based potential games with vector payoffs.By solving a linear potential equation,a simple formula is obtained to calculate the corresponding potential function.Finally,some examples are presented and discussed in detail to illustrate the theoretical results.
文摘This paper studies the policy iteration algorithm(PIA)for zero-sum stochastic differential games with the basic long-run average criterion,as well as with its more selective version,the so-called bias criterion.The system is assumed to be a nondegenerate diffusion.We use Lyapunov-like stability conditions that ensure the existence and boundedness of the solution to certain Poisson equation.We also ensure the convergence of a sequence of such solutions,of the corresponding sequence of policies,and,ultimately,of the PIA.
基金supported by National Natural Science Foundation and GDUPS (2010)supported by CONACyT Grant 104001
文摘This paper concerns two-person zero-sum games for a class of average-payoff continuous-time Markov processes in Polish spaces.The underlying processes are determined by transition rates that are allowed to be unbounded,and the payoff function may have neither upper nor lower bounds.We use two optimality inequalities to replace the so-called optimality equation in the previous literature.Under more general conditions,these optimality inequalities yield the existence of the value of the game and of a pair of optimal stationary strategies.Under some additional conditions we further establish the optimality equation itself.Finally,we use several examples to illustrate our results,and also to show the difference between the conditions in this paper and those in the literature.In particular,one of these examples shows that our approach is more general than all of the existing ones because it allows nonergodic Markov processes.
基金supported by National Science Foundation for Distinguished Young Scholars of China (Grant No. 10925107)Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2011)
文摘This paper attempts to study two-person nonzero-sum games for denumerable continuous-time Markov chains determined by transition rates,with an expected average criterion.The transition rates are allowed to be unbounded,and the payoff functions may be unbounded from above and from below.We give suitable conditions under which the existence of a Nash equilibrium is ensured.More precisely,using the socalled "vanishing discount" approach,a Nash equilibrium for the average criterion is obtained as a limit point of a sequence of equilibrium strategies for the discounted criterion as the discount factors tend to zero.Our results are illustrated with a birth-and-death game.
